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import pickle
import json
from collections import OrderedDict
from math import log
from sklearn.metrics.pairwise import cosine_similarity
from numpy.linalg import norm
from datasets import DATASET
import datetime
import os.path
import numpy as np
class TFIDFVectorizer():
def __init__(self, k=1.5, b=0.75):
self.k = k
self.b = b
def tf(self,word,doc, doc_list):
all_num=sum([doc[key] for key in doc])
avg = 0
for vb in doc_list:
avg += sum([vb[key] for key in vb])
avg = avg/len(doc_list)
return (doc[word]*(self.k + 1))/(doc[word] + self.k*(1 - self.b + self.b*all_num/avg))
def idf(self, word,doc_list):
all_num=len(doc_list)
word_count=0
for doc in doc_list:
if word in doc:
word_count+=1
return log((all_num+1)/(word_count+0.5))
def tfidf(self, word,doc,doc_list):
score = self.tf(word,doc, doc_list)*self.idf(word,doc_list)
return score
def compute_tfidf_summary(self, bug_reports):
vocab = []
docs = []
for report in bug_reports.values():
doc = {}
for word in report.summary['unstemmed']:
if word not in vocab:
vocab.append(word)
if word in doc.keys():
doc[word] += 1
else:
doc[word] = 1
for word in report.description['unstemmed']:
if word not in vocab:
vocab.append(word)
if word in doc.keys():
doc[word] += 1
else:
doc[word] = 1
docs.append(doc)
x_tfidf = []
for doc in docs:
for word in doc:
doc[word] = self.tfidf(word,doc,docs)
row = []
for f in vocab:
if f in doc.keys():
row.append(doc[word])
else:
row.append(0)
x_tfidf.append(row)
# should save sparse matrix
return x_tfidf
def compute_similarity(self, x_tfidf, y_tfidf):
"""
compute similarity
"""
n = len(x_tfidf)
size = len(x_tfidf[n-1])
x_tfidf = | np.asarray(x_tfidf) | numpy.asarray |
"""Functions and classes for creating particle grids, counting bins and transition matrices."""
# Imports
import pandas as pd
import numpy as np
import xarray as xr
import networkx as nx
from scipy.interpolate import griddata
from scipy.spatial import cKDTree, SphericalVoronoi
from scipy import sparse
from astropy.coordinates import cartesian_to_spherical
import matplotlib.pyplot as plt
import cartopy as cart
from datetime import datetime
import warnings
import pickle
import os
try:
import stripy
except ImportError:
print("Stripy is not available on this machine.")
def get_cartesian(lon, lat, R=1, mode='rad', ):
"""
Convert spherical coordinates to cartesian coordinates.
Parameters
----------
lon : float, np.array
longitude coordinate(s)
lat : float, np.array
latitude coordinate(s)
R : int, float
radius of sphere
mode : str
Either 'rad' or 'deg', indicating whether coordinates are supplied
in radians or degrees respectively.
Returns
-------
x, y, z : (float, float, float)
Cartesian coordinates
"""
if mode=='deg':
lat, lon = np.radians(lat), np.radians(lon)
x = R * np.cos(lat) * np.cos(lon)
y = R * np.cos(lat) * np.sin(lon)
z = R *np.sin(lat)
return x, y, z
def lonlat_from_pset(pset, timedelta64=None):
"""
Extract latitude and longitude data from particleSet.
Parameters
----------
pset : str
string with path to ``parcels.ParticleSet`` output file
timedelta64 : np.timedelta64
relative timestamp to load data from pset at, relative to start time
Returns
-------
lonlat_init
np.array with initial longitude-latitude pairs
lonlat_final
np.array with final longitude-latitude pairs
"""
ds = xr.open_dataset(pset)
lons = ds['lon'].data
lats = ds['lat'].data
ids = ds['traj'].data
times = ds['time'].data
if np.any(np.diff(times[:,0]).astype(bool)):
warnings.warn("Not all starting times are equal. Behaviour may not be as expected.", Warning)
if timedelta64:
# Determine which trajectory idx to use for searchsorted,
# since it must contain timestamps in the last index.
firstFullTrajectoryIdx = np.searchsorted(~np.isnat(times[:, -1]), True)
# Find index at which trajectories shoudl be investigated
final_tidx = np.searchsorted(times[firstFullTrajectoryIdx,:],
times[firstFullTrajectoryIdx,0] + timedelta64)
if final_tidx == times.shape[1]:
warnings.warn("`final_tidx` lies outside of time window. Choosing last index instead", Warning)
final_tidx = times.shape[1]-1
else:
final_tidx = times.shape[1]-1
lonlatInit = np.dstack((lons[:,0], lats[:,0]))
lonlatFinal = np.dstack((lons[:,final_tidx], lats[:, final_tidx]))
ds.close()
return lonlatInit, lonlatFinal
class particles:
"""
Basic instance of particles object has lists holding the latitudes and longitudes of its points.
Attributes
----------
lats : np.array
list of latitudes (in degrees)
lons : np.array
list of longitudes (in degrees)
lonlat : np.ndarray
2D array holding pairs of latitude and longitude of each particle
n : int
number of gridpoints
idx : np.ndarray
index of each gridpoint
_releaseTime : datetime
release time of particles
"""
def __init__(self, lons, lats, idx = None, releaseTime = None):
assert len(lats) == len(lons), "lats and lons should be of equal size"
self._releaseTime = releaseTime
self.lons = lons
self.lats = lats
self.lonlat = np.dstack((lons, lats)) #First axis corresponds to time
# idx should not be updated since this makes triangle points harder to track down
if idx:
self.idx = idx
else:
self.idx = np.arange(self.n)
@property
def n(self):
"""
Returns
-------
int
number of particles
"""
return self.lonlat.shape[1]
@property
def releaseTimes(self):
"""
Returns
-------
list
Release times of particles
"""
if self._releaseTime:
return [self._releaseTime for part in range(self.n)]
else:
pass
@classmethod
def from_regular_grid(cls, nlon, nlat, minLat=60., maxLat=90., minLon=-180, maxLon=180, **kwargs):
"""
Grid construction by dividing latitude and longitude ranges into a discrete amount of points.
Parameters
----------
nlat : int
number of latitudes.
nlon : int
number of longitudes.
minLat : float
minimum latitude of grid (southern boundary)
maxLat : float
maximum latitude of grid (northern boundary)
minLon : float
minimum longitude of grid (western boundary)
maxLon : float
maximum longitude of grid (eastern boundary)
"""
lonRange = np.linspace(minLon, maxLon, nlon)
latRange = np.linspace(minLat, maxLat, nlat)
lon2D, lat2D = np.meshgrid(lonRange, latRange)
return cls(lon2D.flatten(), lat2D.flatten(), **kwargs)
@classmethod
def from_pickle(cls, pickFile, lonKey='lons', latKey='lats', **kwargs):
"""
Load longitudes and latitudes of particles from pickled dictionary
Parameters
----------
pickFile : str
Path to pickled dictionary
lonKey : str
Key for longitudes in dictionary
latKey : str
Key for latitudes in dictionary
"""
with open(pickFile, 'rb') as pickFile:
lonlat_dict = pickle.load(pickFile)
return cls(lonlat_dict[lonKey], lonlat_dict[latKey], **kwargs)
def remove_on_land(self, fieldset):
"""
Uses the fieldset.landMask to remove particles that are located on land (where u, v == 0 or -1)
Parameters
----------
fieldset : Parcels.FieldSet
should have a landMask attribute (created by fieldSetter)
"""
nBefore = self.n
# Load landmask and initialize mask for particles on land
landMask = fieldset.landMask
try:
landMask = landMask.compute()
except AttributeError:
pass
# Use scipy.interpolate.griddata to have particles adopt value of landmask from nearest neighbor
if fieldset.U.grid.lon.ndim == 1:
mesh = np.meshgrid(fieldset.U.grid.lon, fieldset.U.grid.lat)
lonlatMask = griddata(np.dstack((mesh[0].flatten(),
mesh[1].flatten()))[0,:,:],
landMask.flatten(),
self.lonlat[0,:,:],
method='nearest')
else:
lonlatMask = griddata(np.dstack((fieldset.U.grid.lon.flatten(),
fieldset.U.grid.lat.flatten()))[0,:,:],
landMask.flatten(),
self.lonlat[0,:,:],
method='nearest')
self.lonlat = self.lonlat[:, ~lonlatMask, :]
self.lons = self.lonlat[0, :, 0]
self.lats = self.lonlat[0, :, 1]
nAfter = self.n
self.removedParticleCount = nBefore - nAfter
def add_advected_from_pset(self, *args, **kwargs):
"""
Add final particle locations by loading them from a pset. See `lonlat_from_pset()`.
"""
lonlatFinal = lonlat_from_pset(pset, *args, **kwargs)[1]
self.lonlat = np.concatenate((self.lonlat, lonlat_final), axis=0)
def show(self, tindex = 0, export = None, projection=None, **kwargs):
"""
Create a plot of the particle locations in particles object.
Parameters
----------
tindex : int
Index of lonlat pairs (0 is initial, 1 is final).
export : str
Name of exported figure. A directory 'figures' is created.
projection : cartopy.crs
Projection for showing particle set on.
"""
fig = plt.figure()
if projection:
ax = plt.axes(projection = projection)
else:
ax = plt.axes(projection = cart.crs.PlateCarree())
ax.scatter(self.lonlat[tindex, :, 0], self.lonlat[tindex, :, 1], transform = cart.crs.Geodetic(), **kwargs)
ax.add_feature(cart.feature.COASTLINE)
if export:
if not os.path.exists('figures'):
os.makedirs('figures')
if export[-4] == '.':
plt.savefig(f'figures/{export}', dpi=300)
else:
plt.savefig(f'figures/{export}.png', dpi=300)
return ax
class countBins:
"""
Bins used for counting particles.
Attributes
----------
binType : str
Indicates the type of bin: `regular` or `hexagonal`
"""
def load_communities(self, comFile):
"""
Load communities determined by a community detection algorithm on a regular grid
Parameters
----------
comFile : str
Filename of community file
"""
with open(comFile) as cluFile:
clu = cluFile.read().split('\n')
self.codelength = float(clu[0].split(' ')[3])
header = clu[1].split(' ')[1:]
body = [line.split(' ') for line in clu[2:] if line is not '']
self.communityDF = pd.DataFrame(body, columns=header).astype({"node" : 'int',
"module" : 'int',
"flow" : 'float' }).set_index("node")
communityID = -np.ones(self.n, dtype=int)
communityFlow = -np.ones(self.n, dtype=float)
if hasattr(self, 'oceanMask'):
bindex = self.bindex[self.oceanMask]
else:
bindex = self.bindex
assert self.communityDF.shape[0] == bindex.shape[0], "Number of nodes in `.clu` file must equal the amount of non-empty bins."
for index, row in self.communityDF.iterrows():
# -1 because counting in clu file starts at 1
communityID[bindex[index-1]] = row['module'].astype(int)
communityFlow[bindex[index-1]] = row['flow']
self.communityID = np.ma.masked_equal(communityID, -1)
self.communityFlow = np.ma.masked_equal(communityFlow, -1)
self.communityIdx = {}
for community in np.unique(self.communityID).data[np.unique(self.communityID).data != -1]:
self.communityIdx[community] = {'bindex' : {},
'oceanBindex' : {}}
self.communityIdx[community]['bindex'] = self.bindex[self.communityID == community]
nonZeroCommunityID = self.communityID.data[self.communityID.data != -1]
self.communityIdx[community]['oceanBindex'] = np.arange(nonZeroCommunityID.size)[nonZeroCommunityID == community]
def color_communities(self, colors=4):
"""Associate new colors to existing communities by using graph coloring.
Returns
-------
np.array
Array containing new community IDs, corresponding to different colors.
"""
try:
self.communityNetwork = nx.Graph()
for community in self.adjacencyDict:
for neighbor in self.adjacencyDict[community]:
self.communityNetwork.add_edge(community, neighbor)
# Remove self-loops
self.communityNetwork.remove_edges_from(self.communityNetwork.selfloop_edges())
except NameError:
raise RuntimeError('The counting grid does not yet have an adjacency dictionary for determining the coloring of communities. Try calling the `find_adjacency()` method first.')
self.colorMapping = nx.coloring.greedy_color(self.communityNetwork, strategy='largest_first')
colorID = -np.ones(self.n, dtype=int)
maxColor = max(list(self.colorMapping.values()))
for i in range(len(self.communityID.flatten())):
if not np.ma.is_masked(self.communityID.flatten()[i]):
colorID[i] = self.colorMapping.get(self.communityID.flatten()[i], maxColor + 1)
self.colorID = np.ma.masked_equal(colorID, -1).reshape(self.communityID.shape)
return self.colorID
def calculate_coherence_ratio(self, transMat):
"""
Calculate the coherence ratio for each community.
Parameters
----------
transMat : transMat
Transition matrix to calculate coherence ratios.
Returns
-------
np.array
Array containing the coherence ratio of the community that each bin is part of.
"""
self.coherenceRatioDict = {}
for community, idx in self.communityIdx.items():
denom = np.sum(np.sum(transMat.counter[idx["oceanBindex"], :], axis=1))
if denom != 0:
self.coherenceRatioDict[community] = np.sum(np.sum(transMat.counter[idx["oceanBindex"], :][:, idx["oceanBindex"]], axis=1))/denom
coherenceRatio = -np.ones(self.n, dtype=float)
for i in range(len(self.communityID.flatten())):
if not np.ma.is_masked(self.communityID.flatten()[i]):
coherenceRatio[i] = self.coherenceRatioDict.get(self.communityID.flatten()[i], -1)
self.coherenceRatio = np.ma.masked_equal(coherenceRatio, -1).reshape(self.communityID.shape)
return self.coherenceRatio
def calculate_global_coherence(self):
"""
Calculate the global coherence ratio, which is a weighted average of the coherence ratio.
Returns
-------
float
Global coherence ratio
"""
assert hasattr(self, "coherenceRatio"), "Coherence ratios must be calculated first. Try calling the `calculate_coherence_ratio(transMat)` method."
# Note that this is self.coherenceRatio[~self.coherenceRatio.mask] provides values for each bin, such that the mean of this is a weighted average.
self.globalCoherenceRatio = self.coherenceRatio[~self.coherenceRatio.mask].mean()
return self.globalCoherenceRatio
def calculate_mixing(self, transMat):
"""
Parameters
----------
transMat : transMat
Transition matrix to calculate mixing parameters.
Returns
-------
np.array
Array containing the mixing parameter of the community that each bin is part of.
"""
self.mixingDict = {}
for community, idx in self.communityIdx.items():
subsetCounter = transMat.counter[idx["oceanBindex"], :][:, idx["oceanBindex"]]
subsetSums = np.tile(subsetCounter.sum(axis=1), (subsetCounter.shape[1],1)).T
R = np.divide(subsetCounter, subsetSums, out=np.zeros_like(subsetSums), where=subsetSums!=0)
if R.shape[0] > 1:
self.mixingDict[community] = np.divide(-np.sum(R*np.log(R, out=np.zeros_like(R), where=R!=0)), R.shape[0]* | np.log(R.shape[0]) | numpy.log |
import numpy as np
import scipy.stats
import scipy.special
from .density import density
from .methods import get_func
def density_fit(xx, nbins, k, edge = None, sq = True, alpha = None):
#this function attempts to fit a density having a power law behavior to eigenvalues supplied by xx
# xx should be decreasing.
# the method is to first find the empirical cdf F(x) = | { x_i : x_i < x } |, evaluated at nbins number of points
# which are a grid evenly spaced around the minimal and maximal eigenvalues in xx.
# then a polynomial linear regression is fit to F^(1 / (1+ alpha ))
# k is the degree of the fitted polynomial
# a density.density object is returned.
#sort in descending order.
if (np.diff(xx) >0).any():
xx = np.sort(xx)[::-1]
fit_edge = (edge is None)
if sq:
alpha = 0.5
if (not sq) and (alpha is None):
print('Fit an alpha first!')
return
if fit_edge:
xbulk = xx[0] - xx
else:
xbulk = edge - xx
bulkmin, bulkmax = xbulk[0], xbulk[-1]
xbulk = xbulk / xbulk[-1]
b, a = fit_cdf_power(xbulk, nbins, fit_edge=fit_edge, k=k, alpha=alpha)
# scaling factor calculated (see density.density object definition for details)
if sq:
sf = 1 / (np.power(3 / 2, 2 / 3) * a[1] / np.power((bulkmax-bulkmin), 1/3))
sf = sf / np.power(np.pi, 2 / 3)
else:
sf = (alpha+1)*np.power(a[1], alpha+1) #F' = sf*(x-b)^alpha
G, Gd = get_func(a, alpha)
rescal = lambda x: x / bulkmax
F = lambda x: G(rescal(x) - b) / G(1 - b)
Fd = lambda x: Gd(rescal(x) - b) / (G(1 - b) * (bulkmax))
if sq:
sf = sf* np.power(G(1-b), 2/3)
else:
sf = sf*np.power(bulkmax, alpha-1)
sf = sf / G(1-b)
if fit_edge:
p = lambda x : Fd(xx[0]-x)
cdf = lambda x : F(xx[0]-x)
r = xx[0] -b * bulkmax
l = xx[0] - bulkmax
else:
p = lambda x: Fd(edge - x)
cdf = lambda x: F(edge - x)
r = edge
l = edge - bulkmax
dens = density(p, l, r, F=cdf, scaling_factor = sf, sq=sq, alpha=alpha)
return dens
def fit_cdf_power(x, n, k=1, alpha=0.5, fit_edge= True, verbose = False):
#assume x is increasing
# Behavior is best when x begins at 0.
#n is number of points to evaluate the cdf on F
#k is order of polynomial
#alpha is power of density, p(x) ~ x^\alpha
# if fit_edge = False, will assume that the edge is at 0, and so the polynomial fit will not include a 0th order term
#what is returned is a scalar b, and a vector a.
#the fit is F^(1/(1+alpha)) = \sum_{i=1}^k a_i (x-b)^i
#note a[0] = 0.
F, right = get_cdf(x, n) #this returns the empirical CDF of x evaluated at n points.
# Right is the location of the points F is evaluated at, i.e. F_i = F ( right(i)).
# Note this function heavily relies on x increasing.
F = F / F[-1]
y = np.power(F, 1 / (1 + alpha))
#try to find the root of of the fit polynomial closest to the origin.
# if no root, return instead a linear polynomial (basically guaranteed to have a root)
if fit_edge:
P = np.polynomial.polynomial.Polynomial.fit(right, y, k)
P.convert(domain=np.array([-1, 1]))
ro = P.roots()
if not np.isreal(ro).any():
if verbose:
print('no real roots found for initial fit of k= ', k,'. Instead fit k=1')
k=1
P = np.polynomial.polynomial.Polynomial.fit(right, y, k)
P.convert(domain=np.array([-1, 1]))
ro = P.roots()
I = np.where(np.isreal(ro))[0]
rero = ro[I]
b = rero[np.argmin(np.abs(rero))]
b = np.real(b)
#fit y = a[0] (x-b) + a[1](x-b)^2 + ...
a = | np.zeros(shape=k) | numpy.zeros |
from __future__ import division
from future.utils import viewitems
from builtins import int, zip
import concurrent.futures
import os
import itertools
from ._adaptive_threshold import threshold as athreshold
from .pool import pooler
from ._moving_window import moving_window
# from mpglue.raster_tools import create_raster
# from mpglue import moving_window
import numpy as np
import cv2
# SciPy
from scipy.ndimage.measurements import label as nd_label
from scipy.ndimage.measurements import mean as nd_mean
import scipy.stats as sci_stats
from scipy.stats import mode as sci_mode
from sklearn.preprocessing import StandardScaler
# Scikit-image
from skimage.exposure import rescale_intensity
from skimage.filters import threshold_local
from skimage.morphology import remove_small_objects, skeletonize
from skimage.morphology import thin as sk_thin
from skimage.feature import peak_local_max
from skimage.measure import regionprops
from skimage.measure import label as sk_label
import pymorph
from mahotas import thin as mthin
from mahotas.morph import hitmiss as mhitmiss
# from tqdm import tqdm
# from joblib import Parallel, delayed
def local_straightness(arr, kernel_filter, w, sigma_color, sigma_space):
"""
https://ieeexplore-ieee-org.ezproxy.library.uq.edu.au/document/1334256
https://docs.opencv.org/master/d4/d70/tutorial_anisotropic_image_segmentation_by_a_gst.html
Example:
>>> conv_kernels = set_kernel_pairs(methods=['compass'])
>>> kernel_filter = conv_kernels['compass']['kernels']
>>> local_straightness(array, kernel_filter, 3, 1, 1)
"""
diff_x = cv2.filter2D(np.float32(arr),
cv2.CV_32F,
kernel_filter[1],
borderType=cv2.BORDER_CONSTANT)
diff_y = cv2.filter2D(np.float32(arr),
cv2.CV_32F,
kernel_filter[0],
borderType=cv2.BORDER_CONSTANT)
diff_xy = diff_x * diff_y
diff_xx = diff_x * diff_x
diff_yy = diff_y * diff_y
c11 = cv2.boxFilter(np.float32(diff_xx), cv2.CV_32F, (w, w))
c22 = cv2.boxFilter(np.float32(diff_yy), cv2.CV_32F, (w, w))
c12 = cv2.boxFilter(np.float32(diff_xy), cv2.CV_32F, (w, w))
# c11 = cv2.bilateralFilter(np.float32(diff_xx), w, sigma_color, sigma_space)
# c22 = cv2.bilateralFilter(np.float32(diff_yy), w, sigma_color, sigma_space)
# c12 = cv2.bilateralFilter(np.float32(diff_xy), w, sigma_color, sigma_space)
gamma_max = (c11 + c22 + np.sqrt((c11 - c22)**2 + 4*c12**2)) / 2.0
gamma_min = (c11 + c22 - np.sqrt((c11 - c22)**2 + 4*c12**2)) / 2.0
s = 1.0 - (gamma_min / gamma_max)
return s
def logistic(x, **params):
return sci_stats.logistic.cdf(x, **params)
def sigmoid(x, a, b):
return 1.0 / (1.0 + | np.exp(-b * (x - a)) | numpy.exp |
# This module has been generated automatically from space group information
# obtained from the Computational Crystallography Toolbox
#
"""
Space groups
This module contains a list of all the 230 space groups that can occur in
a crystal. The variable space_groups contains a dictionary that maps
space group numbers and space group names to the corresponding space
group objects.
.. moduleauthor:: <NAME> <<EMAIL>>
"""
#-----------------------------------------------------------------------------
# Copyright (C) 2013 The Mosaic Development Team
#
# Distributed under the terms of the BSD License. The full license is in
# the file LICENSE.txt, distributed as part of this software.
#-----------------------------------------------------------------------------
import numpy as N
class SpaceGroup(object):
"""
Space group
All possible space group objects are created in this module. Other
modules should access these objects through the dictionary
space_groups rather than create their own space group objects.
"""
def __init__(self, number, symbol, transformations):
"""
:param number: the number assigned to the space group by
international convention
:type number: int
:param symbol: the Hermann-Mauguin space-group symbol as used
in PDB and mmCIF files
:type symbol: str
:param transformations: a list of space group transformations,
each consisting of a tuple of three
integer arrays (rot, tn, td), where
rot is the rotation matrix and tn/td
are the numerator and denominator of the
translation vector. The transformations
are defined in fractional coordinates.
:type transformations: list
"""
self.number = number
self.symbol = symbol
self.transformations = transformations
self.transposed_rotations = N.array([N.transpose(t[0])
for t in transformations])
self.phase_factors = N.exp(N.array([(-2j*N.pi*t[1])/t[2]
for t in transformations]))
def __repr__(self):
return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol))
def __len__(self):
"""
:return: the number of space group transformations
:rtype: int
"""
return len(self.transformations)
def symmetryEquivalentMillerIndices(self, hkl):
"""
:param hkl: a set of Miller indices
:type hkl: Scientific.N.array_type
:return: a tuple (miller_indices, phase_factor) of two arrays
of length equal to the number of space group
transformations. miller_indices contains the Miller
indices of each reflection equivalent by symmetry to the
reflection hkl (including hkl itself as the first element).
phase_factor contains the phase factors that must be applied
to the structure factor of reflection hkl to obtain the
structure factor of the symmetry equivalent reflection.
:rtype: tuple
"""
hkls = N.dot(self.transposed_rotations, hkl)
p = N.multiply.reduce(self.phase_factors**hkl, -1)
return hkls, p
space_groups = {}
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(1, 'P 1', transformations)
space_groups[1] = sg
space_groups['P 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(2, 'P -1', transformations)
space_groups[2] = sg
space_groups['P -1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(3, 'P 1 2 1', transformations)
space_groups[3] = sg
space_groups['P 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(4, 'P 1 21 1', transformations)
space_groups[4] = sg
space_groups['P 1 21 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(5, 'C 1 2 1', transformations)
space_groups[5] = sg
space_groups['C 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(6, 'P 1 m 1', transformations)
space_groups[6] = sg
space_groups['P 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(7, 'P 1 c 1', transformations)
space_groups[7] = sg
space_groups['P 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(8, 'C 1 m 1', transformations)
space_groups[8] = sg
space_groups['C 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(9, 'C 1 c 1', transformations)
space_groups[9] = sg
space_groups['C 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(10, 'P 1 2/m 1', transformations)
space_groups[10] = sg
space_groups['P 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(11, 'P 1 21/m 1', transformations)
space_groups[11] = sg
space_groups['P 1 21/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(12, 'C 1 2/m 1', transformations)
space_groups[12] = sg
space_groups['C 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(13, 'P 1 2/c 1', transformations)
space_groups[13] = sg
space_groups['P 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(14, 'P 1 21/c 1', transformations)
space_groups[14] = sg
space_groups['P 1 21/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(15, 'C 1 2/c 1', transformations)
space_groups[15] = sg
space_groups['C 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(16, 'P 2 2 2', transformations)
space_groups[16] = sg
space_groups['P 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(17, 'P 2 2 21', transformations)
space_groups[17] = sg
space_groups['P 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(18, 'P 21 21 2', transformations)
space_groups[18] = sg
space_groups['P 21 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(19, 'P 21 21 21', transformations)
space_groups[19] = sg
space_groups['P 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(20, 'C 2 2 21', transformations)
space_groups[20] = sg
space_groups['C 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(21, 'C 2 2 2', transformations)
space_groups[21] = sg
space_groups['C 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(22, 'F 2 2 2', transformations)
space_groups[22] = sg
space_groups['F 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(23, 'I 2 2 2', transformations)
space_groups[23] = sg
space_groups['I 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(24, 'I 21 21 21', transformations)
space_groups[24] = sg
space_groups['I 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(25, 'P m m 2', transformations)
space_groups[25] = sg
space_groups['P m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(26, 'P m c 21', transformations)
space_groups[26] = sg
space_groups['P m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(27, 'P c c 2', transformations)
space_groups[27] = sg
space_groups['P c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(28, 'P m a 2', transformations)
space_groups[28] = sg
space_groups['P m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(29, 'P c a 21', transformations)
space_groups[29] = sg
space_groups['P c a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(30, 'P n c 2', transformations)
space_groups[30] = sg
space_groups['P n c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(31, 'P m n 21', transformations)
space_groups[31] = sg
space_groups['P m n 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(32, 'P b a 2', transformations)
space_groups[32] = sg
space_groups['P b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(33, 'P n a 21', transformations)
space_groups[33] = sg
space_groups['P n a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(34, 'P n n 2', transformations)
space_groups[34] = sg
space_groups['P n n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(35, 'C m m 2', transformations)
space_groups[35] = sg
space_groups['C m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(36, 'C m c 21', transformations)
space_groups[36] = sg
space_groups['C m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(37, 'C c c 2', transformations)
space_groups[37] = sg
space_groups['C c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(38, 'A m m 2', transformations)
space_groups[38] = sg
space_groups['A m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(39, 'A b m 2', transformations)
space_groups[39] = sg
space_groups['A b m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(40, 'A m a 2', transformations)
space_groups[40] = sg
space_groups['A m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(41, 'A b a 2', transformations)
space_groups[41] = sg
space_groups['A b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(42, 'F m m 2', transformations)
space_groups[42] = sg
space_groups['F m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(43, 'F d d 2', transformations)
space_groups[43] = sg
space_groups['F d d 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(44, 'I m m 2', transformations)
space_groups[44] = sg
space_groups['I m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(45, 'I b a 2', transformations)
space_groups[45] = sg
space_groups['I b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(46, 'I m a 2', transformations)
space_groups[46] = sg
space_groups['I m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(47, 'P m m m', transformations)
space_groups[47] = sg
space_groups['P m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(48, 'P n n n :2', transformations)
space_groups[48] = sg
space_groups['P n n n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(49, 'P c c m', transformations)
space_groups[49] = sg
space_groups['P c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(50, 'P b a n :2', transformations)
space_groups[50] = sg
space_groups['P b a n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(51, 'P m m a', transformations)
space_groups[51] = sg
space_groups['P m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(52, 'P n n a', transformations)
space_groups[52] = sg
space_groups['P n n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(53, 'P m n a', transformations)
space_groups[53] = sg
space_groups['P m n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(54, 'P c c a', transformations)
space_groups[54] = sg
space_groups['P c c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(55, 'P b a m', transformations)
space_groups[55] = sg
space_groups['P b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(56, 'P c c n', transformations)
space_groups[56] = sg
space_groups['P c c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(57, 'P b c m', transformations)
space_groups[57] = sg
space_groups['P b c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(58, 'P n n m', transformations)
space_groups[58] = sg
space_groups['P n n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(59, 'P m m n :2', transformations)
space_groups[59] = sg
space_groups['P m m n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(60, 'P b c n', transformations)
space_groups[60] = sg
space_groups['P b c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(61, 'P b c a', transformations)
space_groups[61] = sg
space_groups['P b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(62, 'P n m a', transformations)
space_groups[62] = sg
space_groups['P n m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(63, 'C m c m', transformations)
space_groups[63] = sg
space_groups['C m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(64, 'C m c a', transformations)
space_groups[64] = sg
space_groups['C m c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(65, 'C m m m', transformations)
space_groups[65] = sg
space_groups['C m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(66, 'C c c m', transformations)
space_groups[66] = sg
space_groups['C c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(67, 'C m m a', transformations)
space_groups[67] = sg
space_groups['C m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(68, 'C c c a :2', transformations)
space_groups[68] = sg
space_groups['C c c a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(69, 'F m m m', transformations)
space_groups[69] = sg
space_groups['F m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(70, 'F d d d :2', transformations)
space_groups[70] = sg
space_groups['F d d d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(71, 'I m m m', transformations)
space_groups[71] = sg
space_groups['I m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(72, 'I b a m', transformations)
space_groups[72] = sg
space_groups['I b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(73, 'I b c a', transformations)
space_groups[73] = sg
space_groups['I b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(74, 'I m m a', transformations)
space_groups[74] = sg
space_groups['I m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(75, 'P 4', transformations)
space_groups[75] = sg
space_groups['P 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(76, 'P 41', transformations)
space_groups[76] = sg
space_groups['P 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(77, 'P 42', transformations)
space_groups[77] = sg
space_groups['P 42'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(78, 'P 43', transformations)
space_groups[78] = sg
space_groups['P 43'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(79, 'I 4', transformations)
space_groups[79] = sg
space_groups['I 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(80, 'I 41', transformations)
space_groups[80] = sg
space_groups['I 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(81, 'P -4', transformations)
space_groups[81] = sg
space_groups['P -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(82, 'I -4', transformations)
space_groups[82] = sg
space_groups['I -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(83, 'P 4/m', transformations)
space_groups[83] = sg
space_groups['P 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(84, 'P 42/m', transformations)
space_groups[84] = sg
space_groups['P 42/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(85, 'P 4/n :2', transformations)
space_groups[85] = sg
space_groups['P 4/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(86, 'P 42/n :2', transformations)
space_groups[86] = sg
space_groups['P 42/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(87, 'I 4/m', transformations)
space_groups[87] = sg
space_groups['I 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(88, 'I 41/a :2', transformations)
space_groups[88] = sg
space_groups['I 41/a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(89, 'P 4 2 2', transformations)
space_groups[89] = sg
space_groups['P 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(90, 'P 4 21 2', transformations)
space_groups[90] = sg
space_groups['P 4 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(91, 'P 41 2 2', transformations)
space_groups[91] = sg
space_groups['P 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(92, 'P 41 21 2', transformations)
space_groups[92] = sg
space_groups['P 41 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(93, 'P 42 2 2', transformations)
space_groups[93] = sg
space_groups['P 42 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(94, 'P 42 21 2', transformations)
space_groups[94] = sg
space_groups['P 42 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(95, 'P 43 2 2', transformations)
space_groups[95] = sg
space_groups['P 43 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(96, 'P 43 21 2', transformations)
space_groups[96] = sg
space_groups['P 43 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(97, 'I 4 2 2', transformations)
space_groups[97] = sg
space_groups['I 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(98, 'I 41 2 2', transformations)
space_groups[98] = sg
space_groups['I 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(99, 'P 4 m m', transformations)
space_groups[99] = sg
space_groups['P 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(100, 'P 4 b m', transformations)
space_groups[100] = sg
space_groups['P 4 b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(101, 'P 42 c m', transformations)
space_groups[101] = sg
space_groups['P 42 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(102, 'P 42 n m', transformations)
space_groups[102] = sg
space_groups['P 42 n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(103, 'P 4 c c', transformations)
space_groups[103] = sg
space_groups['P 4 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(104, 'P 4 n c', transformations)
space_groups[104] = sg
space_groups['P 4 n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(105, 'P 42 m c', transformations)
space_groups[105] = sg
space_groups['P 42 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(106, 'P 42 b c', transformations)
space_groups[106] = sg
space_groups['P 42 b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(107, 'I 4 m m', transformations)
space_groups[107] = sg
space_groups['I 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(108, 'I 4 c m', transformations)
space_groups[108] = sg
space_groups['I 4 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(109, 'I 41 m d', transformations)
space_groups[109] = sg
space_groups['I 41 m d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(110, 'I 41 c d', transformations)
space_groups[110] = sg
space_groups['I 41 c d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(111, 'P -4 2 m', transformations)
space_groups[111] = sg
space_groups['P -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(112, 'P -4 2 c', transformations)
space_groups[112] = sg
space_groups['P -4 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(113, 'P -4 21 m', transformations)
space_groups[113] = sg
space_groups['P -4 21 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(114, 'P -4 21 c', transformations)
space_groups[114] = sg
space_groups['P -4 21 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(115, 'P -4 m 2', transformations)
space_groups[115] = sg
space_groups['P -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(116, 'P -4 c 2', transformations)
space_groups[116] = sg
space_groups['P -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(117, 'P -4 b 2', transformations)
space_groups[117] = sg
space_groups['P -4 b 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(118, 'P -4 n 2', transformations)
space_groups[118] = sg
space_groups['P -4 n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(119, 'I -4 m 2', transformations)
space_groups[119] = sg
space_groups['I -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(120, 'I -4 c 2', transformations)
space_groups[120] = sg
space_groups['I -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(121, 'I -4 2 m', transformations)
space_groups[121] = sg
space_groups['I -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(122, 'I -4 2 d', transformations)
space_groups[122] = sg
space_groups['I -4 2 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(123, 'P 4/m m m', transformations)
space_groups[123] = sg
space_groups['P 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(124, 'P 4/m c c', transformations)
space_groups[124] = sg
space_groups['P 4/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(125, 'P 4/n b m :2', transformations)
space_groups[125] = sg
space_groups['P 4/n b m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(126, 'P 4/n n c :2', transformations)
space_groups[126] = sg
space_groups['P 4/n n c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(127, 'P 4/m b m', transformations)
space_groups[127] = sg
space_groups['P 4/m b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(128, 'P 4/m n c', transformations)
space_groups[128] = sg
space_groups['P 4/m n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(129, 'P 4/n m m :2', transformations)
space_groups[129] = sg
space_groups['P 4/n m m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(130, 'P 4/n c c :2', transformations)
space_groups[130] = sg
space_groups['P 4/n c c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(131, 'P 42/m m c', transformations)
space_groups[131] = sg
space_groups['P 42/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(132, 'P 42/m c m', transformations)
space_groups[132] = sg
space_groups['P 42/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(133, 'P 42/n b c :2', transformations)
space_groups[133] = sg
space_groups['P 42/n b c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(134, 'P 42/n n m :2', transformations)
space_groups[134] = sg
space_groups['P 42/n n m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(135, 'P 42/m b c', transformations)
space_groups[135] = sg
space_groups['P 42/m b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(136, 'P 42/m n m', transformations)
space_groups[136] = sg
space_groups['P 42/m n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(137, 'P 42/n m c :2', transformations)
space_groups[137] = sg
space_groups['P 42/n m c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(138, 'P 42/n c m :2', transformations)
space_groups[138] = sg
space_groups['P 42/n c m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(139, 'I 4/m m m', transformations)
space_groups[139] = sg
space_groups['I 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(140, 'I 4/m c m', transformations)
space_groups[140] = sg
space_groups['I 4/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(141, 'I 41/a m d :2', transformations)
space_groups[141] = sg
space_groups['I 41/a m d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(142, 'I 41/a c d :2', transformations)
space_groups[142] = sg
space_groups['I 41/a c d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(143, 'P 3', transformations)
space_groups[143] = sg
space_groups['P 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(144, 'P 31', transformations)
space_groups[144] = sg
space_groups['P 31'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(145, 'P 32', transformations)
space_groups[145] = sg
space_groups['P 32'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(146, 'R 3 :H', transformations)
space_groups[146] = sg
space_groups['R 3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(147, 'P -3', transformations)
space_groups[147] = sg
space_groups['P -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(148, 'R -3 :H', transformations)
space_groups[148] = sg
space_groups['R -3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(149, 'P 3 1 2', transformations)
space_groups[149] = sg
space_groups['P 3 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(150, 'P 3 2 1', transformations)
space_groups[150] = sg
space_groups['P 3 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(151, 'P 31 1 2', transformations)
space_groups[151] = sg
space_groups['P 31 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(152, 'P 31 2 1', transformations)
space_groups[152] = sg
space_groups['P 31 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(153, 'P 32 1 2', transformations)
space_groups[153] = sg
space_groups['P 32 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(154, 'P 32 2 1', transformations)
space_groups[154] = sg
space_groups['P 32 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(155, 'R 3 2 :H', transformations)
space_groups[155] = sg
space_groups['R 3 2 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(156, 'P 3 m 1', transformations)
space_groups[156] = sg
space_groups['P 3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(157, 'P 3 1 m', transformations)
space_groups[157] = sg
space_groups['P 3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(158, 'P 3 c 1', transformations)
space_groups[158] = sg
space_groups['P 3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(159, 'P 3 1 c', transformations)
space_groups[159] = sg
space_groups['P 3 1 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(160, 'R 3 m :H', transformations)
space_groups[160] = sg
space_groups['R 3 m :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(161, 'R 3 c :H', transformations)
space_groups[161] = sg
space_groups['R 3 c :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(162, 'P -3 1 m', transformations)
space_groups[162] = sg
space_groups['P -3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(163, 'P -3 1 c', transformations)
space_groups[163] = sg
space_groups['P -3 1 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(164, 'P -3 m 1', transformations)
space_groups[164] = sg
space_groups['P -3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(165, 'P -3 c 1', transformations)
space_groups[165] = sg
space_groups['P -3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(166, 'R -3 m :H', transformations)
space_groups[166] = sg
space_groups['R -3 m :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(167, 'R -3 c :H', transformations)
space_groups[167] = sg
space_groups['R -3 c :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(168, 'P 6', transformations)
space_groups[168] = sg
space_groups['P 6'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(169, 'P 61', transformations)
space_groups[169] = sg
space_groups['P 61'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(170, 'P 65', transformations)
space_groups[170] = sg
space_groups['P 65'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(171, 'P 62', transformations)
space_groups[171] = sg
space_groups['P 62'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(172, 'P 64', transformations)
space_groups[172] = sg
space_groups['P 64'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(173, 'P 63', transformations)
space_groups[173] = sg
space_groups['P 63'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(174, 'P -6', transformations)
space_groups[174] = sg
space_groups['P -6'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(175, 'P 6/m', transformations)
space_groups[175] = sg
space_groups['P 6/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(176, 'P 63/m', transformations)
space_groups[176] = sg
space_groups['P 63/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(177, 'P 6 2 2', transformations)
space_groups[177] = sg
space_groups['P 6 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(178, 'P 61 2 2', transformations)
space_groups[178] = sg
space_groups['P 61 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(179, 'P 65 2 2', transformations)
space_groups[179] = sg
space_groups['P 65 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(180, 'P 62 2 2', transformations)
space_groups[180] = sg
space_groups['P 62 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(181, 'P 64 2 2', transformations)
space_groups[181] = sg
space_groups['P 64 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(182, 'P 63 2 2', transformations)
space_groups[182] = sg
space_groups['P 63 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(183, 'P 6 m m', transformations)
space_groups[183] = sg
space_groups['P 6 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(184, 'P 6 c c', transformations)
space_groups[184] = sg
space_groups['P 6 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(185, 'P 63 c m', transformations)
space_groups[185] = sg
space_groups['P 63 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(186, 'P 63 m c', transformations)
space_groups[186] = sg
space_groups['P 63 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(187, 'P -6 m 2', transformations)
space_groups[187] = sg
space_groups['P -6 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(188, 'P -6 c 2', transformations)
space_groups[188] = sg
space_groups['P -6 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(189, 'P -6 2 m', transformations)
space_groups[189] = sg
space_groups['P -6 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(190, 'P -6 2 c', transformations)
space_groups[190] = sg
space_groups['P -6 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(191, 'P 6/m m m', transformations)
space_groups[191] = sg
space_groups['P 6/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(192, 'P 6/m c c', transformations)
space_groups[192] = sg
space_groups['P 6/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(193, 'P 63/m c m', transformations)
space_groups[193] = sg
space_groups['P 63/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(194, 'P 63/m m c', transformations)
space_groups[194] = sg
space_groups['P 63/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(195, 'P 2 3', transformations)
space_groups[195] = sg
space_groups['P 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(196, 'F 2 3', transformations)
space_groups[196] = sg
space_groups['F 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(197, 'I 2 3', transformations)
space_groups[197] = sg
space_groups['I 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(198, 'P 21 3', transformations)
space_groups[198] = sg
space_groups['P 21 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(199, 'I 21 3', transformations)
space_groups[199] = sg
space_groups['I 21 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(200, 'P m -3', transformations)
space_groups[200] = sg
space_groups['P m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(201, 'P n -3 :2', transformations)
space_groups[201] = sg
space_groups['P n -3 :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(202, 'F m -3', transformations)
space_groups[202] = sg
space_groups['F m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(203, 'F d -3 :2', transformations)
space_groups[203] = sg
space_groups['F d -3 :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(204, 'I m -3', transformations)
space_groups[204] = sg
space_groups['I m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(205, 'P a -3', transformations)
space_groups[205] = sg
space_groups['P a -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(206, 'I a -3', transformations)
space_groups[206] = sg
space_groups['I a -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(207, 'P 4 3 2', transformations)
space_groups[207] = sg
space_groups['P 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(208, 'P 42 3 2', transformations)
space_groups[208] = sg
space_groups['P 42 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(209, 'F 4 3 2', transformations)
space_groups[209] = sg
space_groups['F 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(210, 'F 41 3 2', transformations)
space_groups[210] = sg
space_groups['F 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(211, 'I 4 3 2', transformations)
space_groups[211] = sg
space_groups['I 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(212, 'P 43 3 2', transformations)
space_groups[212] = sg
space_groups['P 43 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(213, 'P 41 3 2', transformations)
space_groups[213] = sg
space_groups['P 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(214, 'I 41 3 2', transformations)
space_groups[214] = sg
space_groups['I 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(215, 'P -4 3 m', transformations)
space_groups[215] = sg
space_groups['P -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(216, 'F -4 3 m', transformations)
space_groups[216] = sg
space_groups['F -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(217, 'I -4 3 m', transformations)
space_groups[217] = sg
space_groups['I -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(218, 'P -4 3 n', transformations)
space_groups[218] = sg
space_groups['P -4 3 n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(219, 'F -4 3 c', transformations)
space_groups[219] = sg
space_groups['F -4 3 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(220, 'I -4 3 d', transformations)
space_groups[220] = sg
space_groups['I -4 3 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(221, 'P m -3 m', transformations)
space_groups[221] = sg
space_groups['P m -3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(222, 'P n -3 n :2', transformations)
space_groups[222] = sg
space_groups['P n -3 n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(223, 'P m -3 n', transformations)
space_groups[223] = sg
space_groups['P m -3 n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(224, 'P n -3 m :2', transformations)
space_groups[224] = sg
space_groups['P n -3 m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(225, 'F m -3 m', transformations)
space_groups[225] = sg
space_groups['F m -3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(226, 'F m -3 c', transformations)
space_groups[226] = sg
space_groups['F m -3 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(227, 'F d -3 m :2', transformations)
space_groups[227] = sg
space_groups['F d -3 m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,5,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,5,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,5])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,3,5])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,5,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([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([1,1,5])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
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([0,3,5])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-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([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
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([0,1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,5])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,0,5])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
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([3,0,5])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([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([1,1,5])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
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([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
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,-1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
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([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([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([3,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([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([1,3,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([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,-3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([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([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([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,-3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
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,-3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(228, 'F d -3 c :2', transformations)
space_groups[228] = sg
space_groups['F d -3 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([1,0,0,0,0,-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]) | numpy.array |
import abc
import itertools
import inspect
import pandas as pd
import numpy as np
from skimage.measure import regionprops_table, perimeter
from scipy.ndimage.measurements import labeled_comprehension
from scipy.ndimage.morphology import distance_transform_edt
from scipy.ndimage import find_objects
# TODO test for 3D feature extraction/conversion
# TODO test with empty labels
class BaseFeatureExtractor():
'''Base class for feature extractors. Extract features from all combinations
of label-channel in labels,channels input dicts. Optionaly target keys can be filtered.
Returns the result a pandas dataframe.
'''
def __init__(self,
label_targets='all',
channel_targets='all',
*args,
**kwargs):
'''
Args:
label_targets: list of keys to filter label images
channel_targets: list of keys to filter channel images
'''
self.label_targets = label_targets
self.channel_targets = channel_targets
def __call__(self, labels, channels):
if not (isinstance(labels, dict) or labels is None):
raise ValueError(
'Expects labels to be a dictionnary of images. received {}'.
format(type(labels)))
if not (isinstance(channels, dict) or channels is None):
raise ValueError(
'Expects channels to be a dictionnary of images. received {}'.
format(type(channels)))
# filter targets
if self.label_targets is None:
labels = None
elif self.label_targets != 'all':
labels = {
key: val
for key, val in labels.items() if key in self.label_targets
}
if self.channel_targets is None:
channels = None
elif self.channel_targets != 'all':
channels = {
key: val
for key, val in channels.items() if key in self.channel_targets
}
if labels is None and channels is None:
raise ValueError(
'At least one label image or one intensity channel must be provided'
)
if labels is None:
# measure image properties --> single label covering entire image
labels = {
'img': np.ones_like(next(iter(channels.values())),
dtype=np.uint8)
}
if channels is None:
channels = {'na': None}
all_props = pd.DataFrame(columns=[
'channel', 'region', 'object_id', 'feature_name', 'feature_value'
])
# all combination of labels and channel
for (label_key,
label), (ch_key, ch) in itertools.product(labels.items(),
channels.items()):
if label.max() == 0: # empty label image
continue
props = self._extract_features(label, ch)
props = pd.DataFrame(props)
props = props.set_index(
'label').stack().reset_index() #.set_index('label')
props.columns = ['object_id', 'feature_name', 'feature_value']
props['channel'] = ch_key
props['region'] = label_key
all_props = all_props.append(props, sort=False)
all_props = all_props.apply(self._dataframe_hook, axis=1)
return all_props
def _dataframe_hook(self, row):
'''Function applied to each row of the final dataframe'''
return row
@abc.abstractmethod
def _extract_features(self, label, intensity):
'''Method to extract feature for the given label,intensity_image pair.
Is expected to return a dict with the followng format:
example:
{'label':[1,2,3],
'area':[101,45,1000],
'mean_intensity': [10,100,25]}
'''
pass
class QuantilesFeatureExtractor(BaseFeatureExtractor):
'''Extract quantiles intensities over each labeled region'''
def __init__(self, quantiles=[0., 0.25, 0.5, 0.75, 1.0], *args, **kwargs):
super().__init__(*args, **kwargs)
self.quantiles = quantiles
def _extract_features(self, labels, intensity):
unique_l = np.unique(labels)
unique_l = unique_l[unique_l != 0]
q_vals = np.stack([
np.quantile(intensity[labels == l], self.quantiles)
for l in unique_l
],
axis=-1)
props = {
'q{:.3f}'.format(q).replace('.', '_'): qv
for q, qv in zip(self.quantiles, q_vals)
}
props['label'] = unique_l
return props
class IntensityFeatureExtractor(BaseFeatureExtractor):
'''Extract mean,std,mad (median absolute deviation) intensities
over each labeled region'''
_features_functions = {
'mean': np.mean,
'std': np.std,
'mad': lambda x: np.median(
np.abs(x - np.median(x))
), # median absolute deviation defined as median(|xi - median(x)|)
}
_implemented_features = set(_features_functions.keys())
def __init__(self, features=['mean'], *args, **kwargs):
super().__init__(*args, **kwargs)
for f in set(features) - self._implemented_features:
raise NotImplementedError('feature {} not implemented'.format(f))
self.features = features
def _extract_features(self, labels, intensity):
unique_l = np.unique(labels)
unique_l = unique_l[unique_l != 0]
props = {
feature_name:
labeled_comprehension(intensity,
labels,
unique_l,
self._features_functions[feature_name],
out_dtype=float,
default=np.nan)
for feature_name in self.features
}
props['label'] = unique_l
return props
class DistanceTransformFeatureExtractor(BaseFeatureExtractor):
'''Extract features based on distance transform (mean|max|median radius)
over each labeled region'''
_features_functions = {
'mean_radius': np.mean,
'max_radius': np.max,
'median_radius': np.median,
}
_implemented_features = set(_features_functions.keys())
_require_isotropic = {'median_radius'}
def __init__(self,
features=['mean_radius', 'max_radius', 'median_radius'],
physical_coords=False,
spacing=1,
*args,
**kwargs):
'''
Args:
features: list of features to compute
physical_coords: whether to convert px coordinates to physical coordinates
spacing: voxel size to do the coordinate conversion
'''
# override channel target
try:
del kwargs['channel_targets']
except KeyError:
pass
super().__init__(channel_targets=None, *args, **kwargs)
for f in set(features) - self._implemented_features:
raise NotImplementedError('feature {} not implemented'.format(f))
if not isinstance(
spacing,
(int, float)) and not np.all(np.array(spacing) == spacing[0]):
for f in self._require_isotropic.intersection(features):
raise ValueError(
'{} feature requires isotropic spacing'.format(f))
# add compulsory 'label' needed of indexing
self.features = set(features)
self.spacing = spacing
self.physical_coords = physical_coords
def _extract_features(self, labels, intensity):
if self.physical_coords:
self.ndim = labels.ndim
self.spacing = np.broadcast_to(np.array(self.spacing), self.ndim)
sampling = self.spacing
else:
sampling = None
props = {f: [] for f in self.features}
unique_l = []
# compute distance transform separately for each label (in case they are touching)
locs = find_objects(labels)
for l, loc in enumerate(locs, start=1):
if loc:
unique_l.append(l)
mask = np.pad(labels[loc] > 0, 1)
dist = distance_transform_edt(mask, sampling=sampling)
radii = dist[mask]
for f in self.features:
props[f].append(self._features_functions[f](radii))
props['label'] = unique_l
return props
class SKRegionPropFeatureExtractor(BaseFeatureExtractor):
'''scikit-image regionprops wrapper.
Notes:
for details see https://scikit-image.org/docs/dev/api/skimage.measure.html#skimage.measure.regionprops
Also compute the convex_perimeter.
'''
# TODO complete name mapping and coord conv
# skimage uses 2D names for 3D features (e.g. area, perimeter, etc.)
_name_mapping_2D_3D = {'area': 'volume'}
_name_mapping_3D_2D = {
val: key
for key, val in _name_mapping_2D_3D.items()
}
_implemented_features = {
'label', 'volume', 'area', 'centroid', 'weighted_centroid',
'minor_axis_length', 'major_axis_length', 'eccentricity', 'perimeter',
'convex_area', 'convex_perimeter', 'solidity', 'moments_hu',
'weighted_moments_hu'
}
_require_isotropic = {
'minor_axis_length', 'major_axis_length', 'perimeter',
'convex_perimeter'
}
_physical_coords_conversion = {
'volume': lambda x, spacing: x * np.prod(spacing),
'perimeter': lambda x, spacing: x * spacing[0],
'convex_perimeter': lambda x, spacing: x * spacing[0],
'area': lambda x, spacing: x * np.prod(spacing),
'convex_area': lambda x, spacing: x * np.prod(spacing),
'centroid-0': lambda c, spacing: c * spacing[0],
'centroid-1': lambda c, spacing: c * spacing[1],
'centroid-2': lambda c, spacing: c * spacing[2],
'weighted_centroid-0': lambda c, spacing: c * spacing[0],
'weighted_centroid-1': lambda c, spacing: c * spacing[1],
'weighted_centroid-2': lambda c, spacing: c * spacing[2],
'minor_axis_length': lambda x, spacing: x * spacing[0],
'major_axis_length': lambda x, spacing: x * spacing[0],
}
def __init__(self,
features=['centroid'],
physical_coords=False,
spacing=1,
*args,
**kwargs):
'''
Args:
features: list of features to compute
physical_coords: whether to convert px coordinates to physical coordinates
spacing: voxel size to do the coordinate conversion
'''
super().__init__(*args, **kwargs)
for f in set(features) - self._implemented_features:
raise NotImplementedError('feature {} not implemented'.format(f))
# add compulsory 'label' needed of indexing
self.features = set(features).union({'label'})
self.spacing = spacing
self.physical_coords = physical_coords
def _px_to_phy(self, row):
if self.physical_coords:
if not self.isotropic and row.feature_name in self._require_isotropic:
raise ValueError(
'{} requires isotropic spacing. spacing: {}'.format(
row.feature_name, self.spacing))
convert_fun = self._physical_coords_conversion.get(
row.feature_name)
if convert_fun is not None:
row.feature_value = convert_fun(row.feature_value,
self.spacing)
return row
def _dataframe_hook(self, row):
'''Function applied to each row of the final dataframe'''
row = self._px_to_phy(row)
return row
def _extract_features(self, labels, intensity):
self.ndim = labels.ndim
self.spacing = np.broadcast_to(np.array(self.spacing), self.ndim)
self.isotropic = np.all(self.spacing == self.spacing[0])
# map 2D feature names if 3D image
if self.ndim == 3:
# skimage regions props uses 2D feature names (e.g. perimeter, area instead of surface, volume respectively)
features = {
self._name_mapping_3D_2D.get(f, f)
for f in self.features
}
else:
features = self.features
# special case pre: extract "convex_image" to compute missing "convex_perimeter" feature
if 'convex_perimeter' in features:
features = [
'convex_image' if x == 'convex_perimeter' else x
for x in features
]
# extract actual features
props = regionprops_table(labels,
intensity_image=intensity,
properties=features,
separator='-')
# special case post: extract compute missing "convex_perimeter" feature
convex_images = props.pop('convex_image', None)
if convex_images is not None:
props['convex_perimeter'] = [
perimeter(hull) for hull in convex_images
]
# map back 3D feature names if 3D image
if self.ndim == 3:
props = {
self._name_mapping_2D_3D.get(key, key): val
for key, val in props.items()
}
return props
class BasedDerivedFeatureCalculator():
'''Base class to compute derived features from a dataframe of existing features.
add new features as static methods with base feature names as arguments.'''
@property
@classmethod
@abc.abstractmethod
def grouping(cls):
'''List of keys to groupby props DataFrame to compute derived features'''
return NotImplementedError
def __init__(self, features, label_targets='all', channel_targets='all'):
for f in features:
fun = getattr(self, f, None)
if fun is None:
raise NotImplementedError(
'feature {} not implemented'.format(f))
self.features = features
self.label_targets = label_targets
self.channel_targets = channel_targets
self.arg_keys = [
a for a in ['channel', 'region', 'object_id']
if a not in self.grouping
] + ['feature_name']
def __call__(self, props):
props = props.set_index(['channel', 'region',
'object_id']).sort_index()
if self.label_targets != 'all':
props = props.loc(axis=0)[:, self.label_targets]
if self.channel_targets != 'all':
props = props.loc(axis=0)[self.channel_targets + ['na']]
derived_props = props.groupby(self.grouping).apply(
self._compute_subdf_features, props=props)
if len(derived_props) > 0:
derived_props = derived_props.droplevel(-1).reset_index()
return derived_props
def _get_arg_value(self, arg, subdf):
'''Returns '''
rows_masks = [
subdf[k].str.startswith(a)
for k, a in zip(self.arg_keys, arg.split('__'))
]
rows_mask = np.prod(rows_masks, axis=0).astype(bool)
return subdf[rows_mask].feature_value.values.squeeze()
def _compute_subdf_features(self, subdf, props):
subdf = subdf.reset_index()
derived_features = []
for feature in self.features:
# get the function computing the requested features
fun = getattr(self, feature)
# get a list of required base features
fun_args = inspect.getfullargspec(fun).args
# get required base features' value
kwargs = {arg: self._get_arg_value(arg, subdf) for arg in fun_args}
try:
feature_value = fun(**kwargs)
except Exception as e:
feature_value = None
if feature_value is not None and isinstance(
feature_value, (float, int, bool)):
derived_features.append({
'feature_name': feature,
'feature_value': feature_value
})
return pd.DataFrame(derived_features)
class HybridDerivedFeatureCalculator(BasedDerivedFeatureCalculator):
'''Computes features that depends on both morphological and intensity features'''
grouping = ['channel', 'region', 'object_id']
def _add_pure_morph_props(self, subdf, props):
'''Adds pure morphological features without assigned channel to df
if available in props.'''
regions = subdf.index.get_level_values(1).unique()
object_ids = subdf.index.get_level_values(2).unique()
if 'region' in self.grouping and subdf.index[0][0] != 'na':
try:
subdf = subdf.append(
props.loc(axis=0)['na', regions, object_ids])
except KeyError as e:
pass
return subdf
def _compute_subdf_features(self, subdf, props):
subdf = self._add_pure_morph_props(subdf, props)
return super()._compute_subdf_features(subdf, props)
@staticmethod
def mass_displacement(centroid, weighted_centroid):
'''distance between the center of mass of the binary image and of the intensity image.'''
return | np.linalg.norm(centroid - weighted_centroid) | numpy.linalg.norm |
import os
import numpy as np
import pandas as pd
import itertools
import matplotlib.pyplot as plt
import seaborn as sns
from config import basedir
sns.set()
def convert_to_num(pd_series):
pd_series = pd.to_numeric(pd_series, errors='coerce')
pd_series = pd_series.replace([np.inf, -np.inf], np.nan)
return pd_series
def woe(df, var_name, good_bad_var, discrete=True):
df = pd.concat([df[var_name], df[good_bad_var]], axis=1)
df = pd.concat([df.groupby(df.columns.values[0], as_index=False)[df.columns.values[1]].count(),
df.groupby(df.columns.values[0], as_index=False)[df.columns.values[1]].mean()], axis=1)
df = df.iloc[:, [0, 1, 3]]
df.columns = [df.columns[0], 'n_obs', 'prop_good']
df['prop_n_obs'] = df['n_obs'] / df['n_obs'].sum()
df['n_good'] = (df['prop_good'] * df['n_obs'])
df['n_bad'] = ((1 - df['prop_good']) * df['n_obs'])
df['prob_n_good'] = df['n_good'] / df['n_good'].sum()
df['prob_n_bad'] = df['n_bad'] / df['n_bad'].sum()
df['woe'] = | np.log(df['prob_n_good'] / df['prob_n_bad']) | numpy.log |
import matplotlib.pyplot as plt
import numpy as np
import torch
import xarray as xr
from . import common
# from src.data import open_data
from .. import thermo
from wave import *
BOX_COLOR = "lightblue"
class paths:
all = "../../nn/NNAll/20.pkl"
lower = "../../nn/NNLowerDecayLR/20.pkl"
nostab = "../../nn/NNLowerNoStabPenalty/20.pkl"
def sortbyvalue(eig):
cp = eig.value.imag
gr = eig.value.real
permutation = cp * 100 + gr
return eig.sortby(permutation)
def get_eigen_pair_xarray(wave, k):
A = wave.system_matrix(k)
lam, r = np.linalg.eig(A)
return xr.Dataset(
{"value": (["m"], lam), "vector": (["f", "m"], r)}, coords={"k": k}
)
def compute_spectrum(wave, long_wave_km=40e6, short_wave_km=100e3) -> xr.Dataset:
high_freq = 2 * np.pi / short_wave_km
low_freq = 2 * np.pi / long_wave_km
k = np.linspace(low_freq, high_freq, 100)
eigs = [get_eigen_pair_xarray(wave, kk) for kk in k]
return xr.concat(eigs, dim="k")
def plot_struct_x(eig):
cp = eig.value.imag / eig.k
targ = 20
i = np.abs(cp - targ).argmin()
eig = eig.isel(m=i)
plot_struct_eig(eig)
def plot_struct_eig(eig):
z = eig["z"]
w, s, q = np.split(eig.vector, 3)
fig, (a, b, c) = plt.subplots(1, 3, figsize=(10, 3), constrained_layout=True)
a.set_title("W")
im = plot_struct_2d(w.values, z, ax=a)
plt.colorbar(im, ax=a, fraction=0.05)
b.set_title("S")
im = plot_struct_2d(s.values, z, ax=b)
plt.colorbar(im, ax=b, fraction=0.05)
c.set_title("Q")
im = plot_struct_2d(q.values, z, ax=c)
plt.colorbar(im, ax=c, fraction=0.05)
cp = float(eig.value.imag / eig.k)
gr = 86400 * float(eig.value.real)
fig.suptitle(f"cp = {cp:.2f} m/s; gr = {gr:.2f} 1/d")
def plot_struct_eig_p(
vec, sources, p, rho, w_range=(-1, 1), s_range=(-0.5, 0.5), q_range=(-0.5, 0.5)
):
fig, axs = plt.subplots(
1, 5, figsize=(8, 3.5), constrained_layout=True, sharey=True, sharex=True
)
axs[0].invert_yaxis()
p = np.asarray(p)
rho = np.asarray(rho)
w, s, q = np.split(vec, 3)
_, q1, q2 = | np.split(sources * 86400, 3) | numpy.split |
# 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]) | numpy.array |
# Copyright (c) 2017 Sony Corporation. 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 six.moves import range
import pytest
import numpy as np
import nnabla as nn
import nnabla.functions as F
from nbla_test_utils import list_context
from nnabla.testing import assert_allclose
ctxs = list_context('FusedBatchNormalization')
cpu_context = nn.Context(["cpu:float"])
def ref_fused_batch_normalization(x, beta, gamma, rmean, rvar, z, axes, decay_rate,
eps, batch_stat, nonlinearity, output_stat):
with nn.context_scope(cpu_context):
xvar = nn.Variable.from_numpy_array(x)
betavar = nn.Variable.from_numpy_array(beta)
gammavar = nn.Variable.from_numpy_array(gamma)
rmeanvar = nn.Variable.from_numpy_array(rmean)
rvarvar = nn.Variable.from_numpy_array(rvar)
if z is not None:
zvar = nn.Variable.from_numpy_array(z)
with nn.auto_forward():
bn = F.batch_normalization(xvar, betavar, gammavar, rmeanvar, rvarvar,
axes, decay_rate, eps, batch_stat, output_stat)
if z is None:
if output_stat:
y = bn[0]
else:
y = bn
else:
if output_stat:
y = F.add2(bn[0], zvar)
else:
y = F.add2(bn, zvar)
y = F.relu(y)
rmean[:] = rmeanvar.d
rvar[:] = rvarvar.d
if output_stat:
return y.d, bn[1].d, bn[2].d
else:
return y.d
def ref_grad_fused_batch_normalization(x, beta, gamma, rmean, rvar, z, dy, axes, decay_rate,
eps, batch_stat, nonlinearity, output_stat, **kw):
with nn.context_scope(cpu_context):
xvar = nn.Variable.from_numpy_array(x, need_grad=True)
xvar.g = 0
betavar = nn.Variable.from_numpy_array(beta, need_grad=True)
betavar.g = 0
gammavar = nn.Variable.from_numpy_array(gamma, need_grad=True)
gammavar.g = 0
rmeanvar = nn.Variable.from_numpy_array(rmean)
rmeanvar.g = 0
rvarvar = nn.Variable.from_numpy_array(rvar)
rvarvar.g = 0
zvar = None
if z is not None:
zvar = nn.Variable.from_numpy_array(z, need_grad=True)
zvar.g = 0
with nn.auto_forward():
bn = F.batch_normalization(xvar, betavar, gammavar, rmeanvar, rvarvar,
axes, decay_rate, eps, batch_stat, output_stat)
if z is None:
if output_stat:
y1 = bn[0]
else:
y1 = bn
else:
if output_stat:
y1 = F.add2(bn[0], zvar)
else:
y1 = F.add2(bn, zvar)
y = F.relu(y1)
y.g = dy
y.backward(dy)
concat = [xvar.g.flatten(), betavar.g.flatten(), gammavar.g.flatten()]
if z is not None:
concat.append(zvar.g.flatten())
return np.concatenate(concat)
def create_inputs(rng, axis, add):
x = rng.randn(2, 3, 5, 4).astype(np.float32) * 2
shape_stat = [1 for _ in range(x.ndim)]
if add:
# Note: The last dimension must be a multiple of 4
# if we want to test cudnn BN persistent mode.
z = rng.randn(2, 3, 5, 4).astype(np.float32) * 2
else:
z = None
shape_stat[axis] = x.shape[axis]
beta = rng.randn(*shape_stat).astype(np.float32)
gamma = rng.randn(*shape_stat).astype(np.float32)
rmean = np.zeros(shape_stat, dtype=np.float32)
rvar = np.zeros(shape_stat, dtype=np.float32)
return x, beta, gamma, rmean, rvar, z
def mask_inputs(inputs, no_scale, no_bias, no_mean, no_variance):
if no_bias:
inputs[1] = np.zeros(inputs[1].shape)
if no_scale:
inputs[2] = np.ones(inputs[2].shape)
if no_mean:
inputs[3] = | np.zeros(inputs[3].shape) | numpy.zeros |
# License: BSD 3-clause
# Authors: <NAME>,
# <NAME>
import numpy as np
from numpy.lib.stride_tricks import as_strided
import scipy.signal as sg
from scipy import linalg, fftpack
from numpy.testing import assert_almost_equal
def rolling_mean(X, window_size):
"""
Calculate the rolling mean
Parameters
----------
X : ndarray
Raw input signal
window_size : int
Length of rolling mean window
Returns
------
mean_averaged_X : ndarray
Rolling mean averaged X
"""
w = 1.0 / window_size * np.ones((window_size))
return np.correlate(X, w, 'valid')
def voiced_unvoiced(X, window_size=256, window_step=128, copy=True):
"""
Voiced unvoiced detection from a raw signal
Based on code from:
https://www.clear.rice.edu/elec532/PROJECTS96/lpc/code.html
Other references:
http://www.seas.ucla.edu/spapl/code/harmfreq_MOLRT_VAD.m
Parameters
----------
X : ndarray
Raw input signal
window_size : int, optional (default=256)
The window size to use, in samples.
window_step : int, optional (default=128)
How far the window steps after each calculation, in samples.
copy : bool, optional (default=True)
Whether to make a copy of the input array or allow in place changes.
"""
X = np.array(X, copy=copy)
if len(X.shape) < 2:
X = X[None]
n_points = X.shape[1]
n_windows = n_points // window_step
# Padding
pad_sizes = [(window_size - window_step) // 2,
window_size - window_step // 2]
# TODO: Handling for odd window sizes / steps
X = np.hstack((np.zeros((X.shape[0], pad_sizes[0])), X,
np.zeros((X.shape[0], pad_sizes[1]))))
clipping_factor = 0.6
b, a = sg.butter(10, np.pi * 9 / 40)
voiced_unvoiced = np.zeros((n_windows, 1))
period = np.zeros((n_windows, 1))
for window in range(max(n_windows - 1, 1)):
XX = X.ravel()[window * window_step + np.arange(window_size)]
XX *= sg.hamming(len(XX))
XX = sg.lfilter(b, a, XX)
left_max = np.max(np.abs(XX[:len(XX) // 3]))
right_max = np.max(np.abs(XX[-len(XX) // 3:]))
clip_value = clipping_factor * np.min([left_max, right_max])
XX_clip = np.clip(XX, clip_value, -clip_value)
XX_corr = np.correlate(XX_clip, XX_clip, mode='full')
center = np.argmax(XX_corr)
right_XX_corr = XX_corr[center:]
prev_window = max([window - 1, 0])
if voiced_unvoiced[prev_window] > 0:
# Want it to be harder to turn off than turn on
strength_factor = .29
else:
strength_factor = .3
start = np.where(right_XX_corr < .3 * XX_corr[center])[0]
# 20 is hardcoded but should depend on samplerate?
start = np.max([20, start[0]])
search_corr = right_XX_corr[start:]
index = np.argmax(search_corr)
second_max = search_corr[index]
if (second_max > strength_factor * XX_corr[center]):
voiced_unvoiced[window] = 1
period[window] = start + index - 1
else:
voiced_unvoiced[window] = 0
period[window] = 0
return np.array(voiced_unvoiced), np.array(period)
def lpc_analysis(X, order=8, window_step=128, window_size=2 * 128,
emphasis=0.9, voiced_start_threshold=.9,
voiced_stop_threshold=.6, truncate=False, copy=True):
"""
Extract LPC coefficients from a signal
Based on code from:
http://labrosa.ee.columbia.edu/matlab/sws/
Parameters
----------
X : ndarray
Signals to extract LPC coefficients from
order : int, optional (default=8)
Order of the LPC coefficients. For speech, use the general rule that the
order is two times the expected number of formants plus 2.
This can be formulated as 2 + 2 * (fs // 2000). For approximately signals
with fs = 7000, this is 8 coefficients - 2 + 2 * (7000 // 2000).
window_step : int, optional (default=128)
The size (in samples) of the space between each window
window_size : int, optional (default=2 * 128)
The size of each window (in samples) to extract coefficients over
emphasis : float, optional (default=0.9)
The emphasis coefficient to use for filtering
voiced_start_threshold : float, optional (default=0.9)
Upper power threshold for estimating when speech has started
voiced_stop_threshold : float, optional (default=0.6)
Lower power threshold for estimating when speech has stopped
truncate : bool, optional (default=False)
Whether to cut the data at the last window or do zero padding.
copy : bool, optional (default=True)
Whether to copy the input X or modify in place
Returns
-------
lp_coefficients : ndarray
lp coefficients to describe the frame
per_frame_gain : ndarray
calculated gain for each frame
residual_excitation : ndarray
leftover energy which is not described by lp coefficents and gain
voiced_frames : ndarray
array of [0, 1] values which holds voiced/unvoiced decision for each
frame.
References
----------
<NAME> (2004), "Sinewave Speech Analysis/Synthesis in Matlab",
Web resource, available: http://www.ee.columbia.edu/ln/labrosa/matlab/sws/
"""
X = np.array(X, copy=copy)
if len(X.shape) < 2:
X = X[None]
n_points = X.shape[1]
n_windows = n_points // window_step
if not truncate:
pad_sizes = [(window_size - window_step) // 2,
window_size - window_step // 2]
# TODO: Handling for odd window sizes / steps
X = np.hstack((np.zeros((X.shape[0], pad_sizes[0])), X,
np.zeros((X.shape[0], pad_sizes[1]))))
else:
pad_sizes = [0, 0]
X = X[0, :n_windows * window_step]
lp_coefficients = np.zeros((n_windows, order + 1))
per_frame_gain = np.zeros((n_windows, 1))
residual_excitation = np.zeros(
((n_windows - 1) * window_step + window_size))
# Pre-emphasis high-pass filter
X = sg.lfilter([1, -emphasis], 1, X)
# stride_tricks.as_strided?
autocorr_X = np.zeros((n_windows, 2 * window_size - 1))
for window in range(max(n_windows - 1, 1)):
XX = X.ravel()[window * window_step + np.arange(window_size)]
WXX = XX * sg.hanning(window_size)
autocorr_X[window] = np.correlate(WXX, WXX, mode='full')
center = np.argmax(autocorr_X[window])
RXX = autocorr_X[window,
np.arange(center, window_size + order)]
R = linalg.toeplitz(RXX[:-1])
solved_R = linalg.pinv(R).dot(RXX[1:])
filter_coefs = np.hstack((1, -solved_R))
residual_signal = sg.lfilter(filter_coefs, 1, WXX)
gain = np.sqrt(np.mean(residual_signal ** 2))
lp_coefficients[window] = filter_coefs
per_frame_gain[window] = gain
assign_range = window * window_step + np.arange(window_size)
residual_excitation[assign_range] += residual_signal / gain
# Throw away first part in overlap mode for proper synthesis
residual_excitation = residual_excitation[pad_sizes[0]:]
return lp_coefficients, per_frame_gain, residual_excitation
def lpc_synthesis(lp_coefficients, per_frame_gain, residual_excitation=None,
voiced_frames=None, window_step=128, emphasis=0.9):
"""
Synthesize a signal from LPC coefficients
Based on code from:
http://labrosa.ee.columbia.edu/matlab/sws/
http://web.uvic.ca/~tyoon/resource/auditorytoolbox/auditorytoolbox/synlpc.html
Parameters
----------
lp_coefficients : ndarray
Linear prediction coefficients
per_frame_gain : ndarray
Gain coefficients
residual_excitation : ndarray or None, optional (default=None)
Residual excitations. If None, this will be synthesized with white noise.
voiced_frames : ndarray or None, optional (default=None)
Voiced frames. If None, all frames assumed to be voiced.
window_step : int, optional (default=128)
The size (in samples) of the space between each window
emphasis : float, optional (default=0.9)
The emphasis coefficient to use for filtering
overlap_add : bool, optional (default=True)
What type of processing to use when joining windows
copy : bool, optional (default=True)
Whether to copy the input X or modify in place
Returns
-------
synthesized : ndarray
Sound vector synthesized from input arguments
References
----------
<NAME> (2004), "Sinewave Speech Analysis/Synthesis in Matlab",
Web resource, available: http://www.ee.columbia.edu/ln/labrosa/matlab/sws/
"""
# TODO: Incorporate better synthesis from
# http://eecs.oregonstate.edu/education/docs/ece352/CompleteManual.pdf
window_size = 2 * window_step
[n_windows, order] = lp_coefficients.shape
n_points = (n_windows + 1) * window_step
n_excitation_points = n_points + window_step + window_step // 2
random_state = np.random.RandomState(1999)
if residual_excitation is None:
# Need to generate excitation
if voiced_frames is None:
# No voiced/unvoiced info, so just use randn
voiced_frames = np.ones((lp_coefficients.shape[0], 1))
residual_excitation = np.zeros((n_excitation_points))
f, m = lpc_to_frequency(lp_coefficients, per_frame_gain)
t = np.linspace(0, 1, window_size, endpoint=False)
hanning = sg.hanning(window_size)
for window in range(n_windows):
window_base = window * window_step
index = window_base + np.arange(window_size)
if voiced_frames[window]:
sig = np.zeros_like(t)
cycles = np.cumsum(f[window][0] * t)
sig += sg.sawtooth(cycles, 0.001)
residual_excitation[index] += hanning * sig
residual_excitation[index] += hanning * 0.01 * random_state.randn(
window_size)
else:
n_excitation_points = residual_excitation.shape[0]
n_points = n_excitation_points + window_step + window_step // 2
residual_excitation = np.hstack((residual_excitation,
np.zeros(window_size)))
if voiced_frames is None:
voiced_frames = np.ones_like(per_frame_gain)
synthesized = np.zeros((n_points))
for window in range(n_windows):
window_base = window * window_step
oldbit = synthesized[window_base + np.arange(window_step)]
w_coefs = lp_coefficients[window]
if not np.all(w_coefs):
# Hack to make lfilter avoid
# ValueError: BUG: filter coefficient a[0] == 0 not supported yet
# when all coeffs are 0
w_coefs = [1]
g_coefs = voiced_frames[window] * per_frame_gain[window]
index = window_base + np.arange(window_size)
newbit = g_coefs * sg.lfilter([1], w_coefs,
residual_excitation[index])
synthesized[index] = np.hstack((oldbit, np.zeros(
(window_size - window_step))))
synthesized[index] += sg.hanning(window_size) * newbit
synthesized = sg.lfilter([1], [1, -emphasis], synthesized)
return synthesized
def soundsc(X, copy=True):
"""
Approximate implementation of soundsc from MATLAB without the audio playing.
Parameters
----------
X : ndarray
Signal to be rescaled
copy : bool, optional (default=True)
Whether to make a copy of input signal or operate in place.
Returns
-------
X_sc : ndarray
(-1, 1) scaled version of X as float32, suitable for writing
with scipy.io.wavfile
"""
X = np.array(X, copy=copy)
X = (X - X.min()) / (X.max() - X.min())
X = 2 * X - 1
return X.astype('float32')
def lpc_to_frequency(lp_coefficients, per_frame_gain):
"""
Extract resonant frequencies and magnitudes from LPC coefficients and gains.
Parameters
----------
lp_coefficients : ndarray
LPC coefficients, such as those calculated by ``lpc_analysis``
per_frame_gain : ndarray
Gain calculated for each frame, such as those calculated
by ``lpc_analysis``
Returns
-------
frequencies : ndarray
Resonant frequencies calculated from LPC coefficients and gain. Returned
frequencies are from 0 to 2 * pi
magnitudes : ndarray
Magnitudes of resonant frequencies
References
----------
<NAME> (2004), "Sinewave Speech Analysis/Synthesis in Matlab",
Web resource, available: http://www.ee.columbia.edu/ln/labrosa/matlab/sws/
"""
n_windows, order = lp_coefficients.shape
frame_frequencies = np.zeros((n_windows, (order - 1) // 2))
frame_magnitudes = np.zeros_like(frame_frequencies)
for window in range(n_windows):
w_coefs = lp_coefficients[window]
g_coefs = per_frame_gain[window]
roots = np.roots(np.hstack(([1], w_coefs[1:])))
# Roots doesn't return the same thing as MATLAB... agh
frequencies, index = np.unique(
np.abs(np.angle(roots)), return_index=True)
# Make sure 0 doesn't show up...
gtz = np.where(frequencies > 0)[0]
frequencies = frequencies[gtz]
index = index[gtz]
magnitudes = g_coefs / (1. - np.abs(roots))
sort_index = np.argsort(frequencies)
frame_frequencies[window, :len(sort_index)] = frequencies[sort_index]
frame_magnitudes[window, :len(sort_index)] = magnitudes[sort_index]
return frame_frequencies, frame_magnitudes
def sinusoid_analysis(X, input_sample_rate, resample_block=128, copy=True):
"""
Contruct a sinusoidal model for the input signal.
Parameters
----------
X : ndarray
Input signal to model
input_sample_rate : int
The sample rate of the input signal
resample_block : int, optional (default=128)
Controls the step size of the sinusoidal model
Returns
-------
frequencies_hz : ndarray
Frequencies for the sinusoids, in Hz.
magnitudes : ndarray
Magnitudes of sinusoids returned in ``frequencies``
References
----------
<NAME> (2004), "Sinewave Speech Analysis/Synthesis in Matlab",
Web resource, available: http://www.ee.columbia.edu/ln/labrosa/matlab/sws/
"""
X = np.array(X, copy=copy)
resample_to = 8000
if input_sample_rate != resample_to:
if input_sample_rate % resample_to != 0:
raise ValueError("Input sample rate must be a multiple of 8k!")
# Should be able to use resample... ?
# resampled_count = round(len(X) * resample_to / input_sample_rate)
# X = sg.resample(X, resampled_count, window=sg.hanning(len(X)))
X = sg.decimate(X, input_sample_rate // resample_to)
step_size = 2 * round(resample_block / input_sample_rate * resample_to / 2.)
a, g, e = lpc_analysis(X, order=8, window_step=step_size,
window_size=2 * step_size)
f, m = lpc_to_frequency(a, g)
f_hz = f * resample_to / (2 * np.pi)
return f_hz, m
def slinterp(X, factor, copy=True):
"""
Slow-ish linear interpolation of a 1D numpy array. There must be some
better function to do this in numpy.
Parameters
----------
X : ndarray
1D input array to interpolate
factor : int
Integer factor to interpolate by
Return
------
X_r : ndarray
"""
sz = np.product(X.shape)
X = np.array(X, copy=copy)
X_s = np.hstack((X[1:], [0]))
X_r = np.zeros((factor, sz))
for i in range(factor):
X_r[i, :] = (factor - i) / float(factor) * X + (i / float(factor)) * X_s
return X_r.T.ravel()[:(sz - 1) * factor + 1]
def sinusoid_synthesis(frequencies_hz, magnitudes, input_sample_rate=16000,
resample_block=128):
"""
Create a time series based on input frequencies and magnitudes.
Parameters
----------
frequencies_hz : ndarray
Input signal to model
magnitudes : int
The sample rate of the input signal
input_sample_rate : int, optional (default=16000)
The sample rate parameter that the sinusoid analysis was run with
resample_block : int, optional (default=128)
Controls the step size of the sinusoidal model
Returns
-------
synthesized : ndarray
Sound vector synthesized from input arguments
References
----------
<NAME> (2004), "Sinewave Speech Analysis/Synthesis in Matlab",
Web resource, available: http://www.ee.columbia.edu/ln/labrosa/matlab/sws/
"""
rows, cols = frequencies_hz.shape
synthesized = np.zeros((1 + ((rows - 1) * resample_block),))
for col in range(cols):
mags = slinterp(magnitudes[:, col], resample_block)
freqs = slinterp(frequencies_hz[:, col], resample_block)
cycles = np.cumsum(2 * np.pi * freqs / float(input_sample_rate))
sines = mags * np.cos(cycles)
synthesized += sines
return synthesized
def compress(X, n_components, window_size=128):
"""
Compress using the DCT
Parameters
----------
X : ndarray, shape=(n_samples,)
The input signal to compress. Should be 1-dimensional
n_components : int
The number of DCT components to keep. Setting n_components to about
.5 * window_size can give compression with fairly good reconstruction.
window_size : int
The input X is broken into windows of window_size, each of which are
then compressed with the DCT.
Returns
-------
X_compressed : ndarray, shape=(num_windows, window_size)
A 2D array of non-overlapping DCT coefficients. For use with uncompress
Reference
---------
http://nbviewer.ipython.org/github/craffel/crucialpython/blob/master/week3/stride_tricks.ipynb
"""
if len(X) % window_size != 0:
append = np.zeros((window_size - len(X) % window_size))
X = np.hstack((X, append))
num_frames = len(X) // window_size
X_strided = X.reshape((num_frames, window_size))
X_dct = fftpack.dct(X_strided, norm='ortho')
if n_components is not None:
X_dct = X_dct[:, :n_components]
return X_dct
def uncompress(X_compressed, window_size=128):
"""
Uncompress a DCT compressed signal (such as returned by ``compress``).
Parameters
----------
X_compressed : ndarray, shape=(n_samples, n_features)
Windowed and compressed array.
window_size : int, optional (default=128)
Size of the window used when ``compress`` was called.
Returns
-------
X_reconstructed : ndarray, shape=(n_samples)
Reconstructed version of X.
"""
if X_compressed.shape[1] % window_size != 0:
append = np.zeros((X_compressed.shape[0], window_size - X_compressed.shape[1] % window_size))
X_compressed = np.hstack((X_compressed, append))
X_r = fftpack.idct(X_compressed, norm='ortho')
return X_r.ravel()
def apply_kaiserbessel_window(X, alpha=6.5):
"""
Apply a Kaiser-Bessel window to X.
Parameters
----------
X : ndarray, shape=(n_samples, n_features)
Input array of samples
alpha : float, optional (default=6.5)
Tuning parameter for Kaiser-Bessel function. alpha=6.5 should make
perfect reconstruction possible for MDCT.
Returns
-------
X_windowed : ndarray, shape=(n_samples, n_features)
Windowed version of X.
"""
beta = np.pi * alpha
win = sg.kaiser(X.shape[1], beta)
row_stride = 0
col_stride = win.itemsize
strided_win = as_strided(win, shape=X.shape,
strides=(row_stride, col_stride))
return X * strided_win
def halfoverlap(X, window_size):
"""
Create an overlapped version of X using 50% of window_size as overlap.
Parameters
----------
X : ndarray, shape=(n_samples,)
Input signal to window and overlap
window_size : int
Size of windows to take
Returns
-------
X_strided : shape=(n_windows, window_size)
2D array of overlapped X
"""
if window_size % 2 != 0:
raise ValueError("Window size must be even!")
window_step = window_size // 2
# Make sure there are an even number of windows before stridetricks
append = np.zeros((window_size - len(X) % window_size))
X = np.hstack((X, append))
num_frames = len(X) // window_step - 1
row_stride = X.itemsize * window_step
col_stride = X.itemsize
X_strided = as_strided(X, shape=(num_frames, window_size),
strides=(row_stride, col_stride))
return X_strided
def stft(X, fftsize=128, mean_normalize=True, compute_onesided=True):
"""
Compute STFT for 1D input X
"""
if compute_onesided:
local_fft = np.fft.rfft
fftsize = 2 * fftsize
cut = -1
else:
local_fft = np.fft.fft
cut = None
if mean_normalize:
X -= X.mean()
X = halfoverlap(X, fftsize)
X = X * np.hanning(X.shape[-1])[None]
X = local_fft(X)[:, :cut]
return X
def invert_halfoverlap(X_strided):
"""
Invert ``halfoverlap`` function to reconstruct X
Parameters
----------
X_strided : ndarray, shape=(n_windows, window_size)
X as overlapped windows
Returns
-------
X : ndarray, shape=(n_samples,)
Reconstructed version of X
"""
# Hardcoded 50% overlap! Can generalize later...
n_rows, n_cols = X_strided.shape
X = np.zeros((((int(n_rows // 2) + 1) * n_cols),))
start_index = 0
end_index = n_cols
window_step = n_cols // 2
for row in range(X_strided.shape[0]):
X[start_index:end_index] += X_strided[row]
start_index += window_step
end_index += window_step
return X
def overlap_compress(X, n_components, window_size):
"""
Overlap (at 50% of window_size) and compress X.
Parameters
----------
X : ndarray, shape=(n_samples,)
Input signal to compress
n_components : int
number of DCT components to keep
window_size : int
Size of windows to take
Returns
-------
X_dct : ndarray, shape=(n_windows, n_components)
Windowed and compressed version of X
"""
X_strided = halfoverlap(X, window_size)
X_dct = fftpack.dct(X_strided, norm='ortho')
if n_components is not None:
X_dct = X_dct[:, :n_components]
return X_dct
# Evil voice is caused by adding double the zeros before inverse DCT...
# Very cool bug but makes sense
def overlap_uncompress(X_compressed, window_size):
"""
Uncompress X as returned from ``overlap_compress``.
Parameters
----------
X_compressed : ndarray, shape=(n_windows, n_components)
Windowed and compressed version of X
window_size : int
Size of windows originally used when compressing X
Returns
-------
X_reconstructed : ndarray, shape=(n_samples,)
Reconstructed version of X
"""
if X_compressed.shape[1] % window_size != 0:
append = np.zeros((X_compressed.shape[0], window_size -
X_compressed.shape[1] % window_size))
X_compressed = np.hstack((X_compressed, append))
X_r = fftpack.idct(X_compressed, norm='ortho')
return invert_halfoverlap(X_r)
def lpc_to_lsf(all_lpc):
if len(all_lpc.shape) < 2:
all_lpc = all_lpc[None]
order = all_lpc.shape[1] - 1
all_lsf = np.zeros((len(all_lpc), order))
for i in range(len(all_lpc)):
lpc = all_lpc[i]
lpc1 = np.append(lpc, 0)
lpc2 = lpc1[::-1]
sum_filt = lpc1 + lpc2
diff_filt = lpc1 - lpc2
if order % 2 != 0:
deconv_diff, _ = sg.deconvolve(diff_filt, [1, 0, -1])
deconv_sum = sum_filt
else:
deconv_diff, _ = sg.deconvolve(diff_filt, [1, -1])
deconv_sum, _ = sg.deconvolve(sum_filt, [1, 1])
roots_diff = np.roots(deconv_diff)
roots_sum = np.roots(deconv_sum)
angle_diff = np.angle(roots_diff[::2])
angle_sum = np.angle(roots_sum[::2])
lsf = np.sort(np.hstack((angle_diff, angle_sum)))
if len(lsf) != 0:
all_lsf[i] = lsf
return np.squeeze(all_lsf)
def lsf_to_lpc(all_lsf):
if len(all_lsf.shape) < 2:
all_lsf = all_lsf[None]
order = all_lsf.shape[1]
all_lpc = np.zeros((len(all_lsf), order + 1))
for i in range(len(all_lsf)):
lsf = all_lsf[i]
zeros = np.exp(1j * lsf)
sum_zeros = zeros[::2]
diff_zeros = zeros[1::2]
sum_zeros = np.hstack((sum_zeros, np.conj(sum_zeros)))
diff_zeros = np.hstack((diff_zeros, np.conj(diff_zeros)))
sum_filt = np.poly(sum_zeros)
diff_filt = np.poly(diff_zeros)
if order % 2 != 0:
deconv_diff = sg.convolve(diff_filt, [1, 0, -1])
deconv_sum = sum_filt
else:
deconv_diff = sg.convolve(diff_filt, [1, -1])
deconv_sum = sg.convolve(sum_filt, [1, 1])
lpc = .5 * (deconv_sum + deconv_diff)
# Last coefficient is 0 and not returned
all_lpc[i] = lpc[:-1]
return np.squeeze(all_lpc)
def test_lpc_to_lsf():
# Matlab style vectors for testing
# lsf = [0.7842 1.5605 1.8776 1.8984 2.3593]
# a = [1.0000 0.6149 0.9899 0.0000 0.0031 -0.0082];
lsf = [[0.7842, 1.5605, 1.8776, 1.8984, 2.3593],
[0.7842, 1.5605, 1.8776, 1.8984, 2.3593]]
a = [[1.0000, 0.6149, 0.9899, 0.0000, 0.0031, -0.0082],
[1.0000, 0.6149, 0.9899, 0.0000, 0.0031, -0.0082]]
a = np.array(a)
lsf = np.array(lsf)
lsf_r = lpc_to_lsf(a)
| assert_almost_equal(lsf, lsf_r, decimal=4) | numpy.testing.assert_almost_equal |
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
TensorFlow Lite YOLOX with OpenCV.
Copyright (c) 2021 <NAME>
This software is released under the MIT License.
See the LICENSE file in the project root for more information.
"""
import argparse
import os
import random
import time
import cv2
import numpy as np
from utils import visualization as visual
from utils.label_util import read_label_file
from utils.tflite_util import (get_output_tensor, make_interpreter,
set_input_tensor)
from yolox.utils.demo_utils import multiclass_nms, demo_postprocess
COCO_CLASSES = (
"person",
"bicycle",
"car",
"motorcycle",
"airplane",
"bus",
"train",
"truck",
"boat",
"traffic light",
"fire hydrant",
"stop sign",
"parking meter",
"bench",
"bird",
"cat",
"dog",
"horse",
"sheep",
"cow",
"elephant",
"bear",
"zebra",
"giraffe",
"backpack",
"umbrella",
"handbag",
"tie",
"suitcase",
"frisbee",
"skis",
"snowboard",
"sports ball",
"kite",
"baseball bat",
"baseball glove",
"skateboard",
"surfboard",
"tennis racket",
"bottle",
"wine glass",
"cup",
"fork",
"knife",
"spoon",
"bowl",
"banana",
"apple",
"sandwich",
"orange",
"broccoli",
"carrot",
"hot dog",
"pizza",
"donut",
"cake",
"chair",
"couch",
"potted plant",
"bed",
"dining table",
"toilet",
"tv",
"laptop",
"mouse",
"remote",
"keyboard",
"cell phone",
"microwave",
"oven",
"toaster",
"sink",
"refrigerator",
"book",
"clock",
"vase",
"scissors",
"teddy bear",
"hair drier",
"toothbrush",
)
mean = (0.485, 0.456, 0.406)
std = (0.229, 0.224, 0.225)
# def preprocess(image, input_size, mean, std, swap=(2, 0, 1)):
def preprocess(image, input_size, mean, std):
# https://github.com/Megvii-BaseDetection/YOLOX/blob/c4714bb97c2f13d26195544d5f9e1ea91241ee2b/yolox/data/data_augment.py#L165 noqa: E501
if len(image.shape) == 3:
padded_img = np.ones((input_size[0], input_size[1], 3)) * 114.0
else:
padded_img = np.ones(input_size) * 114.0
img = np.array(image)
r = min(input_size[0] / img.shape[0], input_size[1] / img.shape[1])
resized_img = cv2.resize(
img,
(int(img.shape[1] * r), int(img.shape[0] * r)),
interpolation=cv2.INTER_LINEAR
).astype(np.float32)
padded_img[: int(img.shape[0] * r), : int(img.shape[1] * r)] = resized_img
image = padded_img
image = image.astype(np.float32)
image = image[:, :, ::-1]
image /= 255.0
if mean is not None:
image -= mean
if std is not None:
image /= std
# image = image.transpose((2, 0, 1))
image = | np.ascontiguousarray(image, dtype=np.float32) | numpy.ascontiguousarray |
import math
import h5py
import numpy as np
import torch
import torch.utils.data
from torch.utils.data.dataloader import default_collate
from ncls import NCLS64
from bisect import bisect_right
from numpy.lib.stride_tricks import as_strided
from scipy.fftpack import fft, fftshift # Fourier features
from scipy.signal import stft # Short-time Fourier Transform
class MusicNetHDF5(torch.utils.data.Dataset):
"""Dataset access to MusicNet stored in HDF5 file.
Parameters
----------
hdf5 : h5py.File
Open HDF5 file handle.
window : int, or tuple
The size of the window. If tuple, then specifies the number of samples
before `t` and after.
stride : int, default=1
The stride of the sliding window.
at : int, or None, default=None
The index within the `window` at which the targets are collected.
Should be thought of as the offset to time `t` in the window. Midpoint
of the window by default (None).
dtype : np.dtype, default=np.float32
The data type of the waveform windows and targets. Defaults to float32
for easier compatibility with torch.
resident : bool, default=False
Whether to cache the raw waveform data into ram on init.
"""
def __init__(self, hdf5, window=4096, stride=512, at=None,
dtype=np.float32, resident=False):
# ensure an open HDF5 handle
assert isinstance(hdf5, h5py.File) and hdf5.id
# assumes note_ids 21..105, i.e. 84 class labels
self.n_outputs, base_note_id = 84, 21
self.probability = np.zeros((len(hdf5), self.n_outputs))
# build object and label lookup
indptr, references = [0], []
for ix, (key, group) in enumerate(hdf5.items()):
obj, label = group["data"], group["labels"]
# construct a fast lookup of music notes: a Nested
# Containment List is much faster than Interval Tree.
note_id = label["note_id"] - base_note_id
start_time, end_time = label["start_time"], label["end_time"]
tree = NCLS64(np.int64(start_time), | np.int64(end_time) | numpy.int64 |
# This module has been generated automatically from space group information
# obtained from the Computational Crystallography Toolbox
#
"""
Space groups
This module contains a list of all the 230 space groups that can occur in
a crystal. The variable space_groups contains a dictionary that maps
space group numbers and space group names to the corresponding space
group objects.
.. moduleauthor:: <NAME> <<EMAIL>>
"""
#-----------------------------------------------------------------------------
# Copyright (C) 2013 The Mosaic Development Team
#
# Distributed under the terms of the BSD License. The full license is in
# the file LICENSE.txt, distributed as part of this software.
#-----------------------------------------------------------------------------
import numpy as N
class SpaceGroup(object):
"""
Space group
All possible space group objects are created in this module. Other
modules should access these objects through the dictionary
space_groups rather than create their own space group objects.
"""
def __init__(self, number, symbol, transformations):
"""
:param number: the number assigned to the space group by
international convention
:type number: int
:param symbol: the Hermann-Mauguin space-group symbol as used
in PDB and mmCIF files
:type symbol: str
:param transformations: a list of space group transformations,
each consisting of a tuple of three
integer arrays (rot, tn, td), where
rot is the rotation matrix and tn/td
are the numerator and denominator of the
translation vector. The transformations
are defined in fractional coordinates.
:type transformations: list
"""
self.number = number
self.symbol = symbol
self.transformations = transformations
self.transposed_rotations = N.array([N.transpose(t[0])
for t in transformations])
self.phase_factors = N.exp(N.array([(-2j*N.pi*t[1])/t[2]
for t in transformations]))
def __repr__(self):
return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol))
def __len__(self):
"""
:return: the number of space group transformations
:rtype: int
"""
return len(self.transformations)
def symmetryEquivalentMillerIndices(self, hkl):
"""
:param hkl: a set of Miller indices
:type hkl: Scientific.N.array_type
:return: a tuple (miller_indices, phase_factor) of two arrays
of length equal to the number of space group
transformations. miller_indices contains the Miller
indices of each reflection equivalent by symmetry to the
reflection hkl (including hkl itself as the first element).
phase_factor contains the phase factors that must be applied
to the structure factor of reflection hkl to obtain the
structure factor of the symmetry equivalent reflection.
:rtype: tuple
"""
hkls = N.dot(self.transposed_rotations, hkl)
p = N.multiply.reduce(self.phase_factors**hkl, -1)
return hkls, p
space_groups = {}
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(1, 'P 1', transformations)
space_groups[1] = sg
space_groups['P 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(2, 'P -1', transformations)
space_groups[2] = sg
space_groups['P -1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(3, 'P 1 2 1', transformations)
space_groups[3] = sg
space_groups['P 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(4, 'P 1 21 1', transformations)
space_groups[4] = sg
space_groups['P 1 21 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(5, 'C 1 2 1', transformations)
space_groups[5] = sg
space_groups['C 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(6, 'P 1 m 1', transformations)
space_groups[6] = sg
space_groups['P 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(7, 'P 1 c 1', transformations)
space_groups[7] = sg
space_groups['P 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(8, 'C 1 m 1', transformations)
space_groups[8] = sg
space_groups['C 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(9, 'C 1 c 1', transformations)
space_groups[9] = sg
space_groups['C 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(10, 'P 1 2/m 1', transformations)
space_groups[10] = sg
space_groups['P 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(11, 'P 1 21/m 1', transformations)
space_groups[11] = sg
space_groups['P 1 21/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(12, 'C 1 2/m 1', transformations)
space_groups[12] = sg
space_groups['C 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(13, 'P 1 2/c 1', transformations)
space_groups[13] = sg
space_groups['P 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(14, 'P 1 21/c 1', transformations)
space_groups[14] = sg
space_groups['P 1 21/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(15, 'C 1 2/c 1', transformations)
space_groups[15] = sg
space_groups['C 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(16, 'P 2 2 2', transformations)
space_groups[16] = sg
space_groups['P 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(17, 'P 2 2 21', transformations)
space_groups[17] = sg
space_groups['P 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(18, 'P 21 21 2', transformations)
space_groups[18] = sg
space_groups['P 21 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(19, 'P 21 21 21', transformations)
space_groups[19] = sg
space_groups['P 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(20, 'C 2 2 21', transformations)
space_groups[20] = sg
space_groups['C 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(21, 'C 2 2 2', transformations)
space_groups[21] = sg
space_groups['C 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(22, 'F 2 2 2', transformations)
space_groups[22] = sg
space_groups['F 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(23, 'I 2 2 2', transformations)
space_groups[23] = sg
space_groups['I 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(24, 'I 21 21 21', transformations)
space_groups[24] = sg
space_groups['I 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(25, 'P m m 2', transformations)
space_groups[25] = sg
space_groups['P m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(26, 'P m c 21', transformations)
space_groups[26] = sg
space_groups['P m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(27, 'P c c 2', transformations)
space_groups[27] = sg
space_groups['P c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(28, 'P m a 2', transformations)
space_groups[28] = sg
space_groups['P m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(29, 'P c a 21', transformations)
space_groups[29] = sg
space_groups['P c a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(30, 'P n c 2', transformations)
space_groups[30] = sg
space_groups['P n c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(31, 'P m n 21', transformations)
space_groups[31] = sg
space_groups['P m n 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(32, 'P b a 2', transformations)
space_groups[32] = sg
space_groups['P b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(33, 'P n a 21', transformations)
space_groups[33] = sg
space_groups['P n a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(34, 'P n n 2', transformations)
space_groups[34] = sg
space_groups['P n n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(35, 'C m m 2', transformations)
space_groups[35] = sg
space_groups['C m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(36, 'C m c 21', transformations)
space_groups[36] = sg
space_groups['C m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(37, 'C c c 2', transformations)
space_groups[37] = sg
space_groups['C c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(38, 'A m m 2', transformations)
space_groups[38] = sg
space_groups['A m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(39, 'A b m 2', transformations)
space_groups[39] = sg
space_groups['A b m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(40, 'A m a 2', transformations)
space_groups[40] = sg
space_groups['A m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(41, 'A b a 2', transformations)
space_groups[41] = sg
space_groups['A b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(42, 'F m m 2', transformations)
space_groups[42] = sg
space_groups['F m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(43, 'F d d 2', transformations)
space_groups[43] = sg
space_groups['F d d 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(44, 'I m m 2', transformations)
space_groups[44] = sg
space_groups['I m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(45, 'I b a 2', transformations)
space_groups[45] = sg
space_groups['I b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(46, 'I m a 2', transformations)
space_groups[46] = sg
space_groups['I m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(47, 'P m m m', transformations)
space_groups[47] = sg
space_groups['P m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(48, 'P n n n :2', transformations)
space_groups[48] = sg
space_groups['P n n n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(49, 'P c c m', transformations)
space_groups[49] = sg
space_groups['P c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(50, 'P b a n :2', transformations)
space_groups[50] = sg
space_groups['P b a n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(51, 'P m m a', transformations)
space_groups[51] = sg
space_groups['P m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(52, 'P n n a', transformations)
space_groups[52] = sg
space_groups['P n n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(53, 'P m n a', transformations)
space_groups[53] = sg
space_groups['P m n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(54, 'P c c a', transformations)
space_groups[54] = sg
space_groups['P c c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(55, 'P b a m', transformations)
space_groups[55] = sg
space_groups['P b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(56, 'P c c n', transformations)
space_groups[56] = sg
space_groups['P c c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(57, 'P b c m', transformations)
space_groups[57] = sg
space_groups['P b c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(58, 'P n n m', transformations)
space_groups[58] = sg
space_groups['P n n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(59, 'P m m n :2', transformations)
space_groups[59] = sg
space_groups['P m m n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(60, 'P b c n', transformations)
space_groups[60] = sg
space_groups['P b c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(61, 'P b c a', transformations)
space_groups[61] = sg
space_groups['P b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(62, 'P n m a', transformations)
space_groups[62] = sg
space_groups['P n m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(63, 'C m c m', transformations)
space_groups[63] = sg
space_groups['C m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(64, 'C m c a', transformations)
space_groups[64] = sg
space_groups['C m c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(65, 'C m m m', transformations)
space_groups[65] = sg
space_groups['C m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(66, 'C c c m', transformations)
space_groups[66] = sg
space_groups['C c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(67, 'C m m a', transformations)
space_groups[67] = sg
space_groups['C m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(68, 'C c c a :2', transformations)
space_groups[68] = sg
space_groups['C c c a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(69, 'F m m m', transformations)
space_groups[69] = sg
space_groups['F m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(70, 'F d d d :2', transformations)
space_groups[70] = sg
space_groups['F d d d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(71, 'I m m m', transformations)
space_groups[71] = sg
space_groups['I m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(72, 'I b a m', transformations)
space_groups[72] = sg
space_groups['I b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(73, 'I b c a', transformations)
space_groups[73] = sg
space_groups['I b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(74, 'I m m a', transformations)
space_groups[74] = sg
space_groups['I m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(75, 'P 4', transformations)
space_groups[75] = sg
space_groups['P 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(76, 'P 41', transformations)
space_groups[76] = sg
space_groups['P 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(77, 'P 42', transformations)
space_groups[77] = sg
space_groups['P 42'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(78, 'P 43', transformations)
space_groups[78] = sg
space_groups['P 43'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(79, 'I 4', transformations)
space_groups[79] = sg
space_groups['I 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(80, 'I 41', transformations)
space_groups[80] = sg
space_groups['I 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(81, 'P -4', transformations)
space_groups[81] = sg
space_groups['P -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(82, 'I -4', transformations)
space_groups[82] = sg
space_groups['I -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(83, 'P 4/m', transformations)
space_groups[83] = sg
space_groups['P 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(84, 'P 42/m', transformations)
space_groups[84] = sg
space_groups['P 42/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(85, 'P 4/n :2', transformations)
space_groups[85] = sg
space_groups['P 4/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(86, 'P 42/n :2', transformations)
space_groups[86] = sg
space_groups['P 42/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(87, 'I 4/m', transformations)
space_groups[87] = sg
space_groups['I 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(88, 'I 41/a :2', transformations)
space_groups[88] = sg
space_groups['I 41/a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(89, 'P 4 2 2', transformations)
space_groups[89] = sg
space_groups['P 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(90, 'P 4 21 2', transformations)
space_groups[90] = sg
space_groups['P 4 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(91, 'P 41 2 2', transformations)
space_groups[91] = sg
space_groups['P 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(92, 'P 41 21 2', transformations)
space_groups[92] = sg
space_groups['P 41 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(93, 'P 42 2 2', transformations)
space_groups[93] = sg
space_groups['P 42 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(94, 'P 42 21 2', transformations)
space_groups[94] = sg
space_groups['P 42 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(95, 'P 43 2 2', transformations)
space_groups[95] = sg
space_groups['P 43 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(96, 'P 43 21 2', transformations)
space_groups[96] = sg
space_groups['P 43 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(97, 'I 4 2 2', transformations)
space_groups[97] = sg
space_groups['I 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(98, 'I 41 2 2', transformations)
space_groups[98] = sg
space_groups['I 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(99, 'P 4 m m', transformations)
space_groups[99] = sg
space_groups['P 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(100, 'P 4 b m', transformations)
space_groups[100] = sg
space_groups['P 4 b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(101, 'P 42 c m', transformations)
space_groups[101] = sg
space_groups['P 42 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(102, 'P 42 n m', transformations)
space_groups[102] = sg
space_groups['P 42 n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(103, 'P 4 c c', transformations)
space_groups[103] = sg
space_groups['P 4 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(104, 'P 4 n c', transformations)
space_groups[104] = sg
space_groups['P 4 n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(105, 'P 42 m c', transformations)
space_groups[105] = sg
space_groups['P 42 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(106, 'P 42 b c', transformations)
space_groups[106] = sg
space_groups['P 42 b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(107, 'I 4 m m', transformations)
space_groups[107] = sg
space_groups['I 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(108, 'I 4 c m', transformations)
space_groups[108] = sg
space_groups['I 4 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(109, 'I 41 m d', transformations)
space_groups[109] = sg
space_groups['I 41 m d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(110, 'I 41 c d', transformations)
space_groups[110] = sg
space_groups['I 41 c d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(111, 'P -4 2 m', transformations)
space_groups[111] = sg
space_groups['P -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(112, 'P -4 2 c', transformations)
space_groups[112] = sg
space_groups['P -4 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(113, 'P -4 21 m', transformations)
space_groups[113] = sg
space_groups['P -4 21 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(114, 'P -4 21 c', transformations)
space_groups[114] = sg
space_groups['P -4 21 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(115, 'P -4 m 2', transformations)
space_groups[115] = sg
space_groups['P -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(116, 'P -4 c 2', transformations)
space_groups[116] = sg
space_groups['P -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(117, 'P -4 b 2', transformations)
space_groups[117] = sg
space_groups['P -4 b 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(118, 'P -4 n 2', transformations)
space_groups[118] = sg
space_groups['P -4 n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(119, 'I -4 m 2', transformations)
space_groups[119] = sg
space_groups['I -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(120, 'I -4 c 2', transformations)
space_groups[120] = sg
space_groups['I -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(121, 'I -4 2 m', transformations)
space_groups[121] = sg
space_groups['I -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(122, 'I -4 2 d', transformations)
space_groups[122] = sg
space_groups['I -4 2 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(123, 'P 4/m m m', transformations)
space_groups[123] = sg
space_groups['P 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(124, 'P 4/m c c', transformations)
space_groups[124] = sg
space_groups['P 4/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(125, 'P 4/n b m :2', transformations)
space_groups[125] = sg
space_groups['P 4/n b m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(126, 'P 4/n n c :2', transformations)
space_groups[126] = sg
space_groups['P 4/n n c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(127, 'P 4/m b m', transformations)
space_groups[127] = sg
space_groups['P 4/m b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(128, 'P 4/m n c', transformations)
space_groups[128] = sg
space_groups['P 4/m n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(129, 'P 4/n m m :2', transformations)
space_groups[129] = sg
space_groups['P 4/n m m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(130, 'P 4/n c c :2', transformations)
space_groups[130] = sg
space_groups['P 4/n c c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(131, 'P 42/m m c', transformations)
space_groups[131] = sg
space_groups['P 42/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(132, 'P 42/m c m', transformations)
space_groups[132] = sg
space_groups['P 42/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(133, 'P 42/n b c :2', transformations)
space_groups[133] = sg
space_groups['P 42/n b c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(134, 'P 42/n n m :2', transformations)
space_groups[134] = sg
space_groups['P 42/n n m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(135, 'P 42/m b c', transformations)
space_groups[135] = sg
space_groups['P 42/m b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(136, 'P 42/m n m', transformations)
space_groups[136] = sg
space_groups['P 42/m n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(137, 'P 42/n m c :2', transformations)
space_groups[137] = sg
space_groups['P 42/n m c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(138, 'P 42/n c m :2', transformations)
space_groups[138] = sg
space_groups['P 42/n c m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(139, 'I 4/m m m', transformations)
space_groups[139] = sg
space_groups['I 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(140, 'I 4/m c m', transformations)
space_groups[140] = sg
space_groups['I 4/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(141, 'I 41/a m d :2', transformations)
space_groups[141] = sg
space_groups['I 41/a m d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(142, 'I 41/a c d :2', transformations)
space_groups[142] = sg
space_groups['I 41/a c d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(143, 'P 3', transformations)
space_groups[143] = sg
space_groups['P 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(144, 'P 31', transformations)
space_groups[144] = sg
space_groups['P 31'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(145, 'P 32', transformations)
space_groups[145] = sg
space_groups['P 32'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(146, 'R 3 :H', transformations)
space_groups[146] = sg
space_groups['R 3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(147, 'P -3', transformations)
space_groups[147] = sg
space_groups['P -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(148, 'R -3 :H', transformations)
space_groups[148] = sg
space_groups['R -3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(149, 'P 3 1 2', transformations)
space_groups[149] = sg
space_groups['P 3 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(150, 'P 3 2 1', transformations)
space_groups[150] = sg
space_groups['P 3 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(151, 'P 31 1 2', transformations)
space_groups[151] = sg
space_groups['P 31 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(152, 'P 31 2 1', transformations)
space_groups[152] = sg
space_groups['P 31 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(153, 'P 32 1 2', transformations)
space_groups[153] = sg
space_groups['P 32 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(154, 'P 32 2 1', transformations)
space_groups[154] = sg
space_groups['P 32 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(155, 'R 3 2 :H', transformations)
space_groups[155] = sg
space_groups['R 3 2 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(156, 'P 3 m 1', transformations)
space_groups[156] = sg
space_groups['P 3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(157, 'P 3 1 m', transformations)
space_groups[157] = sg
space_groups['P 3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(158, 'P 3 c 1', transformations)
space_groups[158] = sg
space_groups['P 3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(159, 'P 3 1 c', transformations)
space_groups[159] = sg
space_groups['P 3 1 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(160, 'R 3 m :H', transformations)
space_groups[160] = sg
space_groups['R 3 m :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(161, 'R 3 c :H', transformations)
space_groups[161] = sg
space_groups['R 3 c :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(162, 'P -3 1 m', transformations)
space_groups[162] = sg
space_groups['P -3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(163, 'P -3 1 c', transformations)
space_groups[163] = sg
space_groups['P -3 1 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(164, 'P -3 m 1', transformations)
space_groups[164] = sg
space_groups['P -3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(165, 'P -3 c 1', transformations)
space_groups[165] = sg
space_groups['P -3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(166, 'R -3 m :H', transformations)
space_groups[166] = sg
space_groups['R -3 m :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(167, 'R -3 c :H', transformations)
space_groups[167] = sg
space_groups['R -3 c :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(168, 'P 6', transformations)
space_groups[168] = sg
space_groups['P 6'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(169, 'P 61', transformations)
space_groups[169] = sg
space_groups['P 61'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(170, 'P 65', transformations)
space_groups[170] = sg
space_groups['P 65'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(171, 'P 62', transformations)
space_groups[171] = sg
space_groups['P 62'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(172, 'P 64', transformations)
space_groups[172] = sg
space_groups['P 64'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(173, 'P 63', transformations)
space_groups[173] = sg
space_groups['P 63'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(174, 'P -6', transformations)
space_groups[174] = sg
space_groups['P -6'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(175, 'P 6/m', transformations)
space_groups[175] = sg
space_groups['P 6/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(176, 'P 63/m', transformations)
space_groups[176] = sg
space_groups['P 63/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(177, 'P 6 2 2', transformations)
space_groups[177] = sg
space_groups['P 6 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(178, 'P 61 2 2', transformations)
space_groups[178] = sg
space_groups['P 61 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(179, 'P 65 2 2', transformations)
space_groups[179] = sg
space_groups['P 65 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(180, 'P 62 2 2', transformations)
space_groups[180] = sg
space_groups['P 62 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(181, 'P 64 2 2', transformations)
space_groups[181] = sg
space_groups['P 64 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(182, 'P 63 2 2', transformations)
space_groups[182] = sg
space_groups['P 63 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(183, 'P 6 m m', transformations)
space_groups[183] = sg
space_groups['P 6 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(184, 'P 6 c c', transformations)
space_groups[184] = sg
space_groups['P 6 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(185, 'P 63 c m', transformations)
space_groups[185] = sg
space_groups['P 63 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(186, 'P 63 m c', transformations)
space_groups[186] = sg
space_groups['P 63 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(187, 'P -6 m 2', transformations)
space_groups[187] = sg
space_groups['P -6 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(188, 'P -6 c 2', transformations)
space_groups[188] = sg
space_groups['P -6 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(189, 'P -6 2 m', transformations)
space_groups[189] = sg
space_groups['P -6 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(190, 'P -6 2 c', transformations)
space_groups[190] = sg
space_groups['P -6 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(191, 'P 6/m m m', transformations)
space_groups[191] = sg
space_groups['P 6/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(192, 'P 6/m c c', transformations)
space_groups[192] = sg
space_groups['P 6/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(193, 'P 63/m c m', transformations)
space_groups[193] = sg
space_groups['P 63/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(194, 'P 63/m m c', transformations)
space_groups[194] = sg
space_groups['P 63/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(195, 'P 2 3', transformations)
space_groups[195] = sg
space_groups['P 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(196, 'F 2 3', transformations)
space_groups[196] = sg
space_groups['F 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(197, 'I 2 3', transformations)
space_groups[197] = sg
space_groups['I 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(198, 'P 21 3', transformations)
space_groups[198] = sg
space_groups['P 21 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(199, 'I 21 3', transformations)
space_groups[199] = sg
space_groups['I 21 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(200, 'P m -3', transformations)
space_groups[200] = sg
space_groups['P m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(201, 'P n -3 :2', transformations)
space_groups[201] = sg
space_groups['P n -3 :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(202, 'F m -3', transformations)
space_groups[202] = sg
space_groups['F m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(203, 'F d -3 :2', transformations)
space_groups[203] = sg
space_groups['F d -3 :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(204, 'I m -3', transformations)
space_groups[204] = sg
space_groups['I m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(205, 'P a -3', transformations)
space_groups[205] = sg
space_groups['P a -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(206, 'I a -3', transformations)
space_groups[206] = sg
space_groups['I a -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(207, 'P 4 3 2', transformations)
space_groups[207] = sg
space_groups['P 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(208, 'P 42 3 2', transformations)
space_groups[208] = sg
space_groups['P 42 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(209, 'F 4 3 2', transformations)
space_groups[209] = sg
space_groups['F 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(210, 'F 41 3 2', transformations)
space_groups[210] = sg
space_groups['F 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(211, 'I 4 3 2', transformations)
space_groups[211] = sg
space_groups['I 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(212, 'P 43 3 2', transformations)
space_groups[212] = sg
space_groups['P 43 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(213, 'P 41 3 2', transformations)
space_groups[213] = sg
space_groups['P 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(214, 'I 41 3 2', transformations)
space_groups[214] = sg
space_groups['I 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(215, 'P -4 3 m', transformations)
space_groups[215] = sg
space_groups['P -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(216, 'F -4 3 m', transformations)
space_groups[216] = sg
space_groups['F -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(217, 'I -4 3 m', transformations)
space_groups[217] = sg
space_groups['I -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(218, 'P -4 3 n', transformations)
space_groups[218] = sg
space_groups['P -4 3 n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(219, 'F -4 3 c', transformations)
space_groups[219] = sg
space_groups['F -4 3 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(220, 'I -4 3 d', transformations)
space_groups[220] = sg
space_groups['I -4 3 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(221, 'P m -3 m', transformations)
space_groups[221] = sg
space_groups['P m -3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(222, 'P n -3 n :2', transformations)
space_groups[222] = sg
space_groups['P n -3 n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(223, 'P m -3 n', transformations)
space_groups[223] = sg
space_groups['P m -3 n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(224, 'P n -3 m :2', transformations)
space_groups[224] = sg
space_groups['P n -3 m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(225, 'F m -3 m', transformations)
space_groups[225] = sg
space_groups['F m -3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(226, 'F m -3 c', transformations)
space_groups[226] = sg
space_groups['F m -3 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = | N.array([3,3,0]) | numpy.array |
"""Code from https://github.com/tambetm/simple_dqn/blob/master/src/replay_memory.py"""
import os
import random
import logging
import numpy as np
from .utils import save_npy, load_npy
class ReplayMemory:
def __init__(self, config, model_dir):
self.model_dir = model_dir
self.cnn_format = config.cnn_format
self.memory_size = config.memory_size
self.actions = np.empty(self.memory_size, dtype = np.uint8)
self.rewards = np.empty(self.memory_size, dtype = np.integer)
self.screens = | np.empty((self.memory_size, config.screen_height, config.screen_width), dtype = np.float16) | numpy.empty |
import MultiCal
import TUGmTRL
import skrf as rf
import numpy as np
c0 = 299792458 # speed of light in vacuum (m/s)
def correct_sw(NW, gamma_f, gamma_r):
# correct for switch-terms
# gamma_f forward (source by port-1)
# gamma_r reverse (source by port-2)
G21 = gamma_f.s.squeeze()
G12 = gamma_r.s.squeeze()
freq = NW.frequency
SS = []
for S,g21,g12 in zip(NW.s,G21,G12):
S11 = (S[0,0]-S[0,1]*S[1,0]*g21)/(1-S[0,1]*S[1,0]*g21*g12)
S12 = (S[0,1]-S[0,0]*S[0,1]*g12)/(1-S[0,1]*S[1,0]*g21*g12)
S21 = (S[1,0]-S[1,1]*S[1,0]*g21)/(1-S[0,1]*S[1,0]*g21*g12)
S22 = (S[1,1]-S[0,1]*S[1,0]*g12)/(1-S[0,1]*S[1,0]*g21*g12)
SS.append([[S11,S12],[S21,S22]])
SS = np.array(SS)
return rf.Network(frequency=freq, s=SS)
class mTRL:
"""
Multiline TRL calibration.
Two algorithms implemented here:
1. The classical mTRL from NIST (MultiCal) [2,3]
2. Improved implementation based on [1]
[1] <NAME>, <NAME>, <NAME>, "Improving the Reliability
of the Multiline TRL Calibration Algorithm," 98th ARFTG Conference, Jan. 2022
[2] <NAME>, <NAME> and <NAME>, "Multiline TRL revealed,"
60th ARFTG Conference Digest, Fall 2002, pp. 131-155
[3] <NAME>, "A multiline method of network analyzer calibration",
IEEE Transactions on Microwave Theory and Techniques,
vol. 39, no. 7, pp. 1205-1215, July 1991.
"""
def __init__(self, lines, line_lengths, reflect,
reflect_est=[-1], reflect_offset=[0], ereff_est=1+0j, switch_term=None):
"""
mTRL initializer.
Parameters
--------------
lines : list of :class:`~skrf.network.Network`
Measured lines. The first one is defined as Thru,
and by default calibration is defined in its middel.
line_lengths : list of float
Lengths of the line. In the same order as the paramter 'lines'
reflect : list of :class:`~skrf.network.Network`
Measured reflect standards (2-port device)
reflect_est : list of float
Estimated reflection coefficient of the reflect standard.
In the same order as the parameter 'reflect'.
E.g., if you have a short : [-1]
reflect_offset : list of float
Offsets of the reflect standards from the reference plane (mid of Thru standard)
Negative: towards the port
Positive: away from port
Units in meters.
ereff_est : complex
Estimated effective permittivity.
switch_term : list of :class:`~skrf.network.Network`
list of 1-port networks. Holds 2 elements:
1. network for forward switch term.
2. network for reverse switch term.
"""
self.lines = lines
self.line_lengths = line_lengths
self.reflect = reflect
self.reflect_est = reflect_est
self.reflect_offset = reflect_offset
self.ereff_est = ereff_est
self.switch_term = switch_term
# correct for switch terms
if self.switch_term is not None:
self.lines = [correct_sw(NT, switch_term[0], switch_term[1]) for NT in self.lines]
self.reflect = [correct_sw(NT, switch_term[0], switch_term[1]) for NT in self.reflect]
def run_multical(self):
# MultiCal
print('\nMultiCal mTRL in progress:')
f = self.lines[0].frequency.f
# measurements
T_lines = [ rf.s2t(x.s) for x in self.lines ]
S_short = [ x.s for x in self.reflect ]
line_lengths = self.line_lengths
reflect_est = self.reflect_est
reflect_offset = self.reflect_offset
# initial arrays to fill
gamma_full = []
X_full = []
K_full = []
# initial estimate
ereff_0 = self.ereff_est
gamma_0 = 2*np.pi*f[0]/c0*np.sqrt(-ereff_0)
gamma_0 = abs(gamma_0.real) + 1j*abs(gamma_0.imag)
# perform the calibration
for inx, ff in enumerate(f):
meas_lines_T = [ x[inx] for x in T_lines ]
meas_reflect_S = [ x[inx] for x in S_short ]
X, K, gamma = MultiCal.mTRL(meas_lines_T, line_lengths, meas_reflect_S,
gamma_0, reflect_est, reflect_offset)
if inx+1 < len(f):
gamma_0 = gamma.real + 1j*gamma.imag*f[inx+1]/ff
X_full.append(X)
K_full.append(K)
gamma_full.append(gamma)
print(f'Frequency: {(ff*1e-9).round(4)} GHz done!', end='\r', flush=True)
self.X = np.array(X_full)
self.K = | np.array(K_full) | numpy.array |
# Copyright 2015 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Tests for tensorflow.ops.tf.gather."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from absl.testing import parameterized
import numpy as np
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import test_util
from tensorflow.python.ops import array_ops
from tensorflow.python.platform import test
_TEST_TYPES = (dtypes.int64, dtypes.float32,
dtypes.complex64, dtypes.complex128)
class GatherTest(test.TestCase, parameterized.TestCase):
def _buildParams(self, data, dtype):
data = data.astype(dtype.as_numpy_dtype)
# For complex types, add an index-dependent imaginary component so we can
# tell we got the right value.
if dtype.is_complex:
return data + 10j * data
return data
@parameterized.parameters(dtypes.int32, dtypes.int64)
def testSimpleGather(self, indices_dtype):
data = np.array([0, 1, 2, 3, 7, 5, 8, 9, 10, 11, 15, 13])
indices = [3, 4]
with self.session(use_gpu=True):
for dtype in _TEST_TYPES:
params_np = self._buildParams(data, dtype)
params = constant_op.constant(params_np)
indices_tf = constant_op.constant(indices, dtype=indices_dtype)
gather_t = array_ops.batch_gather(params, indices_tf)
expected_result = np.array([3, 7])
np_val = self._buildParams(expected_result, dtype)
gather_val = self.evaluate(gather_t)
self.assertAllEqual(np_val, gather_val)
self.assertEqual(np_val.shape, gather_t.get_shape())
@parameterized.parameters(dtypes.int32, dtypes.int64)
def test2DArray(self, indices_dtype):
data = np.array([[0, 1, 2, 3, 7, 5], [8, 9, 10, 11, 15, 13]])
indices = [[3], [4]]
with self.session(use_gpu=True):
for dtype in _TEST_TYPES:
params_np = self._buildParams(data, dtype)
params = constant_op.constant(params_np)
indices_tf = constant_op.constant(indices, dtype=indices_dtype)
gather_t = array_ops.batch_gather(params, indices_tf)
expected_result = np.array([[3], [15]])
np_val = self._buildParams(expected_result, dtype)
gather_val = self.evaluate(gather_t)
self.assertAllEqual(np_val, gather_val)
self.assertEqual(np_val.shape, gather_t.get_shape())
def testHigherRank(self):
data = np.array([[[0, 1, 2], [3, 7, 5]], [[8, 9, 10], [11, 15, 13]]])
indices = [[[2, 0], [1, 2]], [[2, 0], [0, 1]]]
with self.session(use_gpu=True):
for dtype in _TEST_TYPES:
params_np = self._buildParams(data, dtype)
params = constant_op.constant(params_np)
indices_tf = constant_op.constant(indices)
gather_t = array_ops.batch_gather(params, indices_tf)
gather_val = self.evaluate(gather_t)
expected_result = | np.array([[[2, 0], [7, 5]], [[10, 8], [11, 15]]]) | numpy.array |
from numpy import arctan, zeros, pi, real as re, imag as im, linspace,eye, prod, newaxis
from numpy import array as arr, exp, log, arange, diag, kron, savetxt, cumsum, argmax
from numpy.linalg import det, norm, solve
from scipy.optimize import fsolve
import matplotlib.pyplot as plt
from copy import deepcopy
from time import clock
from numpy.random import uniform, shuffle
from scipy import integrate
import matplotlib.patches as pat
import pylab as pl
def ncr(n,r):
if r < 0:
return 0
p,q = 1,1
for j in range(r):
p *= n-j
q *= j+1
return p//q
def ind_draw(o,m,n): #generator giving all ways to draw n elements from range(o,m) without replacement
if n>=0:
l = m-o
if n == 0:
yield []
elif n == l:
yield list(range(o,m))
else:
for k in range(o,m-n+1):
for wha in ind_draw(k+1,m,n-1):
yield [k]+wha
def disect(We): #We is l-dimensional tensor, returns the sum along all but each axes.
w = []
As = We.shape
l = len(As)
for j in range(l):
if As[j] >1:
w.append(We.sum(tuple(range(1,l-j))))
else:
w.append(arr([1]))
We = We.sum(0)
for j in range(l):
if As[j] >1: #don't calculate the full sum rule over and over again on trivial boxes. (empty or full)
w[j] /= We
return w
def boxicles(n,deps): #puts n particles in boxes with maximal capacity deps. oo=None was last input
M = len(deps)
if n == 0:
yield [0 for _ in range(M)]
else:
for preput in boxicles(n-1,deps):
for k in range(M):
#postput = [a for a in preput]
#postput[k] += 1
#yield postput
if preput[k]<deps[k]:
yield [preput[a]+int(a==k) for a in range(M)]
if preput[k]:
break
def TBA(T,c,chempot,givedens = True):
interpts = 101 #odd is best
bdys = 20
la = | linspace(-bdys,bdys,interpts) | numpy.linspace |
import random
import time
from copy import deepcopy
from functools import total_ordering
from multiprocessing.queues import Queue
from queue import PriorityQueue
import numpy as np
import math
from scipy.linalg import cholesky, cho_solve, solve_triangular, LinAlgError
from scipy.optimize import linear_sum_assignment
from sklearn.metrics.pairwise import rbf_kernel
from autokeras.constant import Constant
from autokeras.net_transformer import transform
from autokeras.nn.layers import is_layer, LayerType
def layer_distance(a, b):
"""The distance between two layers."""
if type(a) != type(b):
return 1.0
if is_layer(a, LayerType.CONV):
att_diff = [(a.filters, b.filters),
(a.kernel_size, b.kernel_size),
(a.stride, b.stride)]
return attribute_difference(att_diff)
if is_layer(a, LayerType.POOL):
att_diff = [(a.padding, b.padding),
(a.kernel_size, b.kernel_size),
(a.stride, b.stride)]
return attribute_difference(att_diff)
return 0.0
def attribute_difference(att_diff):
ret = 0
for a_value, b_value in att_diff:
if max(a_value, b_value) == 0:
ret += 0
else:
ret += abs(a_value - b_value) * 1.0 / max(a_value, b_value)
return ret * 1.0 / len(att_diff)
def layers_distance(list_a, list_b):
"""The distance between the layers of two neural networks."""
len_a = len(list_a)
len_b = len(list_b)
f = np.zeros((len_a + 1, len_b + 1))
f[-1][-1] = 0
for i in range(-1, len_a):
f[i][-1] = i + 1
for j in range(-1, len_b):
f[-1][j] = j + 1
for i in range(len_a):
for j in range(len_b):
f[i][j] = min(f[i][j - 1] + 1, f[i - 1][j] + 1, f[i - 1][j - 1] + layer_distance(list_a[i], list_b[j]))
return f[len_a - 1][len_b - 1]
def skip_connection_distance(a, b):
"""The distance between two skip-connections."""
if a[2] != b[2]:
return 1.0
len_a = abs(a[1] - a[0])
len_b = abs(b[1] - b[0])
return (abs(a[0] - b[0]) + abs(len_a - len_b)) / (max(a[0], b[0]) + max(len_a, len_b))
def skip_connections_distance(list_a, list_b):
"""The distance between the skip-connections of two neural networks."""
distance_matrix = np.zeros((len(list_a), len(list_b)))
for i, a in enumerate(list_a):
for j, b in enumerate(list_b):
distance_matrix[i][j] = skip_connection_distance(a, b)
return distance_matrix[linear_sum_assignment(distance_matrix)].sum() + abs(len(list_a) - len(list_b))
def edit_distance(x, y):
"""The distance between two neural networks.
Args:
x: An instance of NetworkDescriptor.
y: An instance of NetworkDescriptor
Returns:
The edit-distance between x and y.
"""
ret = layers_distance(x.layers, y.layers)
ret += Constant.KERNEL_LAMBDA * skip_connections_distance(x.skip_connections, y.skip_connections)
return ret
class IncrementalGaussianProcess:
"""Gaussian process regressor.
Attributes:
alpha: A hyperparameter.
"""
def __init__(self):
self.alpha = 1e-10
self._distance_matrix = None
self._x = None
self._y = None
self._first_fitted = False
self._l_matrix = None
self._alpha_vector = None
@property
def kernel_matrix(self):
return self._distance_matrix
def fit(self, train_x, train_y):
""" Fit the regressor with more data.
Args:
train_x: A list of NetworkDescriptor.
train_y: A list of metric values.
"""
if self.first_fitted:
self.incremental_fit(train_x, train_y)
else:
self.first_fit(train_x, train_y)
def incremental_fit(self, train_x, train_y):
""" Incrementally fit the regressor. """
if not self._first_fitted:
raise ValueError("The first_fit function needs to be called first.")
train_x, train_y = np.array(train_x), np.array(train_y)
# Incrementally compute K
up_right_k = edit_distance_matrix(self._x, train_x)
down_left_k = np.transpose(up_right_k)
down_right_k = edit_distance_matrix(train_x)
up_k = np.concatenate((self._distance_matrix, up_right_k), axis=1)
down_k = np.concatenate((down_left_k, down_right_k), axis=1)
temp_distance_matrix = np.concatenate((up_k, down_k), axis=0)
k_matrix = bourgain_embedding_matrix(temp_distance_matrix)
diagonal = np.diag_indices_from(k_matrix)
diagonal = (diagonal[0][-len(train_x):], diagonal[1][-len(train_x):])
k_matrix[diagonal] += self.alpha
try:
self._l_matrix = cholesky(k_matrix, lower=True) # Line 2
except LinAlgError:
return self
self._x = np.concatenate((self._x, train_x), axis=0)
self._y = np.concatenate((self._y, train_y), axis=0)
self._distance_matrix = temp_distance_matrix
self._alpha_vector = cho_solve((self._l_matrix, True), self._y) # Line 3
return self
@property
def first_fitted(self):
return self._first_fitted
def first_fit(self, train_x, train_y):
""" Fit the regressor for the first time. """
train_x, train_y = np.array(train_x), np.array(train_y)
self._x = | np.copy(train_x) | numpy.copy |
import numpy as np
import pandas as pd
from scipy import sparse, ndimage as ndi
from scipy.sparse import csgraph
from scipy.spatial import distance_matrix
from skimage import morphology
from skimage.graph import central_pixel
from skimage.util._map_array import map_array, ArrayMap
import numba
import warnings
from .nputil import _raveled_offsets_and_distances
from .summary_utils import find_main_branches
def _weighted_abs_diff(values0, values1, distances):
"""A default edge function for complete image graphs.
A pixel graph on an image with no edge values and no mask is a very
boring regular lattice, so we define a default edge weight to be the
absolute difference between values *weighted* by the distance
between them.
Parameters
----------
values0 : array
The pixel values for each node.
values1 : array
The pixel values for each neighbor.
distances : array
The distance between each node and its neighbor.
Returns
-------
edge_values : array of float
The computed values: abs(values0 - values1) * distances.
"""
return np.abs(values0 - values1) * distances
def pixel_graph(
image, *, mask=None, edge_function=None, connectivity=1, spacing=None
):
"""Create an adjacency graph of pixels in an image.
Pixels where the mask is True are nodes in the returned graph, and they are
connected by edges to their neighbors according to the connectivity
parameter. By default, the *value* of an edge when a mask is given, or when
the image is itself the mask, is the euclidean distance betwene the pixels.
However, if an int- or float-valued image is given with no mask, the value
of the edges is the absolute difference in intensity between adjacent
pixels, weighted by the euclidean distance.
Parameters
----------
image : array
The input image. If the image is of type bool, it will be used as the
mask as well.
mask : array of bool
Which pixels to use. If None, the graph for the whole image is used.
edge_function : callable
A function taking an array of pixel values, and an array of neighbor
pixel values, and an array of distances, and returning a value for the
edge. If no function is given, the value of an edge is just the
distance.
connectivity : int
The square connectivity of the pixel neighborhood: the number of
orthogonal steps allowed to consider a pixel a neigbor. See
`scipy.ndimage.generate_binary_structure` for details.
spacing : tuple of float
The spacing between pixels along each axis.
Returns
-------
graph : scipy.sparse.csr_matrix
A sparse adjacency matrix in which entry (i, j) is 1 if nodes i and j
are neighbors, 0 otherwise.
nodes : array of int
The nodes of the graph. These correspond to the raveled indices of the
nonzero pixels in the mask.
"""
if image.dtype == bool and mask is None:
mask = image
if mask is None and edge_function is None:
mask = np.ones_like(image, dtype=bool)
edge_function = _weighted_abs_diff
# Strategy: we are going to build the (i, j, data) arrays of a scipy
# sparse COO matrix, then convert to CSR (which is fast).
# - grab the raveled IDs of the foreground (mask == True) parts of the
# image **in the padded space**.
# - broadcast them together with the raveled offsets to their neighbors.
# This gives us for each foreground pixel a list of neighbors (that
# may or may not be selected by the mask.) (We also track the *distance*
# to each neighbor.)
# - select "valid" entries in the neighbors and distance arrays by indexing
# into the mask, which we can do since these are raveled indices.
# - use np.repeat() to repeat each source index according to the number
# of neighbors selected by the mask it has. Each of these repeated
# indices will be lined up with its neighbor, i.e. **this is the i
# array** of the COO format matrix.
# - use the mask as a boolean index to get a 1D view of the selected
# neighbors. **This is the j array.**
# - by default, the same boolean indexing can be applied to the distances
# to each neighbor, to give the **data array.** Optionally, a
# provided edge function can be computed on the pixel values and the
# distances to give a different value for the edges.
# Note, we use map_array to map the raveled coordinates in the padded
# image to the ones in the original image, and those are the returned
# nodes.
padded = np.pad(mask, 1, mode='constant', constant_values=False)
nodes_padded = np.flatnonzero(padded)
neighbor_offsets_padded, distances_padded = _raveled_offsets_and_distances(
padded.shape, connectivity=connectivity, spacing=spacing
)
neighbors_padded = nodes_padded[:, np.newaxis] + neighbor_offsets_padded
neighbor_distances_full = np.broadcast_to(
distances_padded, neighbors_padded.shape
)
nodes = np.flatnonzero(mask)
nodes_sequential = np.arange(nodes.size)
# neighbors outside the mask get mapped to 0, which is a valid index,
# BUT, they will be masked out in the next step.
neighbors = map_array(neighbors_padded, nodes_padded, nodes)
neighbors_mask = padded.reshape(-1)[neighbors_padded]
num_neighbors = np.sum(neighbors_mask, axis=1)
indices = np.repeat(nodes, num_neighbors)
indices_sequential = np.repeat(nodes_sequential, num_neighbors)
neighbor_indices = neighbors[neighbors_mask]
neighbor_distances = neighbor_distances_full[neighbors_mask]
neighbor_indices_sequential = map_array(
neighbor_indices, nodes, nodes_sequential
)
if edge_function is None:
data = neighbor_distances
else:
image_r = image.reshape(-1)
data = edge_function(
image_r[indices], image_r[neighbor_indices], neighbor_distances
)
m = nodes_sequential.size
mat = sparse.coo_matrix(
(data, (indices_sequential, neighbor_indices_sequential)),
shape=(m, m)
)
graph = mat.tocsr()
return graph, nodes
csr_spec_float = [
('indptr', numba.int32[:]),
('indices', numba.int32[:]),
('data', numba.float64[:]),
('shape', numba.int32[:]),
('node_properties', numba.float64[:]),
] # yapf: disable
csr_spec_bool = [
('indptr', numba.int32[:]),
('indices', numba.int32[:]),
('data', numba.bool_[:]),
('shape', numba.int32[:]),
('node_properties', numba.float64[:]),
] # yapf: disable
class NBGraphBase:
def __init__(self, indptr, indices, data, shape, node_props):
self.indptr = indptr
self.indices = indices
self.data = data
self.shape = shape
self.node_properties = node_props
def edge(self, i, j):
return _csrget(self.indices, self.indptr, self.data, i, j)
def set_edge(self, i, j, value):
return _csrset(self.indices, self.indptr, self.data, i, j, value)
def neighbors(self, row):
loc, stop = self.indptr[row], self.indptr[row + 1]
return self.indices[loc:stop]
@property
def has_node_props(self):
return self.node_properties.strides != (0,)
NBGraph = numba.experimental.jitclass(NBGraphBase, csr_spec_float)
NBGraphBool = numba.experimental.jitclass(NBGraphBase, csr_spec_bool)
def csr_to_nbgraph(csr, node_props=None):
if node_props is None:
node_props = np.broadcast_to(1., csr.shape[0])
node_props.flags.writeable = True
return NBGraph(
csr.indptr, csr.indices, csr.data,
np.array(csr.shape, dtype=np.int32), node_props
)
def _pixel_graph(image, steps, distances, num_edges, height=None):
row = np.empty(num_edges, dtype=int)
col = np.empty(num_edges, dtype=int)
data = np.empty(num_edges, dtype=float)
if height is None:
k = _write_pixel_graph(image, steps, distances, row, col, data)
else:
k = _write_pixel_graph_height(
image, height, steps, distances, row, col, data
)
graph = sparse.coo_matrix((data[:k], (row[:k], col[:k]))).tocsr()
return graph
@numba.jit(nopython=True, cache=True, nogil=True)
def _write_pixel_graph(image, steps, distances, row, col, data):
"""Step over `image` to build a graph of nonzero pixel neighbors.
Parameters
----------
image : int array
The input image.
steps : int array, shape (N,)
The raveled index steps to find a pixel's neighbors in `image`.
distances : float array, shape (N,)
The euclidean distance from a pixel to its corresponding
neighbor in `steps`.
row : int array
Output array to be filled with the "center" pixel IDs.
col : int array
Output array to be filled with the "neighbor" pixel IDs.
data : float array
Output array to be filled with the distances from center to
neighbor pixels.
Returns
-------
k : int
The number of entries written to row, col, and data.
Notes
-----
No size or bounds checking is performed. Users should ensure that
- No index in `indices` falls on any edge of `image` (or the
neighbor computation will fail or segfault).
- The `steps` and `distances` arrays have the same shape.
- The `row`, `col`, `data` are long enough to hold all of the
edges.
"""
image = image.ravel()
n_neighbors = steps.size
start_idx = np.max(steps)
end_idx = image.size + np.min(steps)
k = 0
for i in range(start_idx, end_idx + 1):
if image[i] != 0:
for j in range(n_neighbors):
n = steps[j] + i
if image[n] != 0 and image[n] != image[i]:
row[k] = image[i]
col[k] = image[n]
data[k] = distances[j]
k += 1
return k
@numba.jit(nopython=True, cache=True, nogil=True)
def _write_pixel_graph_height(image, height, steps, distances, row, col, data):
"""Step over `image` to build a graph of nonzero pixel neighbors.
Parameters
----------
image : int array
The input image.
height : float array, same shape as `image`
This is taken to be a height map along an additional
dimension (in addition to the image dimensions), so the distance
between two neighbors `i` and `n` separated by `j` is given by:
`np.sqrt(distances[j]**2 + (height[i] - height[n])**2)`
steps : int array, shape (N,)
The raveled index steps to find a pixel's neighbors in `image`.
distances : float array, shape (N,)
The euclidean distance from a pixel to its corresponding
neighbor in `steps`.
row : int array
Output array to be filled with the "center" pixel IDs.
col : int array
Output array to be filled with the "neighbor" pixel IDs.
data : float array
Output array to be filled with the distances from center to
neighbor pixels.
Returns
-------
k : int
The number of entries written to row, col, and data.
Notes
-----
No size or bounds checking is performed. Users should ensure that
- No index in `indices` falls on any edge of `image` (or the
neighbor computation will fail or segfault).
- The `steps` and `distances` arrays have the same shape.
- The `row`, `col`, `data` are long enough to hold all of the
edges.
"""
image = image.ravel()
height = height.ravel()
n_neighbors = steps.size
start_idx = np.max(steps)
end_idx = image.size + np.min(steps)
k = 0
for i in range(start_idx, end_idx + 1):
if image[i] != 0:
for j in range(n_neighbors):
n = steps[j] + i
if image[n] != 0 and image[n] != image[i]:
row[k] = image[i]
col[k] = image[n]
data[k] = np.sqrt(
distances[j]**2 + (height[i] - height[n])**2
)
k += 1
return k
@numba.jit(nopython=True, cache=False) # change this to True with Numba 1.0
def _build_paths(jgraph, indptr, indices, path_data, visited, degrees):
indptr_i = 0
indices_j = 0
# first, process all nodes in a path to an endpoint or junction
for node in range(jgraph.shape[0]):
if degrees[node] > 2 or degrees[node] == 1:
for neighbor in jgraph.neighbors(node):
if not visited.edge(node, neighbor):
n_steps = _walk_path(
jgraph, node, neighbor, visited, degrees, indices,
path_data, indices_j
)
indptr[indptr_i + 1] = indptr[indptr_i] + n_steps
indptr_i += 1
indices_j += n_steps
# everything else is by definition in isolated cycles
for node in range(jgraph.shape[0]):
if degrees[node] > 0:
neighbor = jgraph.neighbors(node)[0]
if not visited.edge(node, neighbor):
n_steps = _walk_path(
jgraph, node, neighbor, visited, degrees, indices,
path_data, indices_j
)
indptr[indptr_i + 1] = indptr[indptr_i] + n_steps
indptr_i += 1
indices_j += n_steps
return indptr_i + 1, indices_j
@numba.jit(nopython=True, cache=False) # change this to True with Numba 1.0
def _walk_path(
jgraph, node, neighbor, visited, degrees, indices, path_data, startj
):
indices[startj] = node
start_node = node
path_data[startj] = jgraph.node_properties[node]
j = startj + 1
while not visited.edge(node, neighbor):
visited.set_edge(node, neighbor, True)
visited.set_edge(neighbor, node, True)
indices[j] = neighbor
path_data[j] = jgraph.node_properties[neighbor]
if degrees[neighbor] != 2 or neighbor == start_node:
break
n1, n2 = jgraph.neighbors(neighbor)
nextneighbor = n1 if n1 != node else n2
node, neighbor = neighbor, nextneighbor
j += 1
return j - startj + 1
def _build_skeleton_path_graph(graph):
max_num_cycles = graph.indices.size // 4
buffer_size_offset = max_num_cycles
degrees = np.diff(graph.indptr)
visited_data = np.zeros(graph.data.shape, dtype=bool)
visited = NBGraphBool(
graph.indptr, graph.indices, visited_data, graph.shape,
np.broadcast_to(1., graph.shape[0])
)
endpoints = (degrees != 2)
endpoint_degrees = degrees[endpoints]
num_paths = np.sum(endpoint_degrees)
path_indptr = np.zeros(num_paths + buffer_size_offset, dtype=int)
# the number of points that we need to save to store all skeleton
# paths is equal to the number of pixels plus the sum of endpoint
# degrees minus one (since the endpoints will have been counted once
# already in the number of pixels) *plus* the number of isolated
# cycles (since each cycle has one index repeated). We don't know
# the number of cycles ahead of time, but it is bounded by one quarter
# of the number of points.
n_points = (
graph.indices.size + np.sum(endpoint_degrees - 1)
+ buffer_size_offset
)
path_indices = np.zeros(n_points, dtype=int)
path_data = np.zeros(path_indices.shape, dtype=float)
m, n = _build_paths(
graph, path_indptr, path_indices, path_data, visited, degrees
)
paths = sparse.csr_matrix(
(path_data[:n], path_indices[:n], path_indptr[:m]),
shape=(m - 1, n)
)
return paths
class Skeleton:
"""Object to group together all the properties of a skeleton.
In the text below, we use the following notation:
- N: the number of points in the pixel skeleton,
- ndim: the dimensionality of the skeleton
- P: the number of paths in the skeleton (also the number of links in the
junction graph).
- J: the number of junction nodes
- Sd: the sum of the degrees of all the junction nodes
- [Nt], [Np], Nr, Nc: the dimensions of the source image
Parameters
----------
skeleton_image : array
The input skeleton (1-pixel/voxel thick skeleton, all other values 0).
Other Parameters
----------------
spacing : float or array of float, shape ``(ndim,)``
The scale of the pixel spacing along each axis.
source_image : array of float, same shape as `skeleton_image`
The image that `skeleton_image` represents / summarizes / was generated
from. This is used to produce visualizations as well as statistical
properties of paths.
keep_images : bool
Whether or not to keep the original input images. These can be useful
for visualization, but they may take up a lot of memory.
value_is_height : bool
Whether to consider the value of a float skeleton to be the "height"
of the image. This can be useful e.g. when measuring lengths along
ridges in AFM images.
Attributes
----------
graph : scipy.sparse.csr_matrix, shape (N + 1, N + 1)
The skeleton pixel graph, where each node is a non-zero pixel in the
input image, and each edge connects adjacent pixels. The graph is
represented as an adjacency matrix in SciPy sparse matrix format. For
more information see the ``scipy.sparse`` documentation as well as
``scipy.sparse.csgraph``. Note: pixel numbering starts at 1, so the
shape of this matrix is ``(N + 1, N + 1)`` instead of ``(N, N)``.
nbgraph : NBGraph
A thin Numba wrapper around the ``csr_matrix`` format, this provides
faster graph methods. For example, it is much faster to get a list of
neighbors, or test for the presence of a specific edge.
coordinates : array, shape (N, ndim)
skeleton_pixel_id i -> coordinates[i]
The image coordinates of each pixel in the skeleton.
Some values in this matrix are non-sensical — you should only access
them from node ids.
paths : scipy.sparse.csr_matrix, shape (P, N + 1)
A csr_matrix where element [i, j] is on if node j is in path i. This
includes path endpoints. The number of nonzero elements is N - J + Sd.
n_paths : int
The number of paths, P. This is redundant information given `n_paths`,
but it is used often enough that it is worth keeping around.
distances : array of float, shape (P,)
The distance of each path. Note: not initialized until `path_lengths()`
is called on the skeleton; use path_lengths() instead
skeleton_image : array or None
The input skeleton image. Only present if `keep_images` is True. Set to
False to preserve memory.
source_image : array or None
The image from which the skeleton was derived. Only present if
`keep_images` is True. This is useful for visualization.
"""
def __init__(
self,
skeleton_image,
*,
spacing=1,
source_image=None,
keep_images=True,
value_is_height=False,
):
graph, coords = skeleton_to_csgraph(
skeleton_image,
spacing=spacing,
value_is_height=value_is_height,
)
if np.issubdtype(skeleton_image.dtype, np.float_):
self.pixel_values = skeleton_image[coords]
else:
self.pixel_values = None
self.graph = graph
self.nbgraph = csr_to_nbgraph(graph, self.pixel_values)
self.coordinates = np.transpose(coords)
self.paths = _build_skeleton_path_graph(self.nbgraph)
self.n_paths = self.paths.shape[0]
self.distances = np.empty(self.n_paths, dtype=float)
self._distances_initialized = False
self.skeleton_image = None
self.source_image = None
self.degrees = np.diff(self.graph.indptr)
self.spacing = (
np.asarray(spacing) if not np.isscalar(spacing) else
np.full(skeleton_image.ndim, spacing)
)
if keep_images:
self.skeleton_image = skeleton_image
self.source_image = source_image
def path(self, index):
"""Return the pixel indices of path number `index`.
Parameters
----------
index : int
The desired path.
Returns
-------
path : array of int
The indices of the pixels belonging to the path, including
endpoints.
"""
# The below is equivalent to `self.paths[index].indices`, which is much
# more elegant. However the below version is about 25x faster!
# In [14]: %timeit mat[1].indices
# 128 µs ± 421 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
# In [16]: %%timeit
# ...: start, stop = mat.indptr[1:3]
# ...: mat.indices[start:stop]
# ...:
# 5.05 µs ± 77.2 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
start, stop = self.paths.indptr[index:index + 2]
return self.paths.indices[start:stop]
def path_coordinates(self, index):
"""Return the image coordinates of the pixels in the path.
Parameters
----------
index : int
The desired path.
Returns
-------
path_coords : array of float
The (image) coordinates of points on the path, including endpoints.
"""
path_indices = self.path(index)
return self.coordinates[path_indices]
def path_with_data(self, index):
"""Return pixel indices and corresponding pixel values on a path.
Parameters
----------
index : int
The desired path.
Returns
-------
path : array of int
The indices of pixels on the path, including endpoints.
data : array of float
The values of pixels on the path.
"""
start, stop = self.paths.indptr[index:index + 2]
return self.paths.indices[start:stop], self.paths.data[start:stop]
def path_lengths(self):
"""Return the length of each path on the skeleton.
Returns
-------
lengths : array of float
The length of all the paths in the skeleton.
"""
if not self._distances_initialized:
_compute_distances(
self.nbgraph, self.paths.indptr, self.paths.indices,
self.distances
)
self._distances_initialized = True
return self.distances
def paths_list(self):
"""List all the paths in the skeleton, including endpoints.
Returns
-------
paths : list of array of int
The list containing all the paths in the skeleton.
"""
return [list(self.path(i)) for i in range(self.n_paths)]
def path_label_image(self):
"""Image like self.skeleton_image with path_ids as values.
Returns
-------
label_image : array of ints
Image of the same shape as self.skeleton_image where each pixel
has the value of its branch id + 1.
"""
image_out = np.zeros(self.skeleton_image.shape, dtype=int)
for i in range(self.n_paths):
coords_to_wipe = self.path_coordinates(i)
coords_idxs = tuple(np.round(coords_to_wipe).astype(int).T)
image_out[coords_idxs] = i + 1
return image_out
def path_means(self):
"""Compute the mean pixel value along each path.
Returns
-------
means : array of float
The average pixel value along each path in the skeleton.
"""
sums = np.add.reduceat(self.paths.data, self.paths.indptr[:-1])
lengths = np.diff(self.paths.indptr)
return sums / lengths
def path_stdev(self):
"""Compute the standard deviation of values along each path.
Returns
-------
stdevs : array of float
The standard deviation of pixel values along each path.
"""
data = self.paths.data
sumsq = np.add.reduceat(data * data, self.paths.indptr[:-1])
lengths = np.diff(self.paths.indptr)
means = self.path_means()
return np.sqrt(np.clip(sumsq/lengths - means*means, 0, None))
def prune_paths(self, indices) -> 'Skeleton':
# warning: slow
image_cp = np.copy(self.skeleton_image)
for i in indices:
pixel_ids_to_wipe = self.path(i)
junctions = self.degrees[pixel_ids_to_wipe] > 2
pixel_ids_to_wipe = pixel_ids_to_wipe[~junctions]
coords_to_wipe = self.coordinates[pixel_ids_to_wipe]
coords_idxs = tuple(np.round(coords_to_wipe).astype(int).T)
image_cp[coords_idxs] = 0
# optional cleanup:
new_skeleton = morphology.skeletonize(image_cp.astype(bool)) * image_cp
return Skeleton(
new_skeleton,
spacing=self.spacing,
source_image=self.source_image,
)
def __array__(self, dtype=None):
"""Array representation of the skeleton path labels."""
return self.path_label_image()
def summarize(
skel: Skeleton, *, value_is_height=False, find_main_branch=False
):
"""Compute statistics for every skeleton and branch in ``skel``.
Parameters
----------
skel : skan.csr.Skeleton
A Skeleton object.
value_is_height : bool
Whether to consider the value of a float skeleton to be the "height"
of the image. This can be useful e.g. when measuring lengths along
ridges in AFM images.
find_main_branch : bool, optional
Whether to compute main branches. A main branch is defined as the
longest shortest path within a skeleton. This step is very expensive
as it involves computing the shortest paths between all pairs of branch
endpoints, so it is off by default.
Returns
-------
summary : pandas.DataFrame
A summary of the branches including branch length, mean branch value,
branch euclidean distance, etc.
"""
summary = {}
ndim = skel.coordinates.shape[1]
_, skeleton_ids = csgraph.connected_components(skel.graph, directed=False)
endpoints_src = skel.paths.indices[skel.paths.indptr[:-1]]
endpoints_dst = skel.paths.indices[skel.paths.indptr[1:] - 1]
summary['skeleton-id'] = skeleton_ids[endpoints_src]
summary['node-id-src'] = endpoints_src
summary['node-id-dst'] = endpoints_dst
summary['branch-distance'] = skel.path_lengths()
deg_src = skel.degrees[endpoints_src]
deg_dst = skel.degrees[endpoints_dst]
kind = np.full(deg_src.shape, 2) # default: junction-to-junction
kind[(deg_src == 1) | (deg_dst == 1)] = 1 # tip-junction
kind[(deg_src == 1) & (deg_dst == 1)] = 0 # tip-tip
kind[endpoints_src == endpoints_dst] = 3 # cycle
summary['branch-type'] = kind
summary['mean-pixel-value'] = skel.path_means()
summary['stdev-pixel-value'] = skel.path_stdev()
for i in range(ndim): # keep loops separate for best insertion order
summary[f'image-coord-src-{i}'] = skel.coordinates[endpoints_src, i]
for i in range(ndim):
summary[f'image-coord-dst-{i}'] = skel.coordinates[endpoints_dst, i]
coords_real_src = skel.coordinates[endpoints_src] * skel.spacing
for i in range(ndim):
summary[f'coord-src-{i}'] = coords_real_src[:, i]
if value_is_height:
values_src = skel.pixel_values[endpoints_src]
summary[f'coord-src-{ndim}'] = values_src
coords_real_src = np.concatenate(
[coords_real_src, values_src[:, np.newaxis]],
axis=1,
) # yapf: ignore
coords_real_dst = skel.coordinates[endpoints_dst] * skel.spacing
for i in range(ndim):
summary[f'coord-dst-{i}'] = coords_real_dst[:, i]
if value_is_height:
values_dst = skel.pixel_values[endpoints_dst]
summary[f'coord-dst-{ndim}'] = values_dst
coords_real_dst = np.concatenate(
[coords_real_dst, values_dst[:, np.newaxis]],
axis=1,
) # yapf: ignore
summary['euclidean-distance'] = (
np.sqrt((coords_real_dst - coords_real_src)**2
@ np.ones(ndim + int(value_is_height)))
)
df = pd.DataFrame(summary)
if find_main_branch:
# define main branch as longest shortest path within a single skeleton
df['main'] = find_main_branches(df)
return df
@numba.jit(nopython=True, nogil=True, cache=False) # cache with Numba 1.0
def _compute_distances(graph, path_indptr, path_indices, distances):
for i in range(len(distances)):
start, stop = path_indptr[i:i + 2]
path = path_indices[start:stop]
distances[i] = _path_distance(graph, path)
@numba.jit(nopython=True, nogil=True, cache=False) # cache with Numba 1.0
def _path_distance(graph, path):
d = 0.
n = len(path)
for i in range(n - 1):
u, v = path[i], path[i + 1]
d += graph.edge(u, v)
return d
def _mst_junctions(csmat):
"""Replace clustered pixels with degree > 2 by their minimum spanning tree.
This function performs the operation in place.
Parameters
----------
csmat : NBGraph
The input graph.
pixel_indices : array of int
The raveled index in the image of every pixel represented in csmat.
spacing : float, or array-like of float, shape `len(shape)`, optional
The spacing between pixels in the source image along each dimension.
Returns
-------
final_graph : NBGraph
The output csmat.
"""
# make copy
# mask out all degree < 3 entries
# find MST
# replace edges not in MST with zeros
# use .eliminate_zeros() to get a new matrix
csc_graph = csmat.tocsc()
degrees = np.asarray(csmat.astype(bool).astype(int).sum(axis=0))
non_junction = np.flatnonzero(degrees < 3)
non_junction_column_start = csc_graph.indptr[non_junction]
non_junction_column_end = csc_graph.indptr[non_junction + 1]
for start, end in zip(non_junction_column_start, non_junction_column_end):
csc_graph.data[start:end] = 0
csr_graph = csc_graph.tocsr()
non_junction_row_start = csr_graph.indptr[non_junction]
non_junction_row_end = csr_graph.indptr[non_junction + 1]
for start, end in zip(non_junction_row_start, non_junction_row_end):
csr_graph.data[start:end] = 0
csr_graph.eliminate_zeros()
mst = csgraph.minimum_spanning_tree(csr_graph)
non_tree_edges = csr_graph - (mst + mst.T)
final_graph = csmat - non_tree_edges
return final_graph
def distance_with_height(source_values, neighbor_values, distances):
height_diff = source_values - neighbor_values
return np.hypot(height_diff, distances)
def skeleton_to_csgraph(
skel,
*,
spacing=1,
value_is_height=False,
):
"""Convert a skeleton image of thin lines to a graph of neighbor pixels.
Parameters
----------
skel : array
An input image in which every nonzero pixel is considered part of
the skeleton, and links between pixels are determined by a full
n-dimensional neighborhood.
spacing : float, or array-like of float, shape `(skel.ndim,)`
A value indicating the distance between adjacent pixels. This can
either be a single value if the data has the same resolution along
all axes, or it can be an array of the same shape as `skel` to
indicate spacing along each axis.
Other Parameters
----------------
value_is_height : bool, optional
If `True`, the pixel value at each point of the skeleton will be
considered to be a height measurement, and this height will be
incorporated into skeleton branch lengths. Used for analysis of
atomic force microscopy (AFM) images.
Returns
-------
graph : sparse.csr_matrix
A graph of shape (Nnz, Nnz), where Nnz is the number of
nonzero pixels in `skel`. The value graph[i, j] is the distance
between adjacent pixels i and j. In a 2D image, that would be
1 for immediately adjacent pixels and sqrt(2) for diagonally
adjacent ones.
pixel_coordinates : array of float
An array of shape (Nnz, skel.ndim), mapping indices in `graph`
to pixel coordinates in `skel`.
"""
# ensure we have a bool image, since we later use it for bool indexing
skel_im = skel
skel_bool = skel.astype(bool)
ndim = skel.ndim
spacing = np.ones(ndim, dtype=float) * spacing
if value_is_height:
edge_func = distance_with_height
else:
edge_func = None
graph, pixel_indices = pixel_graph(
skel_im,
mask=skel_bool,
edge_function=edge_func,
connectivity=ndim,
spacing=spacing
)
graph = _mst_junctions(graph)
pixel_coordinates = np.unravel_index(pixel_indices, skel.shape)
return graph, pixel_coordinates
@numba.jit(nopython=True, cache=True)
def _csrget(indices, indptr, data, row, col):
"""Fast lookup of value in a scipy.sparse.csr_matrix format table.
Parameters
----------
indices, indptr, data : numpy arrays of int, int, float
The CSR format data.
row, col : int
The matrix coordinates of the desired value.
Returns
-------
dat: float
The data value in the matrix.
"""
start, end = indptr[row], indptr[row + 1]
for i in range(start, end):
if indices[i] == col:
return data[i]
return 0.
@numba.jit(nopython=True, cache=True)
def _csrset(indices, indptr, data, row, col, value):
"""Fast lookup and set of value in a scipy.sparse.csr_matrix format table.
Parameters
----------
indices, indptr, data : numpy arrays of int, int, float
The CSR format data.
row, col : int
The matrix coordinates of the desired value.
value : dtype
The value to set in the matrix.
Notes
-----
This function only sets values that already existed in the matrix.
Returns
-------
success: bool
Whether the data value was successfully written to the matrix.
"""
start, end = indptr[row], indptr[row + 1]
for i in range(start, end):
if indices[i] == col:
data[i] = value
return True
return False
def submatrix(M, idxs):
"""Return the outer-index product submatrix, `M[idxs, :][:, idxs]`.
Parameters
----------
M : scipy.sparse.spmatrix
Input (square) matrix
idxs : array of int
The indices to subset. No index in `idxs` should exceed the
number of rows of `M`.
Returns
-------
Msub : scipy.sparse.spmatrix
The subsetted matrix.
Examples
--------
>>> Md = np.arange(16).reshape((4, 4))
>>> M = sparse.csr_matrix(Md)
>>> print(submatrix(M, [0, 2]).toarray())
[[ 0 2]
[ 8 10]]
"""
Msub = M[idxs, :][:, idxs]
return Msub
def make_degree_image(skeleton_image):
"""Create a array showing the degree of connectivity of each pixel.
Parameters
----------
skeleton_image : array
An input image in which every nonzero pixel is considered part of
the skeleton, and links between pixels are determined by a full
n-dimensional neighborhood.
Returns
-------
degree_image : array of int, same shape as skeleton_image
An image containing the degree of connectivity of each pixel in the
skeleton to neighboring pixels.
"""
bool_skeleton = skeleton_image.astype(bool)
degree_kernel = np.ones((3,) * bool_skeleton.ndim)
degree_kernel[(1,) * bool_skeleton.ndim] = 0 # remove centre pixel
if isinstance(bool_skeleton, np.ndarray):
degree_image = ndi.convolve(
bool_skeleton.astype(int),
degree_kernel,
mode='constant',
) * bool_skeleton
# use dask image for any array other than a numpy array (which isn't
# supported yet anyway)
else:
import dask.array as da
from dask_image.ndfilters import convolve as dask_convolve
if isinstance(bool_skeleton, da.Array):
degree_image = bool_skeleton * dask_convolve(
bool_skeleton.astype(int), degree_kernel, mode='constant'
)
return degree_image
def _simplify_graph(skel):
"""Iterative removal of all nodes of degree 2 while reconnecting their
edges.
Parameters
----------
skel : skan.csr.Skeleton
A Skeleton object containing graph to be simplified.
Returns
-------
simp_csgraph : scipy.sparse.csr_matrix
A sparse adjacency matrix of the simplified graph.
reduced_nodes : tuple of int
The index nodes of original graph in simplified graph.
"""
if np.sum(skel.degrees > 2) == 0: # no junctions
# don't reduce
return skel.graph, np.arange(skel.graph.shape[0])
summary = summarize(skel)
src = np.asarray(summary['node-id-src'])
dst = np.asarray(summary['node-id-dst'])
distance = np.asarray(summary['branch-distance'])
# to reduce the size of simplified graph
nodes = np.unique(np.append(src, dst))
n_nodes = len(nodes)
nodes_sequential = np.arange(n_nodes)
fw_map = ArrayMap(nodes, nodes_sequential)
inv_map = ArrayMap(nodes_sequential, nodes)
src_relab, dst_relab = fw_map[src], fw_map[dst]
edges = sparse.coo_matrix(
(distance, (src_relab, dst_relab)),
shape=(n_nodes, n_nodes)
)
dir_csgraph = edges.tocsr()
simp_csgraph = dir_csgraph + dir_csgraph.T # make undirected
reduced_nodes = inv_map[np.arange(simp_csgraph.shape[0])]
return simp_csgraph, reduced_nodes
def _fast_graph_center_idx(skel):
"""Accelerated graph center finding using simplified graph.
Parameters
----------
skel : skan.csr.Skeleton
A Skeleton object containing graph whose center is to be found.
Returns
-------
original_center_idx : int
The index of central node of graph.
"""
simp_csgraph, reduced_nodes = _simplify_graph(skel)
simp_center_idx, _ = central_pixel(simp_csgraph)
original_center_idx = reduced_nodes[simp_center_idx]
return original_center_idx
def _normalize_shells(shells, *, center, skeleton_coordinates, spacing):
"""Normalize shells from any format allowed by `sholl_analysis` to radii.
Parameters
----------
shells : int or sequence of floats, or None
If an int, it is used as number of evenly spaced concentric shells. If
an array of floats, it is used directly as the different shell radii in
real world units. If None, the number of evenly spaced concentric
shells is automatically calculated.
center : (D,) array of float
The scaled coordinates of the center point for Sholl analysis.
skeleton_coordinates : (N, D) array of float
The scaled coordinates of skeleton pixels. Used when shells is None or
int.
spacing : (D,) array of float
The pixel/voxel spacing of the skeleton data.
Returns
-------
radii : array of float
The computed and normalized shell radii.
"""
if isinstance(shells, (list, tuple, np.ndarray)):
shell_radii = np.asarray(shells)
else: # shells is int, number of shells, or None
# Find max euclidean distance from center to all nodes
distances = np.linalg.norm(skeleton_coordinates - center, axis=1)
start_radius = 0
end_radius = np.max(distances) # largest possible radius
if shells is None:
stepsize = np.linalg.norm(spacing)
else: # scalar
stepsize = (end_radius-start_radius) / shells
epsilon = np.finfo(np.float32).eps
shell_radii = np.arange(start_radius, end_radius + epsilon, stepsize)
if (sp := | np.linalg.norm(spacing) | numpy.linalg.norm |
"""
Tree Meshes
===========
Here we demonstrate various ways that models can be defined and mapped to
OcTree meshes. Some things we consider are:
- Mesh refinement near surface topography
- Adding structures of various shape to the model
- Parameterized models
- Models with 2 or more physical properties
"""
#########################################################################
# Import modules
# --------------
#
from discretize import TreeMesh
from discretize.utils.meshutils import refine_tree_xyz
from SimPEG.utils import mkvc, model_builder, surface2ind_topo
from SimPEG import maps
import numpy as np
import matplotlib.pyplot as plt
# sphinx_gallery_thumbnail_number = 3
#############################################
# Defining the mesh
# -----------------
#
# Here, we create the OcTree mesh that will be used for all examples.
#
def make_example_mesh():
# Base mesh parameters
dh = 5.0 # base cell size
nbc = 32 # total width of mesh in terms of number of base mesh cells
h = dh * np.ones(nbc)
mesh = TreeMesh([h, h, h], x0="CCC")
# Refine to largest possible cell size
mesh.refine(3, finalize=False)
return mesh
def refine_topography(mesh):
# Define topography and refine
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -3 * np.exp((xx**2 + yy**2) / 60**2) + 45.0
topo = np.c_[mkvc(xx), mkvc(yy), mkvc(zz)]
mesh = refine_tree_xyz(
mesh, topo, octree_levels=[3, 2], method="surface", finalize=False
)
return mesh
def refine_box(mesh):
# Refine for sphere
xp, yp, zp = np.meshgrid([-55.0, 50.0], [-50.0, 50.0], [-40.0, 20.0])
xyz = np.c_[mkvc(xp), mkvc(yp), mkvc(zp)]
mesh = refine_tree_xyz(mesh, xyz, octree_levels=[2], method="box", finalize=False)
return mesh
#############################################
# Topography, a block and a vertical dyke
# ---------------------------------------
#
# In this example we create a model containing a block and a vertical dyke
# that strikes along the y direction. The utility *surface2ind_topo* is used
# to find the cells which lie below a set of xyz points defining a surface.
# The model consists of all cells which lie below the surface.
#
mesh = make_example_mesh()
mesh = refine_topography(mesh)
mesh = refine_box(mesh)
mesh.finalize()
background_value = 100.0
dyke_value = 40.0
block_value = 70.0
# Define surface topography as an (N, 3) np.array. You could also load a file
# containing the xyz points
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -3 * np.exp((xx**2 + yy**2) / 60**2) + 45.0
topo = np.c_[mkvc(xx), mkvc(yy), mkvc(zz)]
# Find cells below topography and define mapping
air_value = 0.0
ind_active = surface2ind_topo(mesh, topo)
model_map = maps.InjectActiveCells(mesh, ind_active, air_value)
# Define the model on subsurface cells
model = background_value * np.ones(ind_active.sum())
ind_dyke = (mesh.gridCC[ind_active, 0] > 20.0) & (mesh.gridCC[ind_active, 0] < 40.0)
model[ind_dyke] = dyke_value
ind_block = (
(mesh.gridCC[ind_active, 0] > -40.0)
& (mesh.gridCC[ind_active, 0] < -10.0)
& (mesh.gridCC[ind_active, 1] > -30.0)
& (mesh.gridCC[ind_active, 1] < 30.0)
& (mesh.gridCC[ind_active, 2] > -40.0)
& (mesh.gridCC[ind_active, 2] < 0.0)
)
model[ind_block] = block_value
# We can plot a slice of the model at Y=-2.5
fig = plt.figure(figsize=(5, 5))
ax = fig.add_subplot(111)
ind_slice = int(mesh.hy.size / 2)
mesh.plotSlice(model_map * model, normal="Y", ax=ax, ind=ind_slice, grid=True)
ax.set_title(
"Model slice at y = {} m".format(mesh.x0[1] + np.sum(mesh.hy[0:ind_slice]))
)
plt.show()
#############################################
# Combo Maps
# ----------
#
# Here we demonstrate how combo maps can be used to create a single mapping
# from the model to the mesh. In this case, our model consists of
# log-conductivity values but we want to plot the resistivity. To accomplish
# this we must take the exponent of our model values, then take the reciprocal,
# then map from below surface cell to the mesh.
#
mesh = make_example_mesh()
mesh = refine_topography(mesh)
mesh = refine_box(mesh)
mesh.finalize()
background_value = np.log(1.0 / 100.0)
dyke_value = np.log(1.0 / 40.0)
block_value = np.log(1.0 / 70.0)
# Define surface topography
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -3 * np.exp((xx**2 + yy**2) / 60**2) + 45.0
topo = np.c_[mkvc(xx), mkvc(yy), mkvc(zz)]
# Find cells below topography
air_value = 0.0
ind_active = surface2ind_topo(mesh, topo)
active_map = maps.InjectActiveCells(mesh, ind_active, air_value)
# Define the model on subsurface cells
model = background_value * np.ones(ind_active.sum())
ind_dyke = (mesh.gridCC[ind_active, 0] > 20.0) & (mesh.gridCC[ind_active, 0] < 40.0)
model[ind_dyke] = dyke_value
ind_block = (
(mesh.gridCC[ind_active, 0] > -40.0)
& (mesh.gridCC[ind_active, 0] < -10.0)
& (mesh.gridCC[ind_active, 1] > -30.0)
& (mesh.gridCC[ind_active, 1] < 30.0)
& (mesh.gridCC[ind_active, 2] > -40.0)
& (mesh.gridCC[ind_active, 2] < 0.0)
)
model[ind_block] = block_value
# Define a single mapping from model to mesh
exponential_map = maps.ExpMap()
reciprocal_map = maps.ReciprocalMap()
model_map = active_map * reciprocal_map * exponential_map
# Plot
fig = plt.figure(figsize=(5, 5))
ax = fig.add_subplot(111)
ind_slice = int(mesh.hy.size / 2)
mesh.plotSlice(model_map * model, normal="Y", ax=ax, ind=ind_slice, grid=True)
ax.set_title(
"Model slice at y = {} m".format(mesh.x0[1] + np.sum(mesh.hy[0:ind_slice]))
)
plt.show()
#############################################
# Models with arbitrary shapes
# ----------------------------
#
# Here we show how model building utilities are used to make more complicated
# structural models. The process of adding a new unit is twofold: 1) we must
# find the indicies for mesh cells that lie within the new unit, 2) we
# replace the prexisting physical property value for those cells.
#
mesh = make_example_mesh()
mesh = refine_topography(mesh)
mesh = refine_box(mesh)
mesh.finalize()
background_value = 100.0
dyke_value = 40.0
sphere_value = 70.0
# Define surface topography
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -3 * np.exp((xx**2 + yy**2) / 60**2) + 45.0
topo = np.c_[mkvc(xx), mkvc(yy), mkvc(zz)]
# Set active cells and define unit values
air_value = 0.0
ind_active = surface2ind_topo(mesh, topo)
model_map = maps.InjectActiveCells(mesh, ind_active, air_value)
# Define model for cells under the surface topography
model = background_value * np.ones(ind_active.sum())
# Add a sphere
ind_sphere = model_builder.getIndicesSphere(np.r_[-25.0, 0.0, -15.0], 20.0, mesh.gridCC)
ind_sphere = ind_sphere[ind_active] # So same size and order as model
model[ind_sphere] = sphere_value
# Add dyke defined by a set of points
xp = np.kron(np.ones((2)), [-10.0, 10.0, 55.0, 35.0])
yp = np.kron([-1000.0, 1000.0], np.ones((4)))
zp = np.kron(np.ones((2)), [-120.0, -120.0, 45.0, 45.0])
xyz_pts = np.c_[mkvc(xp), mkvc(yp), mkvc(zp)]
ind_polygon = model_builder.PolygonInd(mesh, xyz_pts)
ind_polygon = ind_polygon[ind_active] # So same size and order as model
model[ind_polygon] = dyke_value
# Plot
fig = plt.figure(figsize=(5, 5))
ax = fig.add_subplot(111)
ind_slice = int(mesh.hy.size / 2)
mesh.plotSlice(model_map * model, normal="Y", ax=ax, ind=ind_slice, grid=True)
ax.set_title(
"Model slice at y = {} m".format(mesh.x0[1] + np.sum(mesh.hy[0:ind_slice]))
)
plt.show()
#############################################
# Parameterized block model
# -------------------------
#
# Instead of defining a model value for each sub-surface cell, we can define
# the model in terms of a small number of parameters. Here we parameterize the
# model as a block in a half-space. We then create a mapping which projects
# this model onto the mesh.
#
mesh = make_example_mesh()
mesh = refine_topography(mesh)
mesh = refine_box(mesh)
mesh.finalize()
background_value = 100.0 # background value
block_value = 40.0 # block value
xc, yc, zc = -20.0, 0.0, -20.0 # center of block
dx, dy, dz = 25.0, 40.0, 30.0 # dimensions in x,y,z
# Define surface topography
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -3 * np.exp((xx**2 + yy**2) / 60**2) + 45.0
topo = np.c_[mkvc(xx), mkvc(yy), mkvc(zz)]
# Set active cells and define unit values
air_value = 0.0
ind_active = surface2ind_topo(mesh, topo)
active_map = maps.InjectActiveCells(mesh, ind_active, air_value)
# Define the model on subsurface cells
model = np.r_[background_value, block_value, xc, dx, yc, dy, zc, dz]
parametric_map = maps.ParametricBlock(mesh, indActive=ind_active, epsilon=1e-10, p=5.0)
# Define a single mapping from model to mesh
model_map = active_map * parametric_map
# Plot
fig = plt.figure(figsize=(5, 5))
ax = fig.add_subplot(111)
ind_slice = int(mesh.hy.size / 2)
mesh.plotSlice(model_map * model, normal="Y", ax=ax, ind=ind_slice, grid=True)
ax.set_title(
"Model slice at y = {} m".format(mesh.x0[1] + np.sum(mesh.hy[0:ind_slice]))
)
plt.show()
#############################################
# Using Wire Maps
# ---------------
#
# Wire maps are needed when the model is comprised of two or more parameter
# types (e.g. conductivity and magnetic permeability). Because the model
# vector contains all values for all parameter types, we need to use "wires"
# to extract the values for a particular parameter type.
#
# Here we will define a model consisting of log-conductivity values and
# magnetic permeability values. We wish to plot the conductivity and
# permeability on the mesh. Wires are used to keep track of the mapping
# between the model vector and a particular physical property type.
#
mesh = make_example_mesh()
mesh = refine_topography(mesh)
mesh = refine_box(mesh)
mesh.finalize()
background_sigma_value = np.log(100.0)
sphere_sigma_value = | np.log(70.0) | numpy.log |
ENABLE_MULTIPROCESSING = True
from dsl import cpp_trace_param_automata
def generate_public_submission():
import numpy as np
import pandas as pd
import os
import json
from pathlib import Path
import matplotlib.pyplot as plt
from matplotlib import colors
import numpy as np
from xgboost import XGBClassifier
import pdb
# data_path = Path('.')
data_path = Path('.')
if not (data_path / 'test').exists():
data_path = Path('../input/abstraction-and-reasoning-challenge')
training_path = data_path / 'training'
evaluation_path = data_path / 'evaluation'
test_path = data_path / 'test'
def plot_result(test_input, test_prediction,
input_shape):
"""
Plots the first train and test pairs of a specified task,
using same color scheme as the ARC app
"""
cmap = colors.ListedColormap(
['#000000', '#0074D9', '#FF4136', '#2ECC40', '#FFDC00',
'#AAAAAA', '#F012BE', '#FF851B', '#7FDBFF', '#870C25'])
norm = colors.Normalize(vmin=0, vmax=9)
fig, axs = plt.subplots(1, 2, figsize=(15, 15))
test_input = test_input.reshape(input_shape[0], input_shape[1])
axs[0].imshow(test_input, cmap=cmap, norm=norm)
axs[0].axis('off')
axs[0].set_title('Actual Target')
test_prediction = test_prediction.reshape(input_shape[0], input_shape[1])
axs[1].imshow(test_prediction, cmap=cmap, norm=norm)
axs[1].axis('off')
axs[1].set_title('Model Prediction')
plt.tight_layout()
plt.show()
def plot_test(test_prediction, task_name):
"""
Plots the first train and test pairs of a specified task,
using same color scheme as the ARC app
"""
cmap = colors.ListedColormap(
['#000000', '#0074D9', '#FF4136', '#2ECC40', '#FFDC00',
'#AAAAAA', '#F012BE', '#FF851B', '#7FDBFF', '#870C25'])
norm = colors.Normalize(vmin=0, vmax=9)
fig, axs = plt.subplots(1, 1, figsize=(15, 15))
axs.imshow(test_prediction, cmap=cmap, norm=norm)
axs.axis('off')
axs.set_title(f'Test Prediction {task_name}')
plt.tight_layout()
plt.show()
# https://www.kaggle.com/inversion/abstraction-and-reasoning-starter-notebook
def flattener(pred):
str_pred = str([row for row in pred])
str_pred = str_pred.replace(', ', '')
str_pred = str_pred.replace('[[', '|')
str_pred = str_pred.replace('][', '|')
str_pred = str_pred.replace(']]', '|')
return str_pred
sample_sub1 = pd.read_csv(data_path / 'sample_submission.csv')
sample_sub1 = sample_sub1.set_index('output_id')
sample_sub1.head()
def get_moore_neighbours(color, cur_row, cur_col, nrows, ncols):
if cur_row <= 0:
top = -1
else:
top = color[cur_row - 1][cur_col]
if cur_row >= nrows - 1:
bottom = -1
else:
bottom = color[cur_row + 1][cur_col]
if cur_col <= 0:
left = -1
else:
left = color[cur_row][cur_col - 1]
if cur_col >= ncols - 1:
right = -1
else:
right = color[cur_row][cur_col + 1]
return top, bottom, left, right
def get_tl_tr(color, cur_row, cur_col, nrows, ncols):
if cur_row == 0:
top_left = -1
top_right = -1
else:
if cur_col == 0:
top_left = -1
else:
top_left = color[cur_row - 1][cur_col - 1]
if cur_col == ncols - 1:
top_right = -1
else:
top_right = color[cur_row - 1][cur_col + 1]
return top_left, top_right
def make_features(input_color, nfeat):
nrows, ncols = input_color.shape
feat = np.zeros((nrows * ncols, nfeat))
cur_idx = 0
for i in range(nrows):
for j in range(ncols):
feat[cur_idx, 0] = i
feat[cur_idx, 1] = j
feat[cur_idx, 2] = input_color[i][j]
feat[cur_idx, 3:7] = get_moore_neighbours(input_color, i, j, nrows, ncols)
feat[cur_idx, 7:9] = get_tl_tr(input_color, i, j, nrows, ncols)
feat[cur_idx, 9] = len(np.unique(input_color[i, :]))
feat[cur_idx, 10] = len(np.unique(input_color[:, j]))
feat[cur_idx, 11] = (i + j)
feat[cur_idx, 12] = len(np.unique(input_color[i - local_neighb:i + local_neighb,
j - local_neighb:j + local_neighb]))
cur_idx += 1
return feat
def features(task, mode='train'):
num_train_pairs = len(task[mode])
feat, target = [], []
global local_neighb
for task_num in range(num_train_pairs):
input_color = np.array(task[mode][task_num]['input'])
target_color = task[mode][task_num]['output']
nrows, ncols = len(task[mode][task_num]['input']), len(task[mode][task_num]['input'][0])
target_rows, target_cols = len(task[mode][task_num]['output']), len(task[mode][task_num]['output'][0])
if (target_rows != nrows) or (target_cols != ncols):
print('Number of input rows:', nrows, 'cols:', ncols)
print('Number of target rows:', target_rows, 'cols:', target_cols)
not_valid = 1
return None, None, 1
imsize = nrows * ncols
# offset = imsize*task_num*3 #since we are using three types of aug
feat.extend(make_features(input_color, nfeat))
target.extend(np.array(target_color).reshape(-1, ))
return np.array(feat), np.array(target), 0
# mode = 'eval'
mode = 'test'
if mode == 'eval':
task_path = evaluation_path
elif mode == 'train':
task_path = training_path
elif mode == 'test':
task_path = test_path
all_task_ids = sorted(os.listdir(task_path))
nfeat = 13
local_neighb = 5
valid_scores = {}
model_accuracies = {'ens': []}
pred_taskids = []
for task_id in all_task_ids:
task_file = str(task_path / task_id)
with open(task_file, 'r') as f:
task = json.load(f)
feat, target, not_valid = features(task)
if not_valid:
print('ignoring task', task_file)
print()
not_valid = 0
continue
xgb = XGBClassifier(n_estimators=10, n_jobs=-1)
xgb.fit(feat, target, verbose=-1)
# training on input pairs is done.
# test predictions begins here
num_test_pairs = len(task['test'])
for task_num in range(num_test_pairs):
cur_idx = 0
input_color = np.array(task['test'][task_num]['input'])
nrows, ncols = len(task['test'][task_num]['input']), len(
task['test'][task_num]['input'][0])
feat = make_features(input_color, nfeat)
print('Made predictions for ', task_id[:-5])
preds = xgb.predict(feat).reshape(nrows, ncols)
if (mode == 'train') or (mode == 'eval'):
ens_acc = (np.array(task['test'][task_num]['output']) == preds).sum() / (nrows * ncols)
model_accuracies['ens'].append(ens_acc)
pred_taskids.append(f'{task_id[:-5]}_{task_num}')
# print('ensemble accuracy',(np.array(task['test'][task_num]['output'])==preds).sum()/(nrows*ncols))
# print()
preds = preds.astype(int).tolist()
# plot_test(preds, task_id)
sample_sub1.loc[f'{task_id[:-5]}_{task_num}',
'output'] = flattener(preds)
if (mode == 'train') or (mode == 'eval'):
df = pd.DataFrame(model_accuracies, index=pred_taskids)
print(df.head(10))
print(df.describe())
for c in df.columns:
print(f'for {c} no. of complete tasks is', (df.loc[:, c] == 1).sum())
df.to_csv('ens_acc.csv')
sample_sub1.head()
training_path = data_path / 'training'
evaluation_path = data_path / 'evaluation'
test_path = data_path / 'test'
training_tasks = sorted(os.listdir(training_path))
eval_tasks = sorted(os.listdir(evaluation_path))
T = training_tasks
Trains = []
for i in range(400):
task_file = str(training_path / T[i])
task = json.load(open(task_file, 'r'))
Trains.append(task)
E = eval_tasks
Evals = []
for i in range(400):
task_file = str(evaluation_path / E[i])
task = json.load(open(task_file, 'r'))
Evals.append(task)
cmap = colors.ListedColormap(
['#000000', '#0074D9', '#FF4136', '#2ECC40', '#FFDC00',
'#AAAAAA', '#F012BE', '#FF851B', '#7FDBFF', '#870C25'])
norm = colors.Normalize(vmin=0, vmax=9)
# 0:black, 1:blue, 2:red, 3:greed, 4:yellow,
# 5:gray, 6:magenta, 7:orange, 8:sky, 9:brown
plt.figure(figsize=(5, 2), dpi=200)
plt.imshow([list(range(10))], cmap=cmap, norm=norm)
plt.xticks(list(range(10)))
plt.yticks([])
# plt.show()
def plot_task(task):
n = len(task["train"]) + len(task["test"])
fig, axs = plt.subplots(2, n, figsize=(4 * n, 8), dpi=50)
plt.subplots_adjust(wspace=0, hspace=0)
fig_num = 0
for i, t in enumerate(task["train"]):
t_in, t_out = np.array(t["input"]), np.array(t["output"])
axs[0][fig_num].imshow(t_in, cmap=cmap, norm=norm)
axs[0][fig_num].set_title(f'Train-{i} in')
axs[0][fig_num].set_yticks(list(range(t_in.shape[0])))
axs[0][fig_num].set_xticks(list(range(t_in.shape[1])))
axs[1][fig_num].imshow(t_out, cmap=cmap, norm=norm)
axs[1][fig_num].set_title(f'Train-{i} out')
axs[1][fig_num].set_yticks(list(range(t_out.shape[0])))
axs[1][fig_num].set_xticks(list(range(t_out.shape[1])))
fig_num += 1
for i, t in enumerate(task["test"]):
t_in, t_out = np.array(t["input"]), np.array(t["output"])
axs[0][fig_num].imshow(t_in, cmap=cmap, norm=norm)
axs[0][fig_num].set_title(f'Test-{i} in')
axs[0][fig_num].set_yticks(list(range(t_in.shape[0])))
axs[0][fig_num].set_xticks(list(range(t_in.shape[1])))
axs[1][fig_num].imshow(t_out, cmap=cmap, norm=norm)
axs[1][fig_num].set_title(f'Test-{i} out')
axs[1][fig_num].set_yticks(list(range(t_out.shape[0])))
axs[1][fig_num].set_xticks(list(range(t_out.shape[1])))
fig_num += 1
plt.tight_layout()
plt.show()
def plot_picture(x):
plt.imshow(np.array(x), cmap=cmap, norm=norm)
plt.show()
def Defensive_Copy(A):
n = len(A)
k = len(A[0])
L = np.zeros((n, k), dtype=int)
for i in range(n):
for j in range(k):
L[i, j] = 0 + A[i][j]
return L.tolist()
def Create(task, task_id=0):
n = len(task['train'])
Input = [Defensive_Copy(task['train'][i]['input']) for i in range(n)]
Output = [Defensive_Copy(task['train'][i]['output']) for i in range(n)]
Input.append(Defensive_Copy(task['test'][task_id]['input']))
return Input, Output
def Recolor(task):
Input = task[0]
Output = task[1]
Test_Picture = Input[-1]
Input = Input[:-1]
N = len(Input)
for x, y in zip(Input, Output):
if len(x) != len(y) or len(x[0]) != len(y[0]):
return -1
Best_Dict = -1
Best_Q1 = -1
Best_Q2 = -1
Best_v = -1
# v ranges from 0 to 3. This gives an extra flexibility of measuring distance from any of the 4 corners
Pairs = []
for t in range(15):
for Q1 in range(1, 8):
for Q2 in range(1, 8):
if Q1 + Q2 == t:
Pairs.append((Q1, Q2))
for Q1, Q2 in Pairs:
for v in range(4):
if Best_Dict != -1:
continue
possible = True
Dict = {}
for x, y in zip(Input, Output):
n = len(x)
k = len(x[0])
for i in range(n):
for j in range(k):
if v == 0 or v == 2:
p1 = i % Q1
else:
p1 = (n - 1 - i) % Q1
if v == 0 or v == 3:
p2 = j % Q2
else:
p2 = (k - 1 - j) % Q2
color1 = x[i][j]
color2 = y[i][j]
if color1 != color2:
rule = (p1, p2, color1)
if rule not in Dict:
Dict[rule] = color2
elif Dict[rule] != color2:
possible = False
if possible:
# Let's see if we actually solve the problem
for x, y in zip(Input, Output):
n = len(x)
k = len(x[0])
for i in range(n):
for j in range(k):
if v == 0 or v == 2:
p1 = i % Q1
else:
p1 = (n - 1 - i) % Q1
if v == 0 or v == 3:
p2 = j % Q2
else:
p2 = (k - 1 - j) % Q2
color1 = x[i][j]
rule = (p1, p2, color1)
if rule in Dict:
color2 = 0 + Dict[rule]
else:
color2 = 0 + y[i][j]
if color2 != y[i][j]:
possible = False
if possible:
Best_Dict = Dict
Best_Q1 = Q1
Best_Q2 = Q2
Best_v = v
if Best_Dict == -1:
return -1 # meaning that we didn't find a rule that works for the traning cases
# Otherwise there is a rule: so let's use it:
n = len(Test_Picture)
k = len(Test_Picture[0])
answer = np.zeros((n, k), dtype=int)
for i in range(n):
for j in range(k):
if Best_v == 0 or Best_v == 2:
p1 = i % Best_Q1
else:
p1 = (n - 1 - i) % Best_Q1
if Best_v == 0 or Best_v == 3:
p2 = j % Best_Q2
else:
p2 = (k - 1 - j) % Best_Q2
color1 = Test_Picture[i][j]
rule = (p1, p2, color1)
if (p1, p2, color1) in Best_Dict:
answer[i][j] = 0 + Best_Dict[rule]
else:
answer[i][j] = 0 + color1
return answer.tolist()
sample_sub2 = pd.read_csv(data_path / 'sample_submission.csv')
sample_sub2.head()
def flattener(pred):
str_pred = str([row for row in pred])
str_pred = str_pred.replace(', ', '')
str_pred = str_pred.replace('[[', '|')
str_pred = str_pred.replace('][', '|')
str_pred = str_pred.replace(']]', '|')
return str_pred
example_grid = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
# display(example_grid)
print(flattener(example_grid))
Solved = []
Problems = sample_sub2['output_id'].values
Proposed_Answers = []
test_paths_my = {task.stem: json.load(task.open()) for task in test_path.iterdir()}
test_task_ids = np.sort(list(test_paths_my.keys()))
print(Problems, len(Problems))
task_number_my = dict(zip(test_task_ids, np.arange(100)))
for i in range(len(Problems)):
output_id = Problems[i]
task_id = output_id.split('_')[0]
pair_id = int(output_id.split('_')[1])
f = str(test_path / str(task_id + '.json'))
with open(f, 'r') as read_file:
task = json.load(read_file)
n = len(task['train'])
Input = [Defensive_Copy(task['train'][j]['input']) for j in range(n)]
Output = [Defensive_Copy(task['train'][j]['output']) for j in range(n)]
Input.append(Defensive_Copy(task['test'][pair_id]['input']))
solution = Recolor([Input, Output])
pred = ''
if solution != -1:
Solved.append(i)
pred1 = flattener(solution)
pred = pred + pred1 + ' '
if pred == '':
pred = flattener(example_grid)
Proposed_Answers.append(pred)
sample_sub2['output'] = Proposed_Answers
sample_sub1 = sample_sub1.reset_index()
sample_sub1 = sample_sub1.sort_values(by="output_id")
sample_sub2 = sample_sub2.sort_values(by="output_id")
out1 = sample_sub1["output"].astype(str).values
out2 = sample_sub2["output"].astype(str).values
merge_output = []
for o1, o2 in zip(out1, out2):
o = o1.strip().split(" ")[:1] + o2.strip().split(" ")[:2]
o = " ".join(o[:3])
merge_output.append(o)
sample_sub1["output"] = merge_output
sample_sub1["output"] = sample_sub1["output"].astype(str)
# test_paths_my = { task.stem: json.load(task.open()) for task in test_path.iterdir() }
# test_task_ids = np.sort(list(test_paths_my.keys()))
# task_number_my = dict(zip(test_task_ids, np.arange(100)))
submission = sample_sub1.copy()
submission.to_csv("public_submission.csv", index=False)
#generate_public_submission()
import numpy as np
from tqdm.notebook import tqdm
from PIL import Image, ImageDraw
import time
from collections import defaultdict
import os
import json
import random
import copy
import networkx as nx
from pathlib import Path
import matplotlib.colors as colors
import matplotlib.pyplot as plt
from itertools import product
import pandas as pd
import multiprocessing
import subprocess
# from moviepy.editor import ImageSequenceClip
# from moviepy.editor import clips_array, CompositeVideoClip
# from moviepy.video.io.html_tools import html_embed, HTML2
# def display_vid(vid, verbose=False, **html_kw):
# """
# Display a moviepy video clip, useful for removing loadbars
# """
# rd_kwargs = {
# 'fps': 10, 'verbose': verbose
# }
# if not verbose:
# rd_kwargs['logger'] = None
# return HTML2(html_embed(vid, filetype=None, maxduration=60,
# center=True, rd_kwargs=rd_kwargs, **html_kw))
data_path = Path('../input/abstraction-and-reasoning-challenge/')
# data_path = Path('.') # Artyom: it's better use symlinks locally
cmap_lookup = [
'#000000', '#0074D9', '#FF4136', '#2ECC40', '#FFDC00',
'#AAAAAA', '#F012BE', '#FF851B', '#7FDBFF', '#870C25'
]
cmap_lookup = [np.array([int(x[1:3], 16), int(x[3:5], 16), int(x[5:], 16)]) for x in cmap_lookup]
def cmap(x):
"""
Translate a task matrix to a color coded version
arguments
x : a h x w task matrix
returns
a h x w x 3 matrix with colors instead of numbers
"""
y = np.zeros((*x.shape, 3))
y[x < 0, :] = np.array([112, 128, 144])
y[x > 9, :] = np.array([255, 248, 220])
for i, c in enumerate(cmap_lookup):
y[x == i, :] = c
return y
def draw_one(x, k=20):
"""
Create a PIL image from a task matrix, the task will be
drawn using the default color coding with grid lines
arguments
x : a task matrix
k = 20 : an up scaling factor
returns
a PIL image
"""
img = Image.fromarray(cmap(x).astype(np.uint8)).resize((x.shape[1] * k, x.shape[0] * k), Image.NEAREST)
draw = ImageDraw.Draw(img)
for i in range(x.shape[0]):
draw.line((0, i * k, img.width, i * k), fill=(80, 80, 80), width=1)
for j in range(x.shape[1]):
draw.line((j * k, 0, j * k, img.height), fill=(80, 80, 80), width=1)
return img
def vcat_imgs(imgs, border=10):
"""
Concatenate images vertically
arguments:
imgs : an array of PIL images
border = 10 : the size of space between images
returns:
a PIL image
"""
h = max(img.height for img in imgs)
w = sum(img.width for img in imgs)
res_img = Image.new('RGB', (w + border * (len(imgs) - 1), h), color=(255, 255, 255))
offset = 0
for img in imgs:
res_img.paste(img, (offset, 0))
offset += img.width + border
return res_img
def plot_task(task):
n = len(task["train"]) + len(task["test"])
fig, axs = plt.subplots(2, n, figsize=(n * 4, 8))
plt.subplots_adjust(wspace=0, hspace=0)
fig_num = 0
def go(ax, title, x):
ax.imshow(draw_one(x), interpolation='nearest')
ax.set_title(title)
ax.set_yticks([])
ax.set_xticks([])
for i, t in enumerate(task["train"]):
go(axs[0][fig_num], f'Train-{i} in', t["input"])
go(axs[1][fig_num], f'Train-{i} out', t["output"])
fig_num += 1
for i, t in enumerate(task["test"]):
go(axs[0][fig_num], f'Test-{i} in', t["input"])
try:
go(axs[1][fig_num], f'Test-{i} out', t["output"])
except:
go(axs[1][fig_num], f'Test-{i} out', np.zeros_like(t["input"]))
fig_num += 1
plt.tight_layout()
plt.show()
def real_trace_param_automata(input, params, n_iter, n_hidden):
"""
Execute an automata and return all the intermediate states
arguments:
step_fn : transition rule function, should take two arguments `input` and `hidden_i`,
should return an output grid an a new hidden hidden grid
n_iter : num of iteration to perform
n_hidden: number of hidden grids, if set to 0 `hidden_i` will be set to None
laodbar = True: weather display loadbars
returns:
an array of tuples if output and hidden grids
"""
# hidden = np.zeros((n_hidden, *input.shape)) if n_hidden > 0 else None
#
# global_rules, ca_rules = params
#
# trace = [(input, hidden)]
#
# for rule in global_rules:
#
# output, hidden = apply_rule(input, hidden, rule)
# trace.append((output, hidden))
# input = output
#
# its = range(n_iter)
#
# for i_it in its:
# output, hidden = compute_parametrized_automata(input, hidden, ca_rules)
# trace.append((output, hidden))
#
# if (input.shape == output.shape) and (output == input).all():
# break
# input = output
hidden = np.zeros((n_hidden, *input.shape)) if n_hidden > 0 else None
global_rules, ca_rules, split_rule, merge_rule = params
grids = apply_split_rule(input, hidden, split_rule)
#print(grids[0][0])
for rule in global_rules:
for i, (inp, hid) in enumerate(grids):
if rule['macro_type'] == 'global_rule':
if rule['apply_to'] == 'all' or \
(rule['apply_to'] == 'index' and i == rule['apply_to_index']%len(grids) or
(rule['apply_to'] == 'last' and i == len(grids) - 1)):
grids[i] = apply_rule(inp, hid, rule)
elif rule['macro_type'] == 'global_interaction_rule':
grids = apply_interaction_rule(grids, rule)
#print(grids[0][0])
#1/0
for i, (input, hidden) in enumerate(grids):
for _ in range(n_iter):
output, hidden = compute_parametrized_automata(input, hidden, ca_rules)
if np.array_equal(input, output):
break
input = output
grids[i] = (output, hidden)
output = apply_merge_rule(grids, merge_rule, split_rule)
return output
def apply_interaction_rule(grids, rule):
if rule['type'] == 'align_pattern':
# index_from = rule['index_from'] % len(grids)
# index_to = rule['index_to'] % len(grids)
# allow_rotation = rule['allow_rotation']
if len(grids) > 5:
return grids
for index_from in range(len(grids)):
for index_to in range(index_from+1, len(grids)):
input_i = grids[index_from][0]
input_j = grids[index_to][0]
# print(np.max(input_i>0, axis=1))
# print(np.max(input_i>0, axis=1).shape)
# print(np.arange(input_i.shape[0]).shape)
#1/0
i_nonzero_rows = np.arange(input_i.shape[0])[np.max(input_i>0, axis=1)]
i_nonzero_columns = np.arange(input_i.shape[1])[np.max(input_i>0, axis=0)]
j_nonzero_rows = np.arange(input_j.shape[0])[np.max(input_j>0, axis=1)]
j_nonzero_columns = np.arange(input_j.shape[1])[np.max(input_j>0, axis=0)]
if i_nonzero_rows.shape[0] == 0 or i_nonzero_columns.shape[0] == 0 or \
j_nonzero_rows.shape[0] == 0 or j_nonzero_columns.shape[0] == 0:
continue
i_minrow = np.min(i_nonzero_rows)
i_mincol = np.min(i_nonzero_columns)
i_maxrow = np.max(i_nonzero_rows) + 1
i_maxcol = np.max(i_nonzero_columns) + 1
j_minrow = np.min(j_nonzero_rows)
j_mincol = np.min(j_nonzero_columns)
j_maxrow = np.max(j_nonzero_rows) + 1
j_maxcol = np.max(j_nonzero_columns) + 1
figure_to_align = input_i[i_minrow:i_maxrow, i_mincol:i_maxcol]
figure_target = input_j[j_minrow:j_maxrow, j_mincol:j_maxcol]
best_fit = 0
best_i_fit, best_j_fit = -1, -1
#print(figure_to_align)
#print(figure_target)
if figure_to_align.shape[0] < figure_target.shape[0] or figure_to_align.shape[1] < figure_target.shape[1]:
continue
#1/0
else:
for i_start in range((figure_to_align.shape[0] - figure_target.shape[0])+1):
for j_start in range((figure_to_align.shape[1] - figure_target.shape[1])+1):
fig_1 = figure_to_align[i_start:(i_start + figure_target.shape[0]), j_start:(j_start + figure_target.shape[1])]
if np.logical_and(np.logical_and(figure_target > 0, figure_target!=rule['allow_color']), figure_target != fig_1).any():
continue
fit = np.sum(figure_target==fig_1)
if fit > best_fit:
best_i_fit, best_j_fit = i_start, j_start
best_fit = fit
if best_fit == 0:
continue
imin = j_minrow-best_i_fit
imax = j_minrow-best_i_fit + figure_to_align.shape[0]
jmin = j_mincol - best_j_fit
jmax = j_mincol - best_j_fit + figure_to_align.shape[1]
begin_i = max(imin, 0)
begin_j = max(jmin, 0)
end_i = min(imax, input_j.shape[0])
end_j = min(jmax, input_j.shape[1])
i_fig_begin = (begin_i-imin)
i_fig_end = figure_to_align.shape[0]-(imax-end_i)
j_fig_begin = (begin_j-jmin)
j_fig_end = figure_to_align.shape[1]-(jmax-end_j)
if rule['fill_with_color'] == 0:
input_j[begin_i:end_i, begin_j:end_j] = figure_to_align[i_fig_begin:i_fig_end, j_fig_begin:j_fig_end]
else:
for i, j in product(range(end_i-begin_i + 1), range(end_j-begin_j + 1)):
if input_j[begin_i + i, begin_j + j] == 0:
input_j[begin_i + i, begin_j + j] = rule['fill_with_color'] * (figure_to_align[i_fig_begin + i, j_fig_begin + j])
return grids
def trace_param_automata(input, params, n_iter, n_hidden):
# expected = real_trace_param_automata(input, params, n_iter, n_hidden)
#
# testcase = {'input': input, 'params': params}
# print(str(testcase).replace('\'', '"').replace('array(', '').replace(')', ''))
output = cpp_trace_param_automata(input, params, n_iter)
# if not np.array_equal(expected, output):
# print('cpp result is wrong')
# print('input:')
# print(input)
# print('expected:')
# print(expected)
# print('got:')
# print(output)
#
# diff = [[str(g) if e != g else '-' for e, g in zip(exp_row, got_row)]
# for exp_row, got_row in zip(expected, output)]
# diff_lines = [' '.join(line) for line in diff]
# diff_str = '[[' + ']\n ['.join(diff_lines)
#
# print('diff:')
# print(diff_str)
# print('rules')
# print(params)
#
# assert False
return [[output]]
# def vis_automata_trace(states, loadbar=False, prefix_image=None):
# """
# Create a video from an array of automata states
#
# arguments:
# states : array of automata steps, returned by `trace_automata()`
# loadbar = True: weather display loadbars
# prefix_image = None: image to add to the beginning of each frame
# returns
# a moviepy ImageSequenceClip
# """
# frames = []
# if loadbar:
# states = tqdm(states, desc='Frame')
# for i, (canvas, hidden) in enumerate(states):
#
# frame = []
# if prefix_image is not None:
# frame.append(prefix_image)
# frame.append(draw_one(canvas))
# frames.append(vcat_imgs(frame))
#
# return ImageSequenceClip(list(map(np.array, frames)), fps=10)
# def vis_automata_paramed_task(tasks, parameters, n_iter, n_hidden, vis_only_ix=None):
# """
# Visualize the automata steps during the task solution
# arguments:
# tasks : the task to be solved by the automata
# step_fn : automata transition function as passed to `trace_automata()`
# n_iter : number of iterations to perform
# n_hidden : number of hidden girds
# """
#
# n_vis = 0
#
# def go(task, n_vis, test=False):
#
# if vis_only_ix is not None and vis_only_ix != n_vis:
# return
# trace = trace_param_automata(task['input'], parameters, n_iter, n_hidden)
# if not test:
# vid = vis_automata_trace(trace, prefix_image=draw_one(task['output']))
# else:
# vid = vis_automata_trace(trace, prefix_image=draw_one(np.zeros_like(task['input'])))
#
# # display(display_vid(vid))
#
# for task in (tasks['train']):
# n_vis += 1
# go(task, n_vis)
#
# for task in (tasks['test']):
# n_vis += 1
# go(task, n_vis, True)
training_path = data_path / 'training'
evaluation_path = data_path / 'evaluation'
test_path = data_path / 'test'
training_tasks = sorted(os.listdir(training_path))
evaluation_tasks = sorted(os.listdir(evaluation_path))
test_tasks = sorted(os.listdir(test_path))
def load_data(p, phase=None):
"""
Load task data
"""
if phase in {'training', 'test', 'evaluation'}:
p = data_path / phase / p
task = json.loads(Path(p).read_text())
dict_vals_to_np = lambda x: {k: np.array(v) for k, v in x.items()}
assert set(task) == {'test', 'train'}
res = dict(test=[], train=[])
for t in task['train']:
assert set(t) == {'input', 'output'}
res['train'].append(dict_vals_to_np(t))
for t in task['test']:
if phase == 'test':
assert set(t) == {'input'}
else:
assert set(t) == {'input', 'output'}
res['test'].append(dict_vals_to_np(t))
return res
nbh = lambda x, i, j: {
(ip, jp) : x[i+ip, j+jp]
for ip, jp in product([1, -1, 0], repeat=2)
if 0 <= i+ip < x.shape[0] and 0 <= j+jp < x.shape[1] and (not (ip==0 and jp==0))
}
def get_random_split_rule(all_colors, best_candidates={}, temp=0, config={}, r_type=None):
rule = {}
rule['type'] = random.choice(['nothing', 'color_figures', 'figures', 'macro_multiply'])
if rule['type'] in ['color_figures', 'figures']:
rule['sort'] = random.choice(['biggest', 'smallest'])
if rule['type'] == 'macro_multiply':
rule['k1'] = np.random.randint(config['mink1'], config['maxk1']+1)
rule['k2'] = np.random.randint(config['mink2'], config['maxk2']+1)
return rule
def get_random_merge_rule(all_colors, best_candidates={}, temp=0, config={}, r_type=None):
rule = {}
rule['type'] = random.choice(['cellwise_or', 'output_first', 'output_last'])
return rule
def apply_split_rule(input, hidden, split_rule):
if split_rule['type'] == 'nothing':
return [(input, hidden)]
if split_rule['type'] == 'macro_multiply':
ks = split_rule['k1'] * split_rule['k2']
grids = [(np.copy(input), np.copy(hidden)) for _ in range(ks)]
return grids
#split_rule['type'] = 'figures'
dif_c_edge = split_rule['type'] == 'figures'
communities = get_connectivity_info(input, ignore_black=True, edge_for_difcolors=dif_c_edge)
if len(communities) > 0:
if split_rule['sort'] == 'biggest':
communities = communities[::-1]
grids = [(np.zeros_like(input), np.zeros_like(hidden)) for _ in range(len(communities))]
for i in range(len(communities)):
for point in communities[i]:
grids[i][0][point] = input[point]
else:
grids = [(input, hidden)]
return grids
def apply_merge_rule(grids, merge_rule, split_rule):
if split_rule['type'] == 'macro_multiply':
shape_base = grids[0][0].shape
shapes = [arr[0].shape for arr in grids]
if not np.array([shape_base == sh for sh in shapes]).all():
return np.zeros((1, 1), dtype=np.int)
ks_1 = split_rule['k1']
ks_2 = split_rule['k2']
output = np.zeros((shape_base[0] * ks_1, shape_base[1] * ks_2), dtype=np.int8)
for k1 in range(ks_1):
for k2 in range(ks_2):
output[(k1*shape_base[0]):((k1+1) * shape_base[0]), (k2*shape_base[1]):((k2+1) * shape_base[1])] = grids[k1*ks_2 + k2][0]
return output
if merge_rule['type'] == 'cellwise_or':
output = np.zeros_like(grids[0][0])
for i in np.arange(len(grids))[::-1]:
if grids[i][0].shape == output.shape:
output[grids[i][0]>0] = grids[i][0][grids[i][0]>0]
return output
elif merge_rule['type'] == 'output_first':
output = grids[0][0]
elif merge_rule['type'] == 'output_last':
output = grids[-1][0]
return output
def get_random_ca_rule(all_colors, best_candidates={}, temp=0, config={}, r_type=None):
types_possible = \
[
'copy_color_by_direction',
'direct_check',
'indirect_check',
'nbh_check',
'corner_check',
'color_distribution',
]
ca_rules = []
best_candidates_items = list(best_candidates.items())
if len(best_candidates_items) > 0:
for best_score, best_candidates_score in best_candidates_items:
for best_c in best_candidates_score:
gl, ca, _, _ = best_c
ca_rules += [c['type'] for c in ca]
type_counts = dict(zip(types_possible, np.zeros(len(types_possible))))
rules, counts = np.unique(ca_rules, return_counts=True)
for i in range(rules.shape[0]):
type_counts[rules[i]] += counts[i]
counts = np.array(list(type_counts.values()))
if np.sum(counts) > 0:
counts /= np.sum(counts)
else:
counts = np.ones(counts.shape[0]) / counts.shape[0]
uniform = np.ones(counts.shape[0]) / counts.shape[0]
probs = temp * counts + (1 - temp) * uniform
else:
probs = np.ones(len(types_possible)) / len(types_possible)
colors = all_colors[1:]
type_probs = np.ones(len(types_possible)) / len(types_possible)
if r_type is None:
random_type = types_possible[np.random.choice(len(types_possible), p=probs)]
else:
random_type = r_type
def get_random_out_color():
possible_colors = config['possible_colors_out']
return np.random.choice(possible_colors)
def get_random_ignore_colors():
if config['possible_ignore_colors'].shape[0] > 0:
possible_colors = config['possible_ignore_colors']
return possible_colors[np.random.randint(2, size=possible_colors.shape[0]) == 1]
else:
return []
def get_random_all_colors():
return all_colors[np.random.randint(2, size=all_colors.shape[0]) == 1]
def get_random_colors():
return get_random_all_colors()
def get_random_all_color():
return np.random.choice(all_colors)
def get_random_color():
return get_random_all_color()
rule = {}
rule['type'] = random_type
rule['macro_type'] = 'ca_rule'
rule['ignore_colors'] = list(config['ignore_colors'])
if np.random.rand() < 0.5 and config['possible_ignore_colors'].shape[0]:
rule['ignore_colors'] += [random.choice(config['possible_ignore_colors'])]
if random_type == 'copy_color_by_direction':
rule['direction'] = random.choice(['everywhere'])
rule['copy_color'] = [get_random_out_color()]
rule['look_back_color'] = rule['copy_color'][0]
elif random_type == 'corner_check':
if np.random.rand() < 0.5:
rule['nbh_check_colors'] = [get_random_all_color()]
else:
rule['nbh_check_colors'] = list(np.unique([get_random_all_color(), get_random_all_color()]))
rule['nbh_check_out'] = get_random_out_color()
rule['ignore_colors'] = list(np.unique(rule['ignore_colors'] + [rule['nbh_check_out']]))
elif random_type == 'direct_check':
rule['nbh_check_sum'] = np.random.randint(4)
if np.random.rand() < 0.5:
rule['nbh_check_colors'] = [get_random_all_color()]
else:
rule['nbh_check_colors'] = list(np.unique([get_random_all_color(), get_random_all_color()]))
rule['nbh_check_out'] = get_random_out_color()
rule['ignore_colors'] = list(np.unique(rule['ignore_colors'] + [rule['nbh_check_out']]))
elif random_type == 'indirect_check':
rule['nbh_check_sum'] = np.random.randint(4)
if np.random.rand() < 0.5:
rule['nbh_check_colors'] = [get_random_all_color()]
else:
rule['nbh_check_colors'] = list(np.unique([get_random_all_color(), get_random_all_color()]))
rule['nbh_check_out'] = get_random_out_color()
rule['ignore_colors'] = list(np.unique(rule['ignore_colors'] + [rule['nbh_check_out']]))
elif random_type == 'nbh_check':
rule['nbh_check_sum'] = np.random.randint(8)
if np.random.rand() < 0.5:
rule['nbh_check_colors'] = [get_random_all_color()]
else:
rule['nbh_check_colors'] = list(np.unique([get_random_all_color(), get_random_all_color()]))
rule['nbh_check_out'] = get_random_out_color()
rule['ignore_colors'] = list(np.unique(rule['ignore_colors'] + [rule['nbh_check_out']]))
elif random_type == 'color_distribution':
rule['direction'] = random.choice(
['top', 'bottom', 'left', 'right', 'top_left', 'bottom_left', 'top_right', 'bottom_right'])
rule['check_in_empty'] = np.random.randint(2)
rule['color_out'] = get_random_out_color()
if rule['check_in_empty'] == 0:
rule['color_in'] = rule['color_out']
else:
rule['color_in'] = get_random_all_color()
rule['ignore_colors'] = list(np.unique(rule['ignore_colors'] + [rule['color_out']]))
return rule
def get_random_global_rule(all_colors, best_candidates={}, temp=0, config={}, r_type=None):
types_possible = \
[
'distribute_colors',
'unity',
'color_for_inners',
'map_color',
'draw_lines',
'draw_line_to',
'gravity',
'make_holes',
'distribute_from_border',
'align_pattern',
'rotate',
'flip'
]
if config['allow_make_smaller']:
types_possible += \
[
'crop_empty',
'crop_figure',
'split_by_H',
'split_by_W',
'reduce'
]
# if config['allow_make_bigger']:
# types_possible += \
# [
# 'macro_multiply_by',
# 'micro_multiply_by',
# 'macro_multiply_k',
# ]
gl_rules = []
best_candidates_items = list(best_candidates.items())
if len(best_candidates_items) > 0:
for best_score, best_candidates_score in best_candidates_items:
for best_c in best_candidates_score:
gl, ca, _, _ = best_c
gl_rules += [c['type'] for c in gl]
type_counts = dict(zip(types_possible, np.zeros(len(types_possible))))
rules, counts = np.unique(gl_rules, return_counts=True)
for i in range(rules.shape[0]):
type_counts[rules[i]] += counts[i]
counts = np.array(list(type_counts.values()))
if np.sum(counts) > 0:
counts /= np.sum(counts)
else:
counts = np.ones(counts.shape[0]) / counts.shape[0]
uniform = np.ones(counts.shape[0]) / counts.shape[0]
probs = temp * counts + (1 - temp) * uniform
else:
probs = np.ones(len(types_possible)) / len(types_possible)
colors = all_colors[1:]
type_probs = np.ones(len(types_possible)) / len(types_possible)
if r_type is None:
random_type = types_possible[np.random.choice(len(types_possible), p=probs)]
else:
random_type = r_type
def get_random_all_colors():
return all_colors[np.random.randint(2, size=all_colors.shape[0]) == 1]
def get_random_colors():
return all_colors[np.random.randint(2, size=all_colors.shape[0]) == 1]
def get_random_all_color():
return np.random.choice(all_colors)
def get_random_color():
return get_random_all_color()
def get_random_out_color():
possible_colors = config['possible_colors_out']
return np.random.choice(possible_colors)
rule = {}
rule['type'] = random_type
rule['macro_type'] = 'global_rule'
rule['apply_to'] = random.choice(['all', 'index'])
if np.random.rand()<0.2:
rule['apply_to'] = 'last'
if rule['apply_to'] == 'index':
rule['apply_to_index'] = np.random.choice(10)
if random_type == 'macro_multiply_k':
rule['k'] = (np.random.randint(1, 4), np.random.randint(1, 4))
elif random_type == 'flip':
rule['how'] = random.choice(['ver', 'hor'])
elif random_type == 'rotate':
rule['rotations_count'] = np.random.randint(1, 4)
elif random_type == 'micro_multiply_by':
rule['how_many'] = random.choice([2, 3, 4, 5, 'size'])
elif random_type == 'macro_multiply_by':
rule['how_many'] = random.choice(['both', 'hor', 'ver'])
rule['rotates'] = [np.random.randint(1) for _ in range(4)]
rule['flips'] = [random.choice(['hor', 'ver', 'horver', 'no']) for _ in range(4)]
elif random_type == 'distribute_from_border':
rule['colors'] = list(np.unique([get_random_out_color(), get_random_all_color()]))
elif random_type == 'draw_lines':
rule['direction'] = random.choice(['everywhere', 'horizontal', 'vertical', 'horver', 'diagonal'])
# 'top', 'bottom', 'left', 'right',
# 'top_left', 'bottom_left', 'top_right', 'bottom_right'])
rule['not_stop_by_color'] = 0 # get_random_all_color()
rule['start_by_color'] = get_random_all_color()
rule['with_color'] = get_random_out_color()
elif random_type == 'reduce':
rule['skip_color'] = get_random_all_color()
elif random_type == 'draw_line_to':
#rule['direction_type'] = random.choice(['border'])
rule['direction_color'] = get_random_all_color()
rule['not_stop_by_color'] = 0
if np.random.rand() < 0.5:
rule['not_stop_by_color_and_skip'] = get_random_all_color()
else:
rule['not_stop_by_color_and_skip'] = 0
rule['start_by_color'] = get_random_all_color()
rule['with_color'] = get_random_out_color()
elif random_type == 'distribute_colors':
rule['colors'] = list(np.unique([get_random_out_color(), get_random_all_color()]))
rule['horizontally'] = np.random.randint(2)
rule['vertically'] = np.random.randint(2)
rule['intersect'] = get_random_out_color()
elif random_type == 'color_for_inners':
rule['color_out'] = get_random_out_color()
elif random_type == 'crop_figure':
rule['mode'] = random.choice(['smallest', 'biggest'])
rule['dif_c_edge'] = random.choice([True, False])
elif random_type == 'unity':
rule['mode'] = random.choice(['diagonal', 'horizontal', 'vertical', 'horver'])
# rule['inner'] = np.random.choice(2)
rule['ignore_colors'] = [0]
if np.random.rand() < 0.5:
rule['ignore_colors'] += [get_random_all_color()]
rule['with_color'] = random.choice([get_random_out_color(), 0])
elif random_type == 'map_color':
rule['color_in'] = get_random_all_color()
rule['color_out'] = get_random_out_color()
elif random_type == 'gravity':
rule['gravity_type'] = random.choice(['figures', 'cells'])
rule['steps_limit'] = np.random.choice(2)
rule['look_at_what_to_move'] = np.random.choice(2)
if rule['look_at_what_to_move'] == 1:
rule['color_what'] = get_random_out_color()
rule['direction_type'] = random.choice(['border', 'color'])
if rule['direction_type'] == 'border':
rule['direction_border'] = random.choice(['top', 'bottom', 'left', 'right'])
else:
rule['direction_color'] = get_random_color()
elif random_type == 'split_by_H' or random_type == 'split_by_W':
rule['merge_rule'] = random.choice(['and', 'equal', 'or', 'xor'])
elif random_type == 'align_pattern':
rule['macro_type'] = 'global_interaction_rule'
# rule['allow_rotation'] = False
rule['allow_color'] = get_random_all_color()
rule['fill_with_color'] = 0 #random.choice([0, get_random_all_color()])
return rule
def get_task_metadata(task):
colors = []
shapes_input = [[], []]
shapes_output = [[], []]
for part in ['train']:
for uni_task in task[part]:
inp = uni_task['input']
colors += list(np.unique(inp))
out = uni_task['output']
colors += list(np.unique(out))
shapes_input[0].append(inp.shape[0])
shapes_input[1].append(inp.shape[1])
shapes_output[0].append(out.shape[0])
shapes_output[1].append(out.shape[1])
all_colors = np.unique(colors)
min_k1 = int(np.floor(np.min(np.array(shapes_output[0])/np.array(shapes_input[0]))))
min_k2 = int(np.floor(np.min(np.array(shapes_output[1])/np.array(shapes_input[1]))))
max_k1 = int(np.ceil(np.max(np.array(shapes_output[0])/np.array(shapes_input[0]))))
max_k2 = int(np.ceil(np.max(np.array(shapes_output[1])/np.array(shapes_input[1]))))
max_shape = np.max([shapes_input])
config = {}
config['mink1'] = max(1, min(min(min_k1, 30//max_shape), 3))
config['mink2'] = max(1, min(min(min_k2, 30//max_shape), 3))
config['maxk1'] = max(1, min(min(max_k1, 30//max_shape), 3))
config['maxk2'] = max(1, min(min(max_k2, 30//max_shape), 3))
config['allow_make_smaller'] = False
config['allow_make_bigger'] = False
for uni_task in task['train']:
if uni_task['input'].shape[0] > uni_task['output'].shape[0] or \
uni_task['input'].shape[1] > uni_task['output'].shape[1]:
config['allow_make_smaller'] = True
if uni_task['input'].shape[0] < uni_task['output'].shape[0] or \
uni_task['input'].shape[1] < uni_task['output'].shape[1]:
config['allow_make_bigger'] = True
colors_out = []
changed_colors = []
inp_colors = []
for uni_task in task['train']:
inp = uni_task['input']
out = uni_task['output']
for i in range(min(inp.shape[0], out.shape[0])):
for j in range(min(inp.shape[1], out.shape[1])):
inp_colors.append(inp[i, j])
if out[i, j] != inp[i, j]:
colors_out.append(out[i, j])
changed_colors.append(inp[i, j])
inp_colors = np.unique(inp_colors)
changed_colors = np.unique(changed_colors)
config['ignore_colors'] = [c for c in inp_colors if not c in changed_colors]
config['possible_ignore_colors'] = np.array([c for c in all_colors if not c in config['ignore_colors']])
if len(colors_out) == 0:
colors_out = [0]
config['possible_colors_out'] = np.unique(colors_out)
return all_colors, config
def compute_parametrized_automata(input, hidden_i, rules):
output = np.zeros_like(input, dtype=int)
hidden_o = np.copy(hidden_i)
for i, j in product(range(input.shape[0]), range(input.shape[1])):
i_c = input[i, j]
i_nbh = nbh(input, i, j)
# cells adagent to the current one
i_direct_nbh = {k: v for k, v in i_nbh.items() if k in {(1, 0), (-1, 0), (0, 1), (0, -1)}}
i_indirect_nbh = {k: v for k, v in i_nbh.items() if k in {(1, 1), (-1, -1), (-1, 1), (1, -1)}}
is_top_b, is_bottom_b = i == 0, i == input.shape[0] - 1
is_left_b, is_right_b = j == 0, j == input.shape[1] - 1
is_b = is_top_b or is_bottom_b or is_left_b or is_right_b
if i_c > 0:
output[i, j] = i_c
for rule in rules:
if i_c in rule['ignore_colors']:
continue
if rule['type'] == 'copy_color_by_direction':
if rule['direction'] == 'bottom' or rule['direction'] == 'everywhere':
if not is_top_b and input[i - 1, j] in rule['copy_color'] and \
(i == 1 or input[i - 2, j] == rule['look_back_color']):
output[i, j] = input[i - 1, j]
break
if rule['direction'] == 'top' or rule['direction'] == 'everywhere':
if not is_bottom_b and input[i + 1, j] in rule['copy_color'] and \
(i == input.shape[0] - 2 or input[i + 2, j] == rule['look_back_color']):
output[i, j] = input[i + 1, j]
break
if rule['direction'] == 'right' or rule['direction'] == 'everywhere':
if not is_left_b and input[i, j - 1] in rule['copy_color'] and \
(j == 1 or input[i, j - 2] == rule['look_back_color']):
output[i, j] = input[i, j - 1]
break
if rule['direction'] == 'left' or rule['direction'] == 'everywhere':
if not is_right_b and input[i, j + 1] in rule['copy_color'] and \
(j == input.shape[1] - 2 or input[i, j + 2] == rule['look_back_color']):
output[i, j] = input[i, j + 1]
break
elif rule['type'] == 'corner_check':
color_nbh = rule['nbh_check_colors']
sum_nbh = 3
out_nbh = rule['nbh_check_out']
i_uplecorner_nbh = {k: v for k, v in i_nbh.items() if k in {(-1, -1), (-1, 0), (0, -1)}}
i_upricorner_nbh = {k: v for k, v in i_nbh.items() if k in {(-1, 1), (-1, 0), (0, 1)}}
i_dolecorner_nbh = {k: v for k, v in i_nbh.items() if k in {(1, -1), (1, 0), (0, -1)}}
i_doricorner_nbh = {k: v for k, v in i_nbh.items() if k in {(1, 1), (1, 0), (0, 1)}}
if sum(1 for v in i_nbh.values() if v in color_nbh) < 3:
continue
did_something = False
for corner_idx in [i_uplecorner_nbh, i_upricorner_nbh, i_dolecorner_nbh, i_doricorner_nbh]:
for color in color_nbh:
if sum(1 for v in corner_idx.values() if v == color) == sum_nbh:
output[i, j] = out_nbh
did_something = True
break
if did_something:
break
if did_something:
break
elif rule['type'] == 'nbh_check':
color_nbh = rule['nbh_check_colors']
sum_nbh = rule['nbh_check_sum']
out_nbh = rule['nbh_check_out']
proper_nbhs = i_nbh.values()
if sum(1 for v in proper_nbhs if v in color_nbh) > sum_nbh:
output[i, j] = out_nbh
break
elif rule['type'] == 'direct_check':
color_nbh = rule['nbh_check_colors']
sum_nbh = rule['nbh_check_sum']
out_nbh = rule['nbh_check_out']
proper_nbhs = i_direct_nbh.values()
if sum(1 for v in proper_nbhs if v in color_nbh) > sum_nbh:
output[i, j] = out_nbh
break
elif rule['type'] == 'indirect_check':
color_nbh = rule['nbh_check_colors']
sum_nbh = rule['nbh_check_sum']
out_nbh = rule['nbh_check_out']
proper_nbhs = i_indirect_nbh.values()
if sum(1 for v in proper_nbhs if v in color_nbh) > sum_nbh:
output[i, j] = out_nbh
break
elif rule['type'] == 'color_distribution':
directions = ['top', 'bottom', 'left', 'right', 'top_left', 'bottom_left', 'top_right', 'bottom_right']
not_border_conditions = \
[
not is_top_b,
not is_bottom_b,
not is_left_b,
not is_right_b,
not is_top_b and not is_left_b,
not is_bottom_b and not is_left_b,
not is_top_b and not is_right_b,
not is_bottom_b and not is_right_b
]
index_from = \
[
(i - 1, j),
(i + 1, j),
(i, j - 1),
(i, j + 1),
(i - 1, j - 1),
(i + 1, j - 1),
(i - 1, j + 1),
(i + 1, j + 1)
]
did_something = False
for i_dir, direction in enumerate(directions):
if rule['direction'] == direction:
if not_border_conditions[i_dir]:
if (rule['check_in_empty'] == 1 and input[index_from[i_dir]] > 0) or \
(rule['check_in_empty'] == 0 and input[index_from[i_dir]] == rule['color_in']):
output[i, j] = rule['color_out']
did_something = True
break
if did_something:
break
return output, hidden_o
def get_connectivity_info(color: np.array, ignore_black = False, von_neumann_only = False, edge_for_difcolors = False):
# UnionFind structure allows us to detect all connected areas in a linear time.
class UnionFind:
def __init__(self) -> None:
self.area = np.ones(color.size)
self.parent = np.arange(color.size)
def find(self, x: int) -> int:
if self.parent[x] != x:
self.parent[x] = self.find(self.parent[x])
return self.parent[x]
def union(self, u: int, v: int) -> None:
root_u, root_v = self.find(u), self.find(v)
if root_u != root_v:
area_u, area_v = self.area[root_u], self.area[root_v]
if area_u < area_v:
root_u, root_v = root_v, root_u
self.parent[root_v] = root_u
self.area[root_u] = area_u + area_v
union_find = UnionFind()
neighbours = [[-1, 0], [0, -1], [1, 0], [0, 1]]
if not von_neumann_only:
neighbours.extend([[-1, -1], [1, -1], [1, 1], [-1, 1]])
nrows, ncols = color.shape
for i in range(nrows):
for j in range(ncols):
for s, t in neighbours:
u, v = i + s, j + t
if u >= 0 and u < nrows and v >= 0 and v < ncols and \
(color[u, v] == color[i, j] or (edge_for_difcolors and (color[u, v]>0) == (color[i, j]>0))):
union_find.union(u * ncols + v, i * ncols + j)
# for every cell: write down the area of its corresponding area
communities = defaultdict(list)
for i, j in product(range(nrows), range(ncols)):
if not ignore_black or color[i, j] > 0:
communities[union_find.find(i * ncols + j)].append((i, j))
# the result is always sorted for consistency
communities = sorted(communities.values(), key = lambda area: (len(area), area))
return communities
def get_graph_communities(im, ignore_black=False):
G = nx.Graph()
I, J = im.shape
for i in range(I):
for j in range(J):
if ignore_black and im[i, j] == 0:
continue
G.add_node((i, j))
edges = []
if j >= 1:
if im[i, j] == im[i, j - 1]:
edges.append(((i, j), (i, j - 1)))
if j < J - 1:
if im[i, j] == im[i, j + 1]:
edges.append(((i, j), (i, j + 1)))
if i >= 1:
if im[i, j] == im[i - 1, j]:
edges.append(((i, j), (i - 1, j)))
if j >= 1:
if im[i, j] == im[i - 1, j - 1]:
edges.append(((i, j), (i - 1, j - 1)))
if j < J - 1:
if im[i, j] == im[i - 1, j + 1]:
edges.append(((i, j), (i - 1, j + 1)))
if i < I - 1:
if im[i, j] == im[i + 1, j]:
edges.append(((i, j), (i + 1, j)))
if j >= 1:
if im[i, j] == im[i + 1, j - 1]:
edges.append(((i, j), (i + 1, j - 1)))
if j < J - 1:
if im[i, j] == im[i + 1, j + 1]:
edges.append(((i, j), (i + 1, j + 1)))
G.add_edges_from(edges)
communities = list(nx.community.k_clique_communities(G, 2))
communities = [list(com) for com in communities]
for i in range(I):
for j in range(J):
i_nbh = nbh(im, i, j)
if sum(1 for v in i_nbh.values() if v == im[i, j]) == 0:
communities.append([(i, j)])
return communities
def apply_rule(input, hidden_i, rule):
output = np.zeros_like(input, dtype=int)
# print(type(input))
# print(input.shape)
hidden = np.zeros_like(input)
output[:, :] = input[:, :]
if rule['type'] == 'macro_multiply_k':
output = np.tile(output, rule['k'])
elif rule['type'] == 'flip':
if rule['how'] == 'ver':
output = output[::-1, :]
elif rule['how'] == 'hor':
output = output[:, ::-1]
elif rule['type'] == 'reduce':
skip_row = np.zeros(input.shape[0])
for i in range(1, input.shape[0]):
skip_row[i] = (input[i] == input[i-1]).all() or (input[i] == rule['skip_color']).all()
if (input[0] == rule['skip_color']).all():
skip_row[0] = 1
if np.sum(skip_row==0)>0:
output = input[skip_row == 0]
skip_column = np.zeros(input.shape[1])
for i in range(1, input.shape[1]):
skip_column[i] = (input[:, i] == input[:, i-1]).all() or (input[:, i] == rule['skip_color']).all()
if (input[:, 0] == rule['skip_color']).all():
skip_column[0] = 1
if np.sum(skip_column==0)>0:
output = output[:, skip_column == 0]
elif rule['type'] == 'rotate':
output = np.rot90(output, rule['rotations_count'])
elif rule['type'] == 'micro_multiply_by':
if rule['how_many'] == 'size':
k = output.shape[0]
else:
k = rule['how_many']
output = np.repeat(output, k, axis=0)
output = np.repeat(output, k, axis=1)
elif rule['type'] == 'macro_multiply_by':
if rule['how_many'] == 'both':
k = (2, 2)
elif rule['how_many'] == 'hor':
k = (1, 2)
elif rule['how_many'] == 'ver':
k = (2, 1)
output = np.tile(output, k)
if input.shape[0] == input.shape[1]:
for i in range(k[0]):
for j in range(k[1]):
sub = output[i * input.shape[0]: (i + 1) * input.shape[0],
j * input.shape[1]: (j + 1) * input.shape[1]]
sub_rotated = np.rot90(sub, rule['rotates'][i * 2 + j])
output[i * input.shape[0]: (i + 1) * input.shape[0],
j * input.shape[1]: (j + 1) * input.shape[1]] = sub_rotated
for i in range(k[0]):
for j in range(k[1]):
sub = output[i * input.shape[0]: (i + 1) * input.shape[0], j * input.shape[1]: (j + 1) * input.shape[1]]
if 'ver' in rule['flips'][i * 2 + j]:
sub = sub[::-1, :]
if 'hor' in rule['flips'][i * 2 + j]:
sub = sub[:, ::-1]
output[i * input.shape[0]: (i + 1) * input.shape[0], j * input.shape[1]: (j + 1) * input.shape[1]] = sub
elif rule['type'] == 'distribute_from_border':
hidden = np.zeros_like(input)
for i in range(1, input.shape[0] - 1):
if output[i, 0] in rule['colors']:
if not output[i, input.shape[1] - 1] in rule['colors'] or output[i, input.shape[1] - 1] == output[i, 0]:
output[i] = output[i, 0]
for j in range(1, input.shape[1] - 1):
if output[0, j] in rule['colors']:
if not output[input.shape[0] - 1, j] in rule['colors'] or output[input.shape[0] - 1, j] == output[0, j]:
output[:, j] = output[0, j]
elif rule['type'] == 'color_for_inners':
hidden = np.zeros_like(input)
changed = 1
while changed == 1:
changed = 0
for i, j in product(range(input.shape[0]), range(input.shape[1])):
i_c = input[i, j]
if i_c > 0 or hidden[i, j] == 1:
continue
if i == 0 or i == input.shape[0] - 1 or j == 0 or j == input.shape[1] - 1:
hidden[i, j] = 1
changed = 1
continue
i_nbh = nbh(hidden, i, j)
# cells adagent to the current one
i_direct_nbh = {k: v for k, v in i_nbh.items() if k in {(1, 0), (-1, 0), (0, 1), (0, -1)}}
if sum(1 for v in i_direct_nbh.values() if v == 1) > 0:
hidden[i, j] = 1
changed = 1
output[((hidden == 0).astype(np.int) * (input == 0).astype(np.int)) == 1] = rule['color_out']
hidden = np.copy(hidden)
elif rule['type'] == 'draw_lines':
hidden = np.zeros_like(input)
if rule['direction'] == 'everywhere':
directions = ['top', 'bottom', 'left', 'right', 'top_left', 'bottom_left', 'top_right', 'bottom_right']
elif rule['direction'] == 'horizontal':
directions = ['left', 'right']
elif rule['direction'] == 'vertical':
directions = ['top', 'bottom']
elif rule['direction'] == 'horver':
directions = ['top', 'bottom', 'left', 'right']
elif rule['direction'] == 'diagonal':
directions = ['top_left', 'bottom_left', 'top_right', 'bottom_right']
else:
directions = [rule['direction']]
possible_directions = ['top', 'bottom', 'left', 'right',
'top_left', 'bottom_left', 'top_right', 'bottom_right']
index_change = \
[
[-1, 0],
[1, 0],
(0, -1),
(0, 1),
(-1, -1),
(+1, -1),
(-1, +1),
(+1, +1)
]
for i_dir, direction in enumerate(possible_directions):
if direction in directions:
idx_ch = index_change[i_dir]
for i in range(input.shape[0]):
for j in range(input.shape[1]):
if input[i, j] == rule['start_by_color']:
tmp_i = i + idx_ch[0]
tmp_j = j + idx_ch[1]
while 0 <= tmp_i < input.shape[0] and \
0 <= tmp_j < input.shape[1] and \
input[tmp_i, tmp_j] == rule['not_stop_by_color']:
output[tmp_i, tmp_j] = rule['with_color']
tmp_i += idx_ch[0]
tmp_j += idx_ch[1]
elif rule['type'] == 'draw_line_to':
hidden = np.zeros_like(input)
index_change = \
[
[-1, 0],
[1, 0],
(0, -1),
(0, 1),
]
for i, j in product(range(input.shape[0]), range(input.shape[1])):
if input[i, j] != rule['start_by_color']:
continue
number_0 = np.sum(output[:i] == rule['direction_color'])
number_1 = np.sum(output[(i + 1):] == rule['direction_color'])
number_2 = np.sum(output[:, :j] == rule['direction_color'])
number_3 = np.sum(output[:, (j + 1):] == rule['direction_color'])
i_dir = np.argmax([number_0, number_1, number_2, number_3])
# print([number_0, number_1, number_2, number_3])
# 1/0
idx_ch = index_change[i_dir]
tmp_i = i + idx_ch[0]
tmp_j = j + idx_ch[1]
while 0 <= tmp_i < input.shape[0] and \
0 <= tmp_j < input.shape[1] and \
(input[tmp_i, tmp_j] in [rule['not_stop_by_color'], rule['not_stop_by_color_and_skip']]):
skip_color = rule['not_stop_by_color_and_skip']
if skip_color == 0 or input[tmp_i, tmp_j] != skip_color:
output[tmp_i, tmp_j] = rule['with_color']
tmp_i += idx_ch[0]
tmp_j += idx_ch[1]
elif rule['type'] == 'distribute_colors':
non_zero_rows = []
non_zero_columns = []
color_for_row = np.zeros(input.shape[0])
color_for_column = np.zeros(input.shape[1])
for i in range(input.shape[0]):
row = input[i]
colors, counts = np.unique(row, return_counts=True)
good_colors = np.array([c in rule['colors'] for c in colors])
if not good_colors.any():
continue
colors = colors[good_colors]
counts = counts[good_colors]
best_color = colors[np.argmax(counts)]
color_for_row[i] = best_color
non_zero_rows.append(i)
for j in range(input.shape[1]):
row = input[:, j]
colors, counts = np.unique(row, return_counts=True)
good_colors = np.array([c in rule['colors'] for c in colors])
if not good_colors.any():
continue
colors = colors[good_colors]
counts = counts[good_colors]
best_color = colors[np.argmax(counts)]
color_for_column[j] = best_color
non_zero_columns.append(j)
if rule['horizontally'] == 1:
for i in non_zero_rows:
output[i] = color_for_row[i]
if rule['vertically'] == 1:
for j in non_zero_columns:
output[:, j] = color_for_column[j]
for i in non_zero_rows:
for j in non_zero_columns:
if input[i, j] == 0:
output[i, j] = rule['intersect']
hidden = np.copy(hidden_i)
elif rule['type'] == 'unity':
hidden = np.copy(hidden_i)
if rule['mode'] == 'vertical':
for j in range(input.shape[1]):
last_color_now = np.zeros(10, dtype=np.int) - 1
for i in range(input.shape[0]):
if not input[i, j] in rule['ignore_colors'] and last_color_now[input[i, j]] >= 0:
if rule['with_color'] == 0:
output[(last_color_now[input[i, j]] + 1):i, j] = input[i, j]
else:
output[(last_color_now[input[i, j]] + 1):i, j] = rule['with_color']
last_color_now[input[i, j]] = i
elif not input[i, j] in rule['ignore_colors']:
last_color_now[input[i, j]] = i
elif rule['mode'] == 'horizontal':
for i in range(input.shape[0]):
last_color_now = np.zeros(10, dtype=np.int) - 1
for j in range(input.shape[1]):
if not input[i, j] in rule['ignore_colors'] and last_color_now[input[i, j]] >= 0:
if rule['with_color'] == 0:
output[i, (last_color_now[input[i, j]] + 1):j] = input[i, j]
else:
output[i, (last_color_now[input[i, j]] + 1):j] = rule['with_color']
last_color_now[input[i, j]] = j
elif not input[i, j] in rule['ignore_colors']:
last_color_now[input[i, j]] = j
elif rule['mode'] == 'horver':
for j in range(input.shape[1]):
last_color_now = np.zeros(10, dtype=np.int) - 1
for i in range(input.shape[0]):
if not input[i, j] in rule['ignore_colors'] and last_color_now[input[i, j]] >= 0:
if rule['with_color'] == 0:
output[(last_color_now[input[i, j]] + 1):i, j] = input[i, j]
else:
output[(last_color_now[input[i, j]] + 1):i, j] = rule['with_color']
last_color_now[input[i, j]] = i
elif not input[i, j] in rule['ignore_colors']:
last_color_now[input[i, j]] = i
for i in range(input.shape[0]):
last_color_now = np.zeros(10, dtype=np.int) - 1
for j in range(input.shape[1]):
if not input[i, j] in rule['ignore_colors'] and last_color_now[input[i, j]] >= 0:
if rule['with_color'] == 0:
output[i, (last_color_now[input[i, j]] + 1):j] = input[i, j]
else:
output[i, (last_color_now[input[i, j]] + 1):j] = rule['with_color']
last_color_now[input[i, j]] = j
elif not input[i, j] in rule['ignore_colors']:
last_color_now[input[i, j]] = j
elif rule['mode'] == 'diagonal':
for diag_id in range(-input.shape[0] - 1, input.shape[1] + 1):
last_color_now_x = np.zeros(10, dtype=np.int) - 1
last_color_now_y = np.zeros(10, dtype=np.int) - 1
for i, j in zip(np.arange(input.shape[0]), diag_id + np.arange(input.shape[0])):
if 0 <= i < input.shape[0] and 0 <= j < input.shape[1]:
if not input[i, j] in rule['ignore_colors'] and last_color_now_x[input[i, j]] >= 0:
if rule['with_color'] == 0:
output[np.arange(last_color_now_x[input[i, j]] + 1, i), np.arange(
last_color_now_y[input[i, j]] + 1, j)] = input[i, j]
else:
output[np.arange(last_color_now_x[input[i, j]] + 1, i), np.arange(
last_color_now_y[input[i, j]] + 1, j)] = rule[
'with_color']
last_color_now_x[input[i, j]] = i
last_color_now_y[input[i, j]] = j
elif not input[i, j] in rule['ignore_colors']:
last_color_now_x[input[i, j]] = i
last_color_now_y[input[i, j]] = j
reflected_input = input[:, ::-1]
output = output[:, ::-1]
for diag_id in range(-reflected_input.shape[0] - 1, reflected_input.shape[1] + 1):
last_color_now_x = np.zeros(10, dtype=np.int) - 1
last_color_now_y = np.zeros(10, dtype=np.int) - 1
for i, j in zip(np.arange(reflected_input.shape[0]), diag_id + np.arange(reflected_input.shape[0])):
if 0 <= i < reflected_input.shape[0] and 0 <= j < reflected_input.shape[1]:
if not reflected_input[i, j] in rule['ignore_colors'] and last_color_now_x[
reflected_input[i, j]] >= 0:
if rule['with_color'] == 0:
output[np.arange(last_color_now_x[reflected_input[i, j]] + 1, i), np.arange(
last_color_now_y[reflected_input[i, j]] + 1, j)] = reflected_input[i, j]
else:
output[np.arange(last_color_now_x[reflected_input[i, j]] + 1, i), np.arange(
last_color_now_y[reflected_input[i, j]] + 1, j)] = rule[
'with_color']
last_color_now_x[reflected_input[i, j]] = i
last_color_now_y[reflected_input[i, j]] = j
elif not reflected_input[i, j] in rule['ignore_colors']:
last_color_now_x[reflected_input[i, j]] = i
last_color_now_y[reflected_input[i, j]] = j
output = output[:, ::-1]
elif rule['type'] == 'split_by_H':
hidden = np.copy(hidden_i)
if output.shape[0] >= 2:
part1 = output[:int(np.floor(output.shape[0] / 2))]
part2 = output[int(np.ceil(output.shape[0] / 2)):]
output = np.zeros_like(part1)
if rule['merge_rule'] == 'or':
output[part1 > 0] = part1[part1 > 0]
output[part2 > 0] = part2[part2 > 0]
elif rule['merge_rule'] == 'equal':
idx = np.logical_and(np.logical_and(part1 > 0, part2 > 0), part1 == part2)
output[idx] = part1[idx]
elif rule['merge_rule'] == 'and':
idx = np.logical_and(part1 > 0, part2 > 0)
output[idx] = part1[idx]
elif rule['merge_rule'] == 'xor':
idx = np.logical_xor(part1 > 0, part2 > 0)
output[idx] = part1[idx]
elif rule['type'] == 'split_by_W':
hidden = np.copy(hidden_i)
if output.shape[1] >= 2:
part1 = output[:, :int(np.floor(output.shape[1] / 2))]
part2 = output[:, int(np.ceil(output.shape[1] / 2)):]
output = np.zeros_like(part1)
if rule['merge_rule'] == 'or':
output[part1 > 0] = part1[part1 > 0]
output[part2 > 0] = part2[part2 > 0]
elif rule['merge_rule'] == 'equal':
idx = np.logical_and(np.logical_and(part1 > 0, part2 > 0), part1 == part2)
output[idx] = part1[idx]
elif rule['merge_rule'] == 'and':
idx = np.logical_and(part1 > 0, part2 > 0)
output[idx] = part1[idx]
elif rule['merge_rule'] == 'xor':
idx = np.logical_xor(part1 > 0, part2 > 0)
output[idx] = part1[idx]
elif rule['type'] == 'map_color':
hidden = np.copy(hidden_i)
output[output == rule['color_in']] = rule['color_out']
elif rule['type'] == 'crop_empty':
hidden = np.copy(hidden_i)
nonzerosi = np.max((output != 0).astype(np.int), axis=1)
nonzerosj = np.max((output != 0).astype(np.int), axis=0)
# print(nonzerosi)
# print(nonzerosj)
if np.max(nonzerosi) == 0 or np.max(nonzerosj) == 0:
output = output * 0
else:
mini = np.min(np.arange(output.shape[0])[nonzerosi == 1])
maxi = np.max(np.arange(output.shape[0])[nonzerosi == 1])
minj = np.min(np.arange(output.shape[1])[nonzerosj == 1])
maxj = np.max(np.arange(output.shape[1])[nonzerosj == 1])
output = output[mini:(maxi + 1), minj:(maxj + 1)]
elif rule['type'] == 'crop_figure':
hidden = np.copy(hidden_i)
communities = get_connectivity_info(output, ignore_black=True, edge_for_difcolors=rule['dif_c_edge'])
if len(communities) == 0:
output = np.zeros_like(output)
else:
if rule['mode'] == 'biggest':
biggest = list(communities[np.argmax([len(list(com)) for com in communities])])
else:
biggest = list(communities[np.argmin([len(list(com)) for com in communities])])
biggest = np.array(biggest)
min_bx = np.min(biggest[:, 0])
min_by = np.min(biggest[:, 1])
biggest[:, 0] -= min_bx
biggest[:, 1] -= min_by
output = np.zeros((np.max(biggest[:, 0]) + 1, np.max(biggest[:, 1]) + 1), dtype=np.int)
for i in range(biggest.shape[0]):
output[tuple(biggest[i])] = input[(min_bx + biggest[i][0], min_by + biggest[i][1])]
elif rule['type'] == 'make_holes':
hidden = np.copy(hidden_i)
for i in range(output.shape[0]):
for j in range(output.shape[1]):
i_nbh = nbh(output, i, j)
proper_nbhs = i_nbh.values()
for color in range(1, 10):
if sum(1 for v in proper_nbhs if v == color) == 8:
output[i, j] = 0
break
elif rule['type'] == 'gravity':
changed_smth = 1
hidden = np.copy(hidden_i)
im = output
if rule['gravity_type'] == 'figures':
communities = get_connectivity_info(im, ignore_black=True)
else:
communities = []
for i in range(output.shape[0]):
for j in range(output.shape[1]):
if output[i, j] > 0:
communities.append([[i, j]])
directions = []
for com in communities:
community = list(com)
color_fig = output[community[0][0], community[0][1]]
if rule['look_at_what_to_move'] == 1 and color_fig != rule['color_what']:
directions.append('None')
continue
xs = [p[0] for p in community]
ys = [p[1] for p in community]
if rule['direction_type'] == 'border':
direction = rule['direction_border']
elif rule['direction_type'] == 'color':
color = rule['direction_color']
xmin, xmax = np.min(xs), np.max(xs)
ymin, ymax = np.min(ys), np.max(ys)
number_0 = np.sum(output[:xmin] == color)
number_1 = np.sum(output[(xmax + 1):] == color)
number_2 = np.sum(output[:, :ymin] == color)
number_3 = np.sum(output[:, (ymax + 1):] == color)
direction = ['top', 'bottom', 'left', 'right'][np.argmax([number_0, number_1, number_2, number_3])]
directions.append(direction)
already_moved = np.zeros(len(communities))
while changed_smth > 0:
changed_smth = 0
for i, com in enumerate(communities):
community = list(com)
color_fig = output[community[0][0], community[0][1]]
xs = [p[0] for p in community]
ys = [p[1] for p in community]
direction = directions[i]
if direction == 'top':
toper = np.array([[p[0] - 1, p[1]] for p in community if (p[0] - 1, p[1]) not in community])
xs = np.array([p[0] for p in toper])
ys = np.array([p[1] for p in toper])
if np.min(xs) < 0:
continue
if (output[xs, ys] == 0).all() and (rule['steps_limit']==1 or already_moved[i]==0):
changed_smth = 1
already_moved[i]=1
com_xs = np.array([p[0] for p in community])
com_ys = np.array([p[1] for p in community])
output[com_xs, com_ys] = 0
output[com_xs - 1, com_ys] = color_fig
communities[i] = [(p[0] - 1, p[1]) for p in community]
if direction == 'bottom':
toper = np.array([[p[0] + 1, p[1]] for p in community if (p[0] + 1, p[1]) not in community])
xs = np.array([p[0] for p in toper])
ys = np.array([p[1] for p in toper])
if np.max(xs) == input.shape[0]:
continue
if (output[xs, ys] == 0).all() and (rule['steps_limit']==1 or already_moved[i]==0):
changed_smth = 1
already_moved[i]=1
com_xs = np.array([p[0] for p in community])
com_ys = np.array([p[1] for p in community])
output[com_xs, com_ys] = 0
output[com_xs + 1, com_ys] = color_fig
communities[i] = [(p[0] + 1, p[1]) for p in community]
if direction == 'left':
toper = np.array([[p[0], p[1] - 1] for p in community if (p[0], p[1] - 1) not in community])
xs = np.array([p[0] for p in toper])
ys = np.array([p[1] for p in toper])
if np.min(ys) < 0:
continue
if (output[xs, ys] == 0).all() and (rule['steps_limit']==1 or already_moved[i]==0):
changed_smth = 1
already_moved[i]=1
com_xs = np.array([p[0] for p in community])
com_ys = np.array([p[1] for p in community])
output[com_xs, com_ys] = 0
output[com_xs, com_ys - 1] = color_fig
communities[i] = [(p[0], p[1] - 1) for p in community]
if direction == 'right':
toper = | np.array([[p[0], p[1] + 1] for p in community if (p[0], p[1] + 1) not in community]) | numpy.array |
import h5py
import numpy as np
pathGTTrain = "CLSA_CFA_GRAHAM_GoodAndUsable.hdf5"
with h5py.File(pathGTTrain, "r") as f: # "with" close the file after its nested commands
everything = f["gt"][:][:]
cog = f["gt"][:][:, 28]
mem = f["gt"][:][:, 29]
spd = f["gt"][:][:, 30]
exe = f["gt"][:][:, 31]
stp = f["gt"][:][:, 24]
max = 100
min = -230
cog_new = (100-0)/(max-min)*(cog-max)+100
#
#
max = 0
min = 10
mem_new = (100-0)/(max-min)*(mem-max)+100
#
max = 0
min = 100
spd_new = (100-0)/(max-min)*(spd-max)+100
#
max = 0
min = 32
exe_new = (100-0)/(max-min)*(exe-max)+100
#
max = 0.5
min = 2.5
stp_new = (100-0)/(max-min)*(stp-max)+100
everything[:, 28] = cog_new
everything[:, 29] = mem_new
everything[:, 30] = spd_new
everything[:, 31] = exe_new
everything[:, 24] = stp_new
print('train')
data = everything[0:18000]
print("age mean" + str(np.mean(data[:, 1])) + '||' "std" + str(np.std(data[:, 1])))
print("bmi mean" + str(np.mean(data[:, 35])) + '||' "std" + str(np.std(data[:, 35])))
print("sbp mean" + str(np.mean(data[:, 32])) + '||' "std" + str(np.std(data[:, 32])))
print("dpb mean" + str(np.mean(data[:, 33])) + '||' "std" + str(np.std(data[:, 33])))
print("exec mean" + str(np.mean(data[:, 31])) + '||' "std" + str(np.std(data[:, 31])))
print("speed mean" + str(np.mean(data[:, 30])) + '||' "std" + str(np.std(data[:, 30])))
print("mem mean" + str(np.mean(data[:, 29])) + '||' "std" + str(np.std(data[:, 29])))
print("inhib mean" + str(np.mean(data[:, 24])) + '||' "std" + str(np.std(data[:, 24])))
print("cog mean" + str(np.mean(data[:, 28])) + '||' "std" + str(np.std(data[:, 28])))
print('val')
data = everything[18000:21860]
print("age mean" + str(np.mean(data[:, 1])) + '||' "std" + str(np.std(data[:, 1])))
print("bmi mean" + str(np.mean(data[:, 35])) + '||' "std" + str(np.std(data[:, 35])))
print("sbp mean" + str(np.mean(data[:, 32])) + '||' "std" + str(np.std(data[:, 32])))
print("dpb mean" + str(np.mean(data[:, 33])) + '||' "std" + str(np.std(data[:, 33])))
print("exec mean" + str( | np.mean(data[:, 31]) | numpy.mean |
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import animation
'''
This package is to be used as a library. Please do not edit.
'''
def runge_function(n: int = 100, min_x: float = -5.0, max_x: float = 5.0) -> (np.ndarray, np.ndarray):
"""
Compute the discrete Runge function on the linearly spaced inverval [min_x, max_x] with n function values.
Arguments:
min_x: left border of the interval
max_x: right border of the interval
n: number of function values inside the interval
Return:
x: vector containing all x values, correspond to values in y
y: vector containing all function values, correspond to values in x
"""
x = np.linspace(min_x, max_x, n)
y = 1.0 / (1.0 + x ** 2)
return x, y
def pad_coefficients(poly, length):
"""Adds zeros to the coefficients of poly if they have not the proper length."""
return np.pad(poly.coeffs, (length - poly.coeffs.size, 0), mode='constant', constant_values=0)
def plot_function(x, y):
""" Plot the function that is given by the discrete point pairs in x and y. """
plt.grid(True)
plt.plot(x, y, 'r-')
min_x = np.min(x)
min_y = np.min(y)
max_x = np.max(x)
max_y = np.max(y)
scale_x = max_x - min_x
scale_y = max_y - min_y
plt.xlim(min_x - 0.05 * scale_x, max_x + 0.05 * scale_x)
plt.ylim(min_y - 0.05 * scale_y, max_y + 0.05 * scale_y)
plt.show()
def plot_function_interpolations(function, support_points, interpolations, bases):
""" Plot a grid with the given function, the support points, interpolation and bases in each plot. """
x_f, y_f = function
fig1 = plt.figure()
for i in range(len(support_points)):
x_s, y_s = support_points[i]
x_i, y_i = interpolations[i]
p = fig1.add_subplot(3, 3, i + 1)
p.grid(True)
p.set_xlim(-5.3, 5.3)
p.set_xticks([-5, 0, 5])
p.set_ylim(-1.2, 2.2)
p.plot(x_f, y_f, 'r-')
p.plot(x_s, y_s, 'ko')
p.plot(x_i, y_i, 'b-')
fig2 = plt.figure()
for i in range(len(bases)):
p1 = fig2.add_subplot(3, 3, i + 1)
p1.grid(True)
p1.set_xlim(-5.3, 5.3)
p1.set_xticks([-5, 0, 5])
p1.set_ylim(-1.2, 2.2)
for base_func in bases[i]: plt.plot(x_f, base_func(x_f), '-')
plt.show()
def plot_spline(points, interpolations):
""" Plot a spline with the interpolation points."""
# Plot interpolation points
plt.plot(points[0], points[1], 'ko')
# Plot piecewise interpolants
for i in range(len(points[0]) - 1):
# plot local interpolant
p = interpolations[i]
px = np.linspace(points[0][i], points[0][i + 1], 100 / len(points[0]))
py = p(px)
plt.plot(px, py, '-')
# Plot Runge function
rx = np.linspace(-5, 5, 100)
ry = 1.0 / (1 + rx ** 2)
plt.plot(rx, ry, '--', color='0.7')
# Beautify plot
plt.grid(True)
plt.xlim(-5.1, 5.1)
plt.xticks(np.linspace(-5, 5, 11))
plt.ylim(-0.1, 1.1)
plt.subplots_adjust(left=0.05, right=0.98, top=0.98, bottom=0.05)
plt.show()
class Stickguy:
""" The stick guy. Only use in this package. """
def __init__(self, ax):
self.spine, = ax.plot([], [], lw=2)
self.left_arm, = ax.plot([], [], lw=2)
self.right_arm, = ax.plot([], [], lw=2)
self.left_leg, = ax.plot([], [], lw=2)
self.right_leg, = ax.plot([], [], lw=2)
def linear_animation(keytime, keyframe):
"""
The returned function computes interpolated keyframe curframe at given time t.
It uses the given keytime and splines parameters for this.
"""
def animation_function(t):
k = np.searchsorted(keytime, t, side='right') - 1
u = (t - keytime[k]) / (keytime[k + 1] - keytime[k])
curframe = (1.0 - u) * keyframe[k] + u * keyframe[k + 1]
return curframe
return animation_function
def cubic_animation(keytime, splines):
"""
The returned function computes interpolated keyframe curframe at given time t.
It uses the given keytime and splines parameters for this.
"""
def animation_function(t):
k = np.searchsorted(keytime, t, side='right') - 1
curframe = np.array([s[k](t) for s in splines])
return curframe
return animation_function
def param2pos(param, stickguy):
"""
Computes positions of joints for the stick guy.
Inputs:
param : list of parameters describing the pose
param[0]: height of hip
param[1]: angle of spine to vertical axis
param[2]: angle of upper arm 0 to spine
param[3]: angle of lower arm 0 to upper arm 0
param[4,5]: as above, other arm
param[6]: angle of neck/head to spine
param[7]: angle of upper leg 0 to vertical axis
param[8]: angle of lower leg 0 to upper leg 0
param[9,10]: as above, other leg
"""
hip_pos = | np.array([0.0, param[0]]) | numpy.array |
# *****************************************************************************
# © Copyright IBM Corp. 2018. All Rights Reserved.
#
# This program and the accompanying materials
# are made available under the terms of the Apache V2.0 license
# which accompanies this distribution, and is available at
# http://www.apache.org/licenses/LICENSE-2.0
#
# *****************************************************************************
"""
The Built In Functions module contains preinstalled functions
"""
import itertools as it
import datetime as dt
import importlib
import logging
import time
import numpy as np
import pandas as pd
import scipy as sp
from pyod.models.cblof import CBLOF
import numpy as np
import pandas as pd
import scipy as sp
from pyod.models.cblof import CBLOF
import ruptures as rpt
# for Spectral Analysis
from scipy import signal, fftpack
import skimage as ski
from skimage import util as skiutil # for nifty windowing
# for KMeans
from sklearn import ensemble
from sklearn import linear_model
from sklearn import metrics
from sklearn.covariance import MinCovDet
from sklearn.neighbors import (KernelDensity, LocalOutlierFactor)
from sklearn.pipeline import Pipeline, TransformerMixin
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import (StandardScaler, RobustScaler, MinMaxScaler,
minmax_scale, PolynomialFeatures)
from sklearn.utils import check_array
# for Matrix Profile
import stumpy
# for KDEAnomalyScorer
import statsmodels.api as sm
from statsmodels.nonparametric.kernel_density import KDEMultivariate
from statsmodels.tsa.arima.model import ARIMA
# EXCLUDED until we upgrade to statsmodels 0.12
#from statsmodels.tsa.forecasting.stl import STLForecast
from .base import (BaseTransformer, BaseRegressor, BaseEstimatorFunction, BaseSimpleAggregator)
from .bif import (AlertHighValue)
from .ui import (UISingle, UIMulti, UIMultiItem, UIFunctionOutSingle, UISingleItem, UIFunctionOutMulti)
# VAE
import torch
import torch.autograd
import torch.nn as nn
logger = logging.getLogger(__name__)
try:
# for gradient boosting
import lightgbm
except (AttributeError, ImportError):
logger.exception('')
logger.debug(f'Could not import lightgm package. Might have issues when using GBMRegressor catalog function')
PACKAGE_URL = 'git+https://github.com/ibm-watson-iot/functions.git@'
_IS_PREINSTALLED = True
Error_SmallWindowsize = 0.0001
Error_Generic = 0.0002
FrequencySplit = 0.3
DefaultWindowSize = 12
SmallEnergy = 1e-20
KMeans_normalizer = 1
Spectral_normalizer = 100 / 2.8
FFT_normalizer = 1
Saliency_normalizer = 1
Generalized_normalizer = 1 / 300
# from
# https://stackoverflow.com/questions/44790072/sliding-window-on-time-series-data
def view_as_windows1(temperature, length, step):
logger.info('VIEW ' + str(temperature.shape) + ' ' + str(length) + ' ' + str(step))
def moving_window(x, length, _step=1):
if type(step) != 'int' or _step < 1:
logger.info('MOVE ' + str(_step))
_step = 1
streams = it.tee(x, length)
return zip(*[it.islice(stream, i, None, _step) for stream, i in zip(streams, it.count(step=1))])
x_ = list(moving_window(temperature, length, step))
return np.asarray(x_)
def view_as_windows(temperature, length, step):
return skiutil.view_as_windows(temperature, window_shape=(length,), step=step)
def custom_resampler(array_like):
# initialize
if 'gap' not in dir():
gap = 0
if array_like.values.size > 0:
gap = 0
return 0
else:
gap += 1
return gap
def min_delta(df):
# minimal time delta for merging
if df is None:
return pd.Timedelta('5 seconds'), df
elif len(df.index.names) > 1:
df2 = df.reset_index(level=df.index.names[1:], drop=True)
else:
df2 = df
try:
mindelta = df2.index.to_series().diff().min()
except Exception as e:
logger.debug('Min Delta error: ' + str(e))
mindelta = pd.Timedelta('5 seconds')
if mindelta == dt.timedelta(seconds=0) or pd.isnull(mindelta):
mindelta = pd.Timedelta('5 seconds')
return mindelta, df2
def set_window_size_and_overlap(windowsize, trim_value=2 * DefaultWindowSize):
# make sure it exists
if windowsize is None:
windowsize = DefaultWindowSize
# make sure it is positive and not too large
trimmed_ws = np.minimum(np.maximum(windowsize, 1), trim_value)
# overlap
if trimmed_ws == 1:
ws_overlap = 0
else:
# larger overlap - half the window
ws_overlap = trimmed_ws // 2
return trimmed_ws, ws_overlap
def dampen_anomaly_score(array, dampening):
if dampening is None:
dampening = 0.9 # gradient dampening
if dampening >= 1:
return array
if dampening < 0.01:
return array
if array.size <= 1:
return array
gradient = np.gradient(array)
# dampened
grad_damp = np.float_power(abs(gradient), dampening) * np.sign(gradient)
# reconstruct (dampened) anomaly score by discrete integration
integral = []
x = array[0]
for x_el in np.nditer(grad_damp):
x = x + x_el
integral.append(x)
# shift array slightly to the right to position anomaly score
array_damp = np.roll(np.asarray(integral), 1)
array_damp[0] = array_damp[1]
# normalize
return array_damp / dampening / 2
# Saliency helper functions
# copied from https://github.com/y-bar/ml-based-anomaly-detection
# remove the boring part from an image resp. time series
def series_filter(values, kernel_size=3):
"""
Filter a time series. Practically, calculated mean value inside kernel size.
As math formula, see https://docs.opencv.org/2.4/modules/imgproc/doc/filtering.html.
:param values:
:param kernel_size:
:return: The list of filtered average
"""
filter_values = np.cumsum(values, dtype=float)
logger.info('SERIES_FILTER: ' + str(values.shape) + ',' + str(filter_values.shape) + ',' + str(kernel_size))
filter_values[kernel_size:] = filter_values[kernel_size:] - filter_values[:-kernel_size]
filter_values[kernel_size:] = filter_values[kernel_size:] / kernel_size
for i in range(1, kernel_size):
filter_values[i] /= i + 1
return filter_values
# Saliency class
# see https://www.inf.uni-hamburg.de/en/inst/ab/cv/research/research1-visual-attention.html
class Saliency(object):
def __init__(self, amp_window_size, series_window_size, score_window_size):
self.amp_window_size = amp_window_size
self.series_window_size = series_window_size
self.score_window_size = score_window_size
def transform_saliency_map(self, values):
"""
Transform a time-series into spectral residual, which is method in computer vision.
For example, See https://docs.opencv.org/master/d8/d65/group__saliency.html
:param values: a list or numpy array of float values.
:return: silency map and spectral residual
"""
freq = np.fft.fft(values)
mag = np.sqrt(freq.real ** 2 + freq.imag ** 2)
# remove the boring part of a timeseries
spectral_residual = np.exp(np.log(mag) - series_filter(np.log(mag), self.amp_window_size))
freq.real = freq.real * spectral_residual / mag
freq.imag = freq.imag * spectral_residual / mag
# and apply inverse fourier transform
saliency_map = np.fft.ifft(freq)
return saliency_map
def transform_spectral_residual(self, values):
saliency_map = self.transform_saliency_map(values)
spectral_residual = np.sqrt(saliency_map.real ** 2 + saliency_map.imag ** 2)
return spectral_residual
def merge_score(dfEntity, dfEntityOrig, column_name, score, mindelta):
"""
Fit interpolated score to original entity slice of the full dataframe
"""
# equip score with time values, make sure it's positive
score[score < 0] = 0
dfEntity[column_name] = score
# merge
dfEntityOrig = pd.merge_asof(dfEntityOrig, dfEntity[column_name], left_index=True, right_index=True,
direction='nearest', tolerance=mindelta)
if column_name + '_y' in dfEntityOrig:
merged_score = dfEntityOrig[column_name + '_y'].to_numpy()
else:
merged_score = dfEntityOrig[column_name].to_numpy()
return merged_score
#######################################################################################
# Scalers
#######################################################################################
class Standard_Scaler(BaseEstimatorFunction):
"""
Learns and applies standard scaling
"""
eval_metric = staticmethod(metrics.r2_score)
# class variables
train_if_no_model = True
def set_estimators(self):
self.estimators['standard_scaler'] = (StandardScaler, self.params)
logger.info('Standard Scaler initialized')
def __init__(self, features=None, targets=None, predictions=None):
super().__init__(features=features, targets=targets, predictions=predictions, keep_current_models=True)
# do not run score and call transform instead of predict
self.is_scaler = True
self.experiments_per_execution = 1
self.normalize = True # support for optional scaling in subclasses
self.prediction = self.predictions[0] # support for subclasses with univariate focus
self.params = {}
self.whoami = 'Standard_Scaler'
# used by all the anomaly scorers based on it
def prepare_data(self, dfEntity):
logger.debug(self.whoami + ': prepare Data for ' + self.prediction + ' column')
# operate on simple timestamp index
# needed for aggregated data with 3 or more indices
if len(dfEntity.index.names) > 1:
index_names = dfEntity.index.names
dfe = dfEntity.reset_index(index_names[1:])
else:
dfe = dfEntity
# interpolate gaps - data imputation
try:
dfe = dfe.interpolate(method="time")
except Exception as e:
logger.error('Prepare data error: ' + str(e))
# one dimensional time series - named temperature for catchyness
temperature = dfe[self.prediction].fillna(0).to_numpy(dtype=np.float64)
return dfe, temperature
# dummy function for scaler, can be replaced with anomaly functions
def kexecute(self, entity, df_copy):
return df_copy
def execute(self, df):
df_copy = df.copy()
entities = np.unique(df_copy.index.levels[0])
logger.debug(str(entities))
missing_cols = [x for x in self.predictions if x not in df_copy.columns]
for m in missing_cols:
df_copy[m] = None
for entity in entities:
normalize_entity = self.normalize
try:
check_array(df_copy.loc[[entity]][self.features].values, allow_nd=True)
except Exception as e:
normalize_entity = False
logger.error(
'Found Nan or infinite value in feature columns for entity ' + str(entity) + ' error: ' + str(e))
# support for optional scaling in subclasses
if normalize_entity:
dfe = super()._execute(df_copy.loc[[entity]], entity)
df_copy.loc[entity, self.predictions] = dfe[self.predictions]
else:
self.prediction = self.features[0]
df_copy = self.kexecute(entity, df_copy)
self.prediction = self.predictions[0]
logger.info('Standard_Scaler: Found columns ' + str(df_copy.columns))
return df_copy
@classmethod
def build_ui(cls):
# define arguments that behave as function inputs
inputs = []
inputs.append(UIMultiItem(name='features', datatype=float, required=True))
inputs.append(UIMultiItem(name='targets', datatype=float, required=True, output_item='predictions',
is_output_datatype_derived=True))
# define arguments that behave as function outputs
outputs = []
return inputs, outputs
class Robust_Scaler(BaseEstimatorFunction):
"""
Learns and applies robust scaling, scaling after outlier removal
"""
eval_metric = staticmethod(metrics.r2_score)
# class variables
train_if_no_model = True
def set_estimators(self):
self.estimators['robust_scaler'] = (RobustScaler, self.params)
logger.info('Robust Scaler initialized')
def __init__(self, features=None, targets=None, predictions=None):
super().__init__(features=features, targets=targets, predictions=predictions, keep_current_models=True)
# do not run score and call transform instead of predict
self.is_scaler = True
self.experiments_per_execution = 1
self.params = {}
def execute(self, df):
df_copy = df.copy()
entities = np.unique(df_copy.index.levels[0])
logger.debug(str(entities))
missing_cols = [x for x in self.predictions if x not in df_copy.columns]
for m in missing_cols:
df_copy[m] = None
for entity in entities:
# per entity - copy for later inplace operations
try:
check_array(df_copy.loc[[entity]][self.features].values, allow_nd=True)
except Exception as e:
logger.error(
'Found Nan or infinite value in feature columns for entity ' + str(entity) + ' error: ' + str(e))
continue
dfe = super()._execute(df_copy.loc[[entity]], entity)
df_copy.loc[entity, self.predictions] = dfe[self.predictions]
return df_copy
@classmethod
def build_ui(cls):
# define arguments that behave as function inputs
inputs = []
inputs.append(UIMultiItem(name='features', datatype=float, required=True))
inputs.append(UIMultiItem(name='targets', datatype=float, required=True, output_item='predictions',
is_output_datatype_derived=True))
# define arguments that behave as function outputs
outputs = []
return inputs, outputs
class MinMax_Scaler(BaseEstimatorFunction):
"""
Learns and applies minmax scaling
"""
eval_metric = staticmethod(metrics.r2_score)
# class variables
train_if_no_model = True
def set_estimators(self):
self.estimators['minmax_scaler'] = (MinMaxScaler, self.params)
logger.info('MinMax Scaler initialized')
def __init__(self, features=None, targets=None, predictions=None):
super().__init__(features=features, targets=targets, predictions=predictions, keep_current_models=True)
# do not run score and call transform instead of predict
self.is_scaler = True
self.experiments_per_execution = 1
self.params = {}
def execute(self, df):
df_copy = df.copy()
entities = | np.unique(df_copy.index.levels[0]) | numpy.unique |
import numpy as np
import os
import sys
import tensorflow as tf
import matplotlib.pyplot as plt
import matplotlib as mpl
if not os.path.exists(outputfolder):
os.makedirs(outputfolder)
for j in range(image_batch.shape[0]):
vis_util.visualize_ordered_boxes_and_labels_on_image_array(
image_temp0[j],
valid_output1['boxes'][j], # 4 * 4, ymin, xmin, ymax, xmax = box
box_classes[j], # (4,)
valid_output1['scores'][j], # (4,)
category_index,
use_normalized_coordinates=True,
max_boxes_to_draw=max_boxes,
min_score_thresh=min_score,
line_thickness=8)
vis_util.visualize_ordered_boxes_and_labels_on_image_array(
image_temp1[j],
foreground_output['boxes'][j], # 4 * 4, ymin, xmin, ymax, xmax = box
box_classes[j], # (4,)
foreground_output['scores'][j], # (4,)
category_index,
use_normalized_coordinates=True,
max_boxes_to_draw=max_boxes,
min_score_thresh=min_score,
line_thickness=8)
# plt.figure(figsize=IMAGE_SIZE)
fig,ax=plt.subplots(2,2,figsize=IMAGE_SIZE)
ax[0,0].imshow(image_temp0[j])
ax[0,1].imshow(image_temp1[j])
# plt.suptitle('min_area={0:.3f} max_area={1:.3f}'.format(min_area,max_area))
#display rescaled depth
rescaled = (image_depth[j] - np.min(image_depth[j]))/(np.max(image_depth[j])-np.min(image_depth[j]))
depth=ax[1,0].imshow(plasma(rescaled)[:,:,:3],cmap='plasma')
plt.colorbar(depth, ticks=[0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0],orientation='vertical')
ave= | np.mean(rescaled,axis=(0,1)) | numpy.mean |
from numpy import diag, arange, ones, sqrt, dot, ravel
from scipy import rand
from pyamg.util.linalg import norm
from scipy.sparse import csr_matrix
from pyamg.gallery import poisson
from pyamg.multilevel import multilevel_solver, coarse_grid_solver
from numpy.testing import TestCase, assert_almost_equal, assert_equal
def precon_norm(v, ml):
''' helper function to calculate preconditioner norm of v '''
v = ravel(v)
w = ml.aspreconditioner()*v
return sqrt(dot(v.conjugate(), w))
class TestMultilevel(TestCase):
def test_coarse_grid_solver(self):
cases = []
cases.append(csr_matrix(diag(arange(1, 5, dtype=float))))
cases.append(poisson((4,), format='csr'))
cases.append(poisson((4, 4), format='csr'))
from pyamg.krylov import cg
def fn(A, b):
return cg(A, b)[0]
# method should be almost exact for small matrices
for A in cases:
for solver in ['splu', 'pinv', 'pinv2', 'lu', 'cholesky',
'cg', fn]:
s = coarse_grid_solver(solver)
b = arange(A.shape[0], dtype=A.dtype)
x = s(A, b)
assert_almost_equal(A*x, b)
# subsequent calls use cached data
x = s(A, b)
assert_almost_equal(A*x, b)
def test_aspreconditioner(self):
from pyamg import smoothed_aggregation_solver
from scipy.sparse.linalg import cg
from pyamg.krylov import fgmres
A = poisson((50, 50), format='csr')
b = rand(A.shape[0])
ml = smoothed_aggregation_solver(A)
for cycle in ['V', 'W', 'F']:
M = ml.aspreconditioner(cycle=cycle)
x, info = cg(A, b, tol=1e-8, maxiter=30, M=M)
# cg satisfies convergence in the preconditioner norm
assert(precon_norm(b - A*x, ml) < 1e-8*precon_norm(b, ml))
for cycle in ['AMLI']:
M = ml.aspreconditioner(cycle=cycle)
x, info = fgmres(A, b, tol=1e-8, maxiter=30, M=M)
# fgmres satisfies convergence in the 2-norm
assert(norm(b - A*x) < 1e-8*norm(b))
def test_accel(self):
from pyamg import smoothed_aggregation_solver
from pyamg.krylov import cg, bicgstab
A = poisson((50, 50), format='csr')
b = rand(A.shape[0])
ml = smoothed_aggregation_solver(A)
# cg halts based on the preconditioner norm
for accel in ['cg', cg]:
x = ml.solve(b, maxiter=30, tol=1e-8, accel=accel)
assert(precon_norm(b - A*x, ml) < 1e-8*precon_norm(b, ml))
residuals = []
x = ml.solve(b, maxiter=30, tol=1e-8, residuals=residuals,
accel=accel)
assert(precon_norm(b - A*x, ml) < 1e-8*precon_norm(b, ml))
# print residuals
assert_almost_equal(precon_norm(b - A*x, ml), residuals[-1])
# cgs and bicgstab use the Euclidean norm
for accel in ['bicgstab', 'cgs', bicgstab]:
x = ml.solve(b, maxiter=30, tol=1e-8, accel=accel)
assert(norm(b - A*x) < 1e-8*norm(b))
residuals = []
x = ml.solve(b, maxiter=30, tol=1e-8, residuals=residuals,
accel=accel)
assert(norm(b - A*x) < 1e-8*norm(b))
# print residuals
assert_almost_equal(norm(b - A*x), residuals[-1])
def test_cycle_complexity(self):
# four levels
levels = []
levels.append(multilevel_solver.level())
levels[0].A = csr_matrix(ones((10, 10)))
levels[0].P = csr_matrix(ones((10, 5)))
levels.append(multilevel_solver.level())
levels[1].A = csr_matrix(ones((5, 5)))
levels[1].P = csr_matrix(ones((5, 3)))
levels.append(multilevel_solver.level())
levels[2].A = csr_matrix(ones((3, 3)))
levels[2].P = csr_matrix(ones((3, 2)))
levels.append(multilevel_solver.level())
levels[3].A = csr_matrix( | ones((2, 2)) | numpy.ones |
import random
import os
import numpy as NP
from Simulations.GameFeatures import GameFeatures as GF
class BehaviouralModelInterface:
def __init__(self, goals, initial_game_state, feasible_actions, result_addr):
self._goals = goals
self._initial_game_state = initial_game_state
self._feasible_actions = feasible_actions
self._coordinate_history = []
self._result_addr = result_addr
self._create_directory(self._result_addr)
def _create_directory(self, addr):
try:
directory = ''.join(folder + "/" for folder in addr.split('/')[:-1])
os.makedirs(directory)
except FileExistsError:
pass
def action(self, game_state): #game_state = [survival_time, health, points, coordinate, map_colors]
score = self._calculate_score(game_state[0], game_state[2], game_state[3])
nr_of_actions = len(self._feasible_actions)
index = random.randint(0, nr_of_actions-1)
return self._feasible_actions[index]
def _calculate_score(self, survival_time, resources, coordinate):
score = 0
if GF.GoalSystem.Time in self._goals:
score += survival_time * 0.1
if GF.GoalSystem.Resources in self._goals:
score += resources * 1
if GF.GoalSystem.Safety in self._goals:
score += (1 / self._coordinate_variance(coordinate, 10)) * 0.1
if score == 0: score = 0.00001
normalized_score = 1 - (1/score)
if normalized_score < 0:
normalized_score = 0
return score
def _coordinate_variance(self, new_coor, filter_size):
self._add_coor_to_history(new_coor, filter_size)
mean = NP.mean(self._coordinate_history, axis=0)
dist_to_mean = [ | NP.linalg.norm(mean-coor) | numpy.linalg.norm |
# -*- coding: UTF-8 -*-
# @Time : 04/02/2020 10:58
# @Author : Lijiannan
# @Update : BubblyYi
# @FileName: data_provider.py
# @Software: PyCharm
from torch.utils.data import Dataset
from torch.utils.data import DataLoader
import torch
import pandas as pd
import os
import numpy as np
import SimpleITK as sitk
import random
class DataGenerater(Dataset):
def __init__(self,data_path, pre_fix_path, number_points, transform = None, flag = '', target_transform = None):
self.flag = flag
data = []
print("csv path:",data_path)
csv_data = pd.read_csv(data_path)
x_data = csv_data['patch_name']
if self.flag == 'train' or self.flag == 'val':
pre_ind = csv_data["pre_ind"]
next_ind = csv_data["next_ind"]
radials = csv_data["radials"]
for i in range(len(x_data)):
if pre_fix_path is None:
data.append((temp, pre_ind[i], next_ind[i], radials[i]))
else:
temp = os.path.join(pre_fix_path,x_data[i])
data.append((temp, pre_ind[i], next_ind[i], radials[i]))
else:
for i in range(len(x_data)):
if pre_fix_path is None:
data.append(x_data[i])
else:
temp = os.path.join(pre_fix_path, x_data[i])
data.append(temp)
self.data = data
self.transform = transform
self.target_transform = target_transform
self.number_points = number_points
self.p_gaussian_noise = 0.2
def __getitem__(self, index):
if self.flag == 'train' or self.flag == 'val':
data_path, p1,p2,r = self.data[index] # 通过index索引返回一个图像路径fn 与 标签label
img = sitk.GetArrayFromImage(sitk.ReadImage(data_path, sitk.sitkFloat32))
shell_data = np.zeros(self.number_points)
shell_data[p1] = 0.5
shell_data[p2] = 0.5
radials = r
upper_bound = | np.percentile(img, 99.5) | numpy.percentile |
"""
Copyright (c) 2014 NavPy Developers. All rights reserved.
Use of this source code is governed by a BSD-style license that can be found in
LICENSE.txt
"""
import numpy as np
from . import wgs84
from ..utils import input_check_Nx3 as _input_check_Nx3
from ..utils import input_check_Nx3x3 as _input_check_Nx3x3
from ..utils import input_check_Nx1 as _input_check_Nx1
def angle2dcm(rotAngle1, rotAngle2, rotAngle3, input_unit='rad',
rotation_sequence='ZYX', output_type='ndarray'):
"""
This function converts Euler Angle into Direction Cosine Matrix (DCM).
The DCM is described by three sucessive rotation rotAngle1, rotAngle2, and
rotAngle3 about the axes described by the rotation_sequence.
The default rotation_sequence='ZYX' is the aerospace sequence and rotAngle1
is the yaw angle, rotAngle2 is the pitch angle, and rotAngle3 is the roll
angle. In this case DCM transforms a vector from the locally level
coordinate frame (i.e. the NED frame) to the body frame.
This function can batch process a series of rotations (e.g., time series
of Euler angles).
Parameters
----------
rotAngle1, rotAngle2, rotAngle3 : angles {(N,), (N,1), or (1,N)}
They are a sequence of angles about successive axes described by
rotation_sequence.
input_unit : {'rad', 'deg'}, optional
Rotation angles. Default is 'rad'.
rotation_sequence : {'ZYX'}, optional
Rotation sequences. Default is 'ZYX'.
output_type : {'ndarray','matrix'}, optional
Output type. Default is 'ndarray'.
Returns
--------
C : {3x3} Direction Cosine Matrix
Notes
-----
Programmer: <NAME>
Created: May 03, 2011
Last Modified: January 12, 2016
"""
rotAngle1, N1 = _input_check_Nx1(rotAngle1)
rotAngle2, N2 = _input_check_Nx1(rotAngle2)
rotAngle3, N3 = _input_check_Nx1(rotAngle3)
if(N1 != N2 or N1 != N3):
raise ValueError('Inputs are not of same dimensions')
if(N1 > 1 and output_type != 'ndarray'):
raise ValueError('Matrix output requires scalar inputs')
R3 = np.zeros((N1, 3, 3))
R2 = np.zeros((N1, 3, 3))
R1 = np.zeros((N1, 3, 3))
if(input_unit == 'deg'):
rotAngle1 = np.deg2rad(rotAngle1)
rotAngle2 = np.deg2rad(rotAngle2)
rotAngle3 = np.deg2rad(rotAngle3)
R3[:, 2, 2] = 1.0
R3[:, 0, 0] = np.cos(rotAngle1)
R3[:, 0, 1] = np.sin(rotAngle1)
R3[:, 1, 0] = -np.sin(rotAngle1)
R3[:, 1, 1] = np.cos(rotAngle1)
R2[:, 1, 1] = 1.0
R2[:, 0, 0] = np.cos(rotAngle2)
R2[:, 0, 2] = -np.sin(rotAngle2)
R2[:, 2, 0] = np.sin(rotAngle2)
R2[:, 2, 2] = np.cos(rotAngle2)
R1[:, 0, 0] = 1.0
R1[:, 1, 1] = np.cos(rotAngle3)
R1[:, 1, 2] = np.sin(rotAngle3)
R1[:, 2, 1] = -np.sin(rotAngle3)
R1[:, 2, 2] = np.cos(rotAngle3)
if rotation_sequence == 'ZYX':
try:
# Equivalent to C = R1.dot(R2.dot(R3)) for each of N inputs but
# implemented efficiently in C extension
C = np.einsum('nij, njk, nkm -> nim', R1, R2, R3)
except AttributeError:
# Older NumPy without einsum
C = np.zeros((N1, 3, 3))
for i, (R1, R2, R3) in enumerate(zip(R1, R2, R3)):
C[i] = R1.dot(R2.dot(R3))
else:
raise NotImplementedError('Rotation sequences other than ZYX are not currently implemented')
if(N1 == 1):
C = C[0]
if(output_type == 'matrix'):
C = np.matrix(C)
return C
def dcm2angle(C, output_unit='rad', rotation_sequence='ZYX'):
"""
This function converts a Direction Cosine Matrix (DCM) into the three
rotation angles.
The DCM is described by three sucessive rotation rotAngle1, rotAngle2, and
rotAngle3 about the axes described by the rotation_sequence.
The default rotation_sequence='ZYX' is the aerospace sequence and rotAngle1
is the yaw angle, rotAngle2 is the pitch angle, and rotAngle3 is the roll
angle. In this case DCM transforms a vector from the locally level
coordinate frame (i.e. the NED frame) to the body frame.
This function can batch process a series of rotations (e.g., time series
of direction cosine matrices).
Parameters
----------
C : {(3,3), (N,3,3), or (3,3,N)}
direction consine matrix that rotates the vector from the first frame
to the second frame according to the specified rotation_sequence.
output_unit : {'rad', 'deg'}, optional
Rotation angles. Default is 'rad'.
rotation_sequence : {'ZYX'}, optional
Rotation sequences. Default is 'ZYX'.
Returns
-------
rotAngle1, rotAngle2, rotAngle3 : angles
They are a sequence of angles about successive axes described by
rotation_sequence.
Notes
-----
The returned rotAngle1 and 3 will be between +/- 180 deg (+/- pi rad).
In contrast, rotAngle2 will be in the interval +/- 90 deg (+/- pi/2 rad).
In the 'ZYX' or '321' aerospace sequence, that means the pitch angle
returned will always be inside the closed interval +/- 90 deg (+/- pi/2 rad).
Applications where pitch angles near or larger than 90 degrees in magnitude
are expected should used alternate attitude parameterizations like
quaternions.
"""
C, N = _input_check_Nx3x3(C)
if(rotation_sequence == 'ZYX'):
rotAngle1 = np.arctan2(C[..., 0, 1], C[..., 0, 0]) # Yaw
rotAngle2 = -np.arcsin(C[..., 0, 2]) # Pitch
rotAngle3 = np.arctan2(C[..., 1, 2], C[..., 2, 2]) # Roll
else:
raise NotImplementedError('Rotation sequences other than ZYX are not currently implemented')
if(output_unit == 'deg'):
rotAngle1 = np.rad2deg(rotAngle1)
rotAngle2 = np.rad2deg(rotAngle2)
rotAngle3 = np.rad2deg(rotAngle3)
return rotAngle1, rotAngle2, rotAngle3
def omega2rates(pitch, roll, input_unit='rad',
euler_angles_order='roll_pitch_yaw', output_type='ndarray'):
"""
This function is used to create the transformation matrix to go from:
[p, q, r] --> [roll_rate, pitch_rate, yaw_rate]
where pqr are xyz body rotation-rate measurements expressed in body frame.
Yaw, pitch, and roll are the Euler angles. We assume the Euler angles are
3-2-1 (i.e Yaw -> Pitch -> Roll) transformations that go from navigation-
frame to body-frame.
Parameters
----------
pitch : pitch angle, units of input_unit.
roll : roll angle , units of input_unit.
input_unit : units for input angles {'rad', 'deg'}, optional
euler_angles_order : {'roll_pitch_yaw', 'yaw_pitch_roll'}, optional
Assumed order of Euler Angles attitude state vector (see ``Notes``).
output_type : {'ndarray' or 'matrix'}, optional
Numpy array (default) or matrix
Returns
-------
R : transformation matrix, from xyz body-rate to Euler angle-rates
numpy 'output_type' 3x3 (Note: default return variable is an ARRAY,
not a matrix)
Notes
-----
Since the returned transformation matrix is used to transform one vector
to another, the assumed attitude variables order matters.
The ``euler_angles_order`` parameter can be used to specify the assumed
order.
The difference is demonstrated by example:
By default euler_angles_order='roll_pitch_yaw'
R = omega2rates(pitch, roll)
[ roll_rate] [omega_x]
[pitch_rate] = dot(R,[omega_y])
[ yaw_rate] [omega_z]
Now assume our attitude state is [yaw, pitch, roll].T
R = omega2rates(pitch, roll, euler_angles_order='yaw_pitch_roll')
[ yaw_rate] [omega_x]
[pitch_rate] = dot(R,[omega_y])
[ roll_rate] [omega_z]
References
----------
[1] Equation 2.74, Aided Navigation: GPS with High Rate Sensors,
<NAME> 2008
[2] omega2rates.m function at:
http://www.gnssapplications.org/downloads/chapter7/Chapter7_GNSS_INS_Functions.tar.gz
"""
# Apply necessary unit transformations.
if input_unit == 'rad':
pitch_rad, roll_rad = pitch, roll
elif input_unit == 'deg':
pitch_rad, roll_rad = np.radians([pitch, roll])
# Build transformation matrix.
s_r, c_r = np.sin( roll_rad), np.cos( roll_rad)
s_p, c_p = | np.sin(pitch_rad) | numpy.sin |
"""
Two way BANOVA
"""
from __future__ import division
import numpy as np
import pymc3 as pm
import pandas as pd
import matplotlib.pyplot as plt
plt.style.use('seaborn-darkgrid')
from scipy.stats import norm
from theano import tensor as tt
# THE DATA.
# Specify data source:
data_source = ["QianS2007" , "Salary" , "Random" , "Ex19.3"][1]
# Load the data:
if data_source == "QianS2007":
data_record = pd.read_csv("QianS2007SeaweedData.txt")
# Logistic transform the COVER value:
# Used by Appendix 3 of QianS2007 to replicate Ramsey and Schafer (2002).
data_record['COVER'] = -np.log((100/data_record['COVER']) -1)
y = data_record['COVER'].values
x1 = pd.Categorical(data_record['TREAT']).codes
x1names = data_record['TREAT'].values
x2 = pd.Categorical(data_record['BLOCK']).codes
x2names = data_record['BLOCK'].values
Ntotal = len(y)
Nx1Lvl = len(set(x1))
Nx2Lvl = len(set(x2))
x1contrastDict = {'f_Effect':[1/2, -1/2, 0, 1/2, -1/2, 0],
'F_Effect':[0, 1/2, -1/2, 0, 1/2, -1/2],
'L_Effect':[1/3, 1/3, 1/3, -1/3, -1/3, -1/3 ]}
x2contrastDict = None # np.zeros(Nx2Lvl)
x1x2contrastDict = None # np.zeros(Nx1Lvl*Nx2Lvl, Nx1Lvl)
if data_source == "Salary":
data_record = pd.read_csv("Salary.csv")
y = data_record['Salary']
x1 = pd.Categorical(data_record['Org']).codes
x1names = data_record['Org'].unique()
x1names.sort()
x2 = pd.Categorical(data_record['Post']).codes
x2names = data_record['Post'].unique()
x2names.sort()
Ntotal = len(y)
Nx1Lvl = len(set(x1))
Nx2Lvl = len(set(x2))
x1contrastDict = {'BFINvCEDP':[1, -1, 0, 0],
'CEDPvTHTR':[0, 1, 0, -1]}
x2contrastDict = {'FT1vFT2':[1, -1, 0],
'FT2vFT3':[0,1,-1]}
x1x2contrastDict = {'CHEMvTHTRxFT1vFT3':np.outer([0, 0, 1, -1], [1,0,-1]),
'BFINvOTHxFT1vOTH':np.outer([1, -1/3, -1/3, -1/3], [1, -1/2, -1/2])}
if data_source == "Random":
np.random.seed(47405)
ysdtrue = 3
a0true = 100
a1true = np.array([2, 0, -2]) # sum to zero
a2true = np.array([3, 1, -1, -3]) # sum to zero
a1a2true = np.array([[1,-1,0, 0], [-1,1,0,0], [0,0,0,0]])
npercell = 8
index = np.arange(len(a1true)*len(a2true)*npercell)
data_record = pd.DataFrame(index=index, columns=["y","x1","x2"])
rowidx = 0
for x1idx in range(0, len(a1true)):
for x2idx in range(0, len(a2true)):
for subjidx in range(0, npercell):
data_record['x1'][rowidx] = x1idx
data_record['x2'][rowidx] = x2idx
data_record['y'][rowidx] = float(a0true + a1true[x1idx] + a2true[x2idx]
+ a1a2true[x1idx, x2idx] + norm.rvs(loc=0, scale=ysdtrue, size=1)[0])
rowidx += 1
y = data_record['y']
x1 = pd.Categorical(data_record['x1']).codes
x1names = data_record['x1'].unique()
x2 = pd.Categorical(data_record['x2']).codes
x2names = data_record['x2'].unique()
Ntotal = len(y)
Nx1Lvl = len(set(x1))
Nx2Lvl = len(set(x2))
x1contrast_dict = {'X1_1v3': [1, 0, -1]} #
x2contrast_dict = {'X2_12v34':[1/2, 1/2, -1/2, -1/2]} #
x1x2contrast_dict = {'IC_11v22': np.outer([1, -1, 0], [1, -1, 0, 0]),
'IC_23v34': np.outer([0, 1, -1], [0, 0, 1, -1])}
if data_source == 'Ex19.3':
y = [101,102,103,105,104, 104,105,107,106,108, 105,107,106,108,109, 109,108,110,111,112]
x1 = [0,0,0,0,0, 0,0,0,0,0, 1,1,1,1,1, 1,1,1,1,1]
x2 = [0,0,0,0,0, 1,1,1,1,1, 0,0,0,0,0, 1,1,1,1,1]
S = [0,1,2,3,4, 0,1,2,3,4, 0,1,2,3,4, 0,1,2,3,4]
x1names = ['x1.1' ,'x1.2']
x2names = ['x2.1', "x2.2"]
Snames = ['S1', 'S2', 'S3', 'S4', 'S5']
Ntotal = len(y)
Nx1Lvl = len(set(x1))
Nx2Lvl = len(set(x2))
NSLvl = len(set(S))
x1contrast_dict = {'X1.2vX1.1':[-1 , 1]}
x2contrast_dict = {'X2.2vX2.1':[-1 , 1]}
x1x2contrast_dict = None #np.arange(0, Nx1Lvl*Nx2Lvl).reshape(Nx1Lvl, -1).T
z = (y - np.mean(y))/np.std(y)
z = (y - np.mean(y))/np.std(y)
# THE MODEL.
with pm.Model() as model:
# define the hyperpriors
a1_SD_unabs = pm.StudentT('a1_SD_unabs', mu=0, lam=0.001, nu=1)
a1_SD = abs(a1_SD_unabs) + 0.1
a1tau = 1 / a1_SD**2
a2_SD_unabs = pm.StudentT('a2_SD_unabs', mu=0, lam=0.001, nu=1)
a2_SD = abs(a2_SD_unabs) + 0.1
a2tau = 1 / a2_SD**2
a1a2_SD_unabs = pm.StudentT('a1a2_SD_unabs', mu=0, lam=0.001, nu=1)
a1a2_SD = abs(a1a2_SD_unabs) + 0.1
a1a2tau = 1 / a1a2_SD**2
# define the priors
sigma = pm.Uniform('sigma', 0, 10) # y values are assumed to be standardized
tau = 1 / sigma**2
a0 = pm.Normal('a0', mu=0, tau=0.001) # y values are assumed to be standardized
a1 = pm.Normal('a1', mu=0 , tau=a1tau, shape=Nx1Lvl)
a2 = pm.Normal('a2', mu=0 , tau=a2tau, shape=Nx2Lvl)
a1a2 = pm.Normal('a1a2', mu=0 , tau=a1a2tau, shape=[Nx1Lvl, Nx2Lvl])
b1 = pm.Deterministic('b1', a1 - tt.mean(a1))
b2 = pm.Deterministic('b2', a2 - tt.mean(a2))
b1b2 = pm.Deterministic('b1b2', a1a2 - tt.mean(a1a2))
mu = a0 + b1[x1] + b2[x2] + b1b2[x1, x2]
# define the likelihood
yl = pm.Normal('yl', mu=mu, tau=tau, observed=z)
# Generate a MCMC chain
trace = pm.sample(2000)
# EXAMINE THE RESULTS
# Print summary for each trace
#pm.summary(trace)
# Check for mixing and autocorrelation
#pm.autocorrplot(trace, vars=model.unobserved_RVs[:-1])
## Plot KDE and sampled values for each parameter.
pm.traceplot(trace)
# Extract values of 'a'
a0_sample = trace['a0']
b1_sample = trace['b1']
b2_sample = trace['b2']
b1b2_sample = trace['b1b2']
b0_sample = a0_sample * np.std(y) + np.mean(y)
b1_sample = b1_sample * np.std(y)
b2_sample = b2_sample * np.std(y)
b1b2_sample = b1b2_sample * np.std(y)
plt.figure(figsize=(25,20))
ax = plt.subplot(451)
pm.plot_posterior(b0_sample, bins=50, ax=ax)
ax.set_xlabel(r'$\beta0$')
ax.set_title('Baseline')
plt.xlim(b0_sample.min(), b0_sample.max());
count = 2
for i in range(len(b1_sample[0])):
ax = plt.subplot(4, 5, count)
pm.plot_posterior(b1_sample[:,i], ax=ax)
ax.set_xlabel(r'$\beta1_{}$'.format(i))
ax.set_title('x1: {}'.format(x1names[i]))
count += 1
for i in range(len(b2_sample[0])):
ax = plt.subplot(4, 5, count)
pm.plot_posterior(b2_sample[:,i], bins=50, ax=ax)
ax.set_xlabel(r'$\beta2_{}$'.format(i)),
ax.set_title('x1: {}'.format(x2names[i]))
count += 1
for j in range(len(b1_sample[0])):
ax = plt.subplot(4, 5, count)
pm.plot_posterior(b1b2_sample[:,j,i], bins=50, ax=ax)
ax.set_title('x1: {}, x2: {}'.format(x1names[j], x2names[i]))
ax.set_xlabel(r'$\beta12_{}{}$'.format(i, j))
count += 1
plt.tight_layout()
plt.savefig('Figure_19.4.png')
## Display contrast analyses
plt.figure(figsize=(10, 12))
count = 1
for key, value in x1contrastDict.items():
contrast = np.dot(b1_sample, value)
ax = plt.subplot(3, 2, count)
pm.plot_posterior(contrast, ref_val=0.0, bins=50, ax=ax)
ax.set_title('Contrast {}'.format(key))
count += 1
for key, value in x2contrastDict.items():
contrast = np.dot(b2_sample, value)
ax = plt.subplot(3, 2, count)
pm.plot_posterior(contrast, ref_val=0.0, bins=50, ax=ax)
ax.set_title('Contrast {}'.format(key))
count += 1
for key, value in x1x2contrastDict.items():
contrast = | np.tensordot(b1b2_sample, value) | numpy.tensordot |
"""
Functions for (super-uniform) sampling from the unit hypercube.
"""
import random
import itertools
import numpy as np
from .distance import distance_matrix, distance_to_boundary
def unitcube(dimension):
"""Shortcut to generate a tuple of bounds of the unit hypercube."""
assert dimension > 0
return [0.0] * dimension, [1.0] * dimension
def grid(n_levels, dimension, sukharev=False):
"""Create conventional grid in the unit hypercube.
Also related to full factorial designs.
Parameters
----------
n_levels : int
The number of levels in each dimension.
dimension : int
The dimension of the space.
sukharev : bool, optional
Switch for creating a Sukharev grid where the points are located at the
centroids of the subcells, e.g. [0.25, 0.75] instead of [0, 1].
Returns
-------
points : (`n_levels` ** `dimension`, `dimension`) numpy array
"""
if sukharev:
x = np.linspace(0, 1, n_levels, endpoint=False) + 0.5 / n_levels
else:
x = np.linspace(0, 1, n_levels)
return np.array(list(itertools.product(x, repeat=dimension)))
def sample_halton(num_points, dimension, skip=20):
"""Generate a Halton point set.
Low discrepency quasi-random sequence using the Van der Corput sequence with the
first `dimension` prime numbers as base.
Parameters
----------
num_points : int
The number of points to generate.
dimension : int
The dimension of the space.
skip : int, optional
The first `skip` points of the sequence will be left out.
Returns
-------
points : (`num_points`, `dimension`) numpy array
"""
def van_der_corput(num_points, base, skip=0):
sequence = []
for i in range(skip + 1, skip + num_points + 1):
nth_number = 0
denom = 1.0
quotient = i
while quotient > 0:
quotient, remainder = divmod(quotient, base)
denom *= base
nth_number += remainder / denom
sequence.append(nth_number)
return sequence
# select at least as many primes as there are dimensions
bases = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]
bases += [73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151]
bases += [157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233]
while len(bases) < dimension:
b = bases[-1] + 2
while np.any(b % np.array(bases) == 0): # while not prime
b += 2
bases.append(b)
points = [van_der_corput(num_points, bases[d], skip=skip) for d in range(dimension)]
return np.array(points).T
def sample_k_means(
num_points,
dimension,
num_steps=None,
initial_points=None,
dist_args={},
callback=None,
):
"""MacQueen's method.
In its default setup, this algorithm converges to a centroidal Voronoi
tesselation of the unit hypercube. Further information is given in
[MacQueen1967]_.
Parameters
----------
num_points : int
The number of points to generate.
dimension : int
The dimension of the space.
num_steps : int, optional
The number of iterations to carry out. Default is
``100 * num_points``.
initial_points : array_like, optional
The point set to improve (if None, a sample is drawn with
:func:`stratified_sampling`).
dist_args : dict, optional
Arguments for the distance calculation.
callback : callable, optional
If provided, it is called in each iteration with the current point
set as argument for monitoring progress.
Returns
-------
cluster_centers : (`num_points`, `dimension`) numpy array
References
----------
.. [MacQueen1967] <NAME>. Some methods for classification and
analysis of multivariate observations. Proceedings of the Fifth
Berkeley Symposium on Mathematical Statistics and Probability,
Volume 1: Statistics, pp. 281--297, University of California Press,
Berkeley, Calif., 1967.
http://projecteuclid.org/euclid.bsmsp/1200512992.
"""
# initialization
if num_steps is None:
num_steps = 100 * num_points
if initial_points is None:
cluster_centers = sample_from_strata(
stratify_generalized(num_points, dimension)
)
elif len(initial_points) == num_points:
cluster_centers = np.array(initial_points)
assert np.all(cluster_centers >= 0.0)
assert np.all(cluster_centers <= 1.0)
else:
raise ValueError("len(initial_points) must be equal to num_points")
weights = [1.0] * num_points
# begin iteration
for _ in range(num_steps):
if callback is not None:
callback(cluster_centers)
sample_point = np.random.rand(1, dimension)
distances = distance_matrix(sample_point, cluster_centers, **dist_args)
sample_point = sample_point.ravel()
nearest_index = int(np.argmin(distances, axis=1))
nearest_cluster_center = cluster_centers[nearest_index, :].ravel()
if dist_args.get("max_dist", None) is not None:
one_dim_dists = np.abs(nearest_cluster_center - sample_point)
virtual_point = | np.array(sample_point) | numpy.array |
# 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) | numpy.mean |
# based on https://github.com/openai/baselines/blob/master/baslines/common/atari_wrappers.py
import numpy as np
import os
os.environ.setdefault('PATH', '')
from collections import deque
import gym
from gym import spaces
import cv2
cv2.ocl.setUseOpenCL(False)
#from matplotlib import pyplot
class NoopResetEnv(gym.Wrapper):
def __init__(self, env, noop_max=30):
"""Sample initial states by taking random number of no-ops on reset.
No-op is assumed to be action 0.
"""
gym.Wrapper.__init__(self, env)
self.noop_max = noop_max
self.override_num_noops = None
self.noop_action = 0
assert env.unwrapped.get_action_meanings()[0] == 'NOOP'
def reset(self, **kwargs):
""" Do no-op action for a number of steps in [1, noop_max]."""
self.env.reset(**kwargs)
if self.override_num_noops is not None:
noops = self.override_num_noops
else:
noops = self.unwrapped.np_random.randint(1, self.noop_max + 1)
assert noops > 0
obs = None
for _ in range(noops):
obs, _, done, _ = self.env.step(self.noop_action)
if done:
obs = self.env.reset(**kwargs)
return obs
def step(self, ac):
return self.env.step(ac)
class TwoLatestFramesEnv(gym.Wrapper):
def __init__(self, env):
"""Return the last two observations"""
gym.Wrapper.__init__(self, env)
# most recent raw observations (for max pooling across time steps)
self._obs_buffer = deque([], maxlen=2) #np.zeros((2,)+env.observation_space.shape, dtype=np.uint8)
self.idx = 0
def step(self, action):
"""Store the last observation and return the storage.
Note that the observation is mutable and must be processed by np.maximum() before using or storing
"""
obs, reward, done, info = self.env.step(action)
self._obs_buffer.append(obs)
return self._obs_buffer, reward, done, info
def reset(self, **kwargs):
ob = self.env.reset(**kwargs)
for _ in range(2):
self._obs_buffer.append(ob)
return self._obs_buffer
class MaxAndSkipAndRewardClipEnv(gym.Wrapper):
def __init__(self, env, skip=4, clip=True):
"""Return only every `skip`-th frame"""
gym.Wrapper.__init__(self, env)
assert type(skip) == int and skip > 0
self._skip = skip
self.clip = clip
def step(self, action):
"""Repeat action, sum reward, and max over last observations."""
total_reward = 0.0
total_clipped_reward = 0.0
for i in range(self._skip):
obs, reward, done, info = self.env.step(action)
total_reward += reward
if self.clip:
total_clipped_reward += np.sign(reward)
if done:
break
# Note that the observation on the done=True frame
# doesn't matter
max_frame = np.maximum(*obs, dtype=np.uint8)
reward = (total_reward, total_clipped_reward) if self.clip else total_reward
return max_frame, reward, done, info
def reset(self, **kwargs):
return np.maximum(*self.env.reset(**kwargs), dtype=np.uint8)
class EpisodicLifeEnv(gym.Wrapper):
def __init__(self, env):
"""Make end-of-life == end-of-episode, but only reset on true game over.
Done by DeepMind for the DQN and co. since it helps value estimation.
"""
gym.Wrapper.__init__(self, env)
self.lives = 0 # env.reset() will be called before it starts. Therefore this initial value does not matter.
self.was_real_done = True
# If it is not waiting for reset, we regard the reset as an accident and we truly reset the environment.
self.waiting_for_reset = False
self.reset_ob = None
def step(self, action):
assert not self.waiting_for_reset
ob, reward, done, info = self.env.step(action)
self.was_real_done = done # this includes the case of "TimeLimit.truncated"
# check current lives, make loss of life terminal,
# then update lives to handle bonus lives
lives = self.env.unwrapped.ale.lives()
# usually "done" must be False with "lives < self.lives and lives > 0", but with "TimeLimit" it can be True
if lives < self.lives and lives > 0 and not done:
# for Qbert sometimes we stay in lives == 0 condtion for a few frames
# so its important to keep lives > 0, so that we only reset once
# the environment advertises done.
done = True
# no-op step to advance from terminal/lost life state
# In order to avoid problems caused by the step "self.env.step(0)" during the reset, we execute "self.env.step(0)" in advance.
self.reset_ob, _, self.was_real_done, _ = self.env.step(0)
self.waiting_for_reset = True
self.lives = lives
return ob, reward, done, info
def reset(self, **kwargs):
"""Reset only when lives are exhausted.
This way all states are still reachable even though lives are episodic,
and the learner need not know about any of this behind-the-scenes.
"""
if not self.was_real_done and self.waiting_for_reset:
# extract the result of the previous no-op step
ob = self.reset_ob
self.reset_ob = None
else:
ob = self.env.reset(**kwargs)
self.was_real_done = False
self.lives = self.env.unwrapped.ale.lives()
self.waiting_for_reset = False
return ob
class FireResetEnv(gym.Wrapper):
def __init__(self, env):
"""Take action on reset for environments that are fixed until firing."""
gym.Wrapper.__init__(self, env)
assert env.unwrapped.get_action_meanings()[1] == 'FIRE'
assert len(env.unwrapped.get_action_meanings()) >= 3
def reset(self, **kwargs):
self.env.reset(**kwargs)
obs, _, done, _ = self.env.step(1)
if done:
self.env.reset(**kwargs)
obs, _, done, _ = self.env.step(2)
if done:
self.env.reset(**kwargs)
return obs
def step(self, ac):
return self.env.step(ac)
class WrapFrame(gym.ObservationWrapper):
def __init__(self, env, downscale=84, grayscale=True):
"""Warp frames to 84x84 as done in the Nature paper and later work."""
super().__init__(env)
# if the size of the image is 160 x 250, we crop it from the top by 28 and from the bottom by 12, so that it becomes the default 160 x 210
shp = env.observation_space.shape
self.crop40 = True if shp[0] == 250 else False
if downscale > 10:
self._width = downscale
self._height = downscale
else:
assert downscale > 0, "invalid downscaling ratio {}".format(downscale)
self._width = round(shp[1]/downscale)
self._height = round(210/downscale) if self.crop40 else round(shp[0]/downscale)
self._grayscale = grayscale
if self._grayscale:
num_colors = 1
else:
num_colors = 3
# we move the color channel dimension from shape[-1] to shape[0]
new_space = gym.spaces.Box(low=0, high=255,
shape=(num_colors, self._height, self._width), dtype=np.uint8)
self.observation_space = new_space
def observation(self, obs):
frame = obs
if self.crop40: frame = frame[28:238,:,:] # crop from the top by 28 and from the bottom by 12
if self._grayscale:
frame = cv2.cvtColor(frame, cv2.COLOR_RGB2GRAY)
# numpy array treated as an image has a shape of (height, width, color)
frame = cv2.resize(frame, (self._width, self._height), interpolation=cv2.INTER_AREA)
if self._grayscale:
frame = np.expand_dims(frame, -1)
frame = np.ascontiguousarray(np.moveaxis(frame, -1, 0))
return frame
class FrameStack(gym.Wrapper):
def __init__(self, env, k=4):
"""Stack k last frames.
Returns lazy array, which is much more memory efficient.
See Also
--------
baselines.common.atari_wrappers.LazyFrames
"""
gym.Wrapper.__init__(self, env)
shp = env.observation_space.shape
self.k = k
self.frames = deque([], maxlen=k)
# the color channel dimension has been moved from shape[-1] to shape[0] in "WrapFrame"
# the observation is supposed to be accessed via np.array(...)
self.observation_space = gym.spaces.Box(low=np.float32(0.0), high= | np.float32(1.0) | numpy.float32 |
#!/usr/bin/env python
from chainer import cuda
import numpy as np
import grasp_fusion_lib
from grasp_fusion_lib.contrib import grasp_fusion
import cv_bridge
from jsk_topic_tools.transport import ConnectionBasedTransport
import message_filters
import rospy
from sensor_msgs.msg import Image
from affordance_segmentation import get_pretrained_model
class SoleAffordanceSegmentation(ConnectionBasedTransport):
def __init__(self):
super(SoleAffordanceSegmentation, self).__init__()
affordance = rospy.get_param('~affordance')
pretrained_model, modal, out_channels = get_pretrained_model(
affordance
)
self.out_channels = out_channels
gpu = rospy.get_param('~gpu', 0)
model = grasp_fusion.models.FCN8sVGG16Sigmoid(
out_channels=out_channels,
pretrained_model=pretrained_model,
modal=modal,
)
if gpu >= 0:
cuda.get_device_from_id(gpu).use()
model.to_gpu()
self.model = model
self.pub_label = self.advertise('~output/label', Image, queue_size=1)
self.pub_prob = self.advertise('~output/prob', Image, queue_size=1)
self.pub_viz = self.advertise('~output/viz', Image, queue_size=1)
def subscribe(self):
sub_rgb = message_filters.Subscriber(
'~input/rgb', Image, queue_size=1, buff_size=2**24,
)
sub_depth = message_filters.Subscriber(
'~input/depth', Image, queue_size=1, buff_size=2**24,
)
sub_ins = message_filters.Subscriber(
'~input/label_ins', Image, queue_size=1, buff_size=2**24,
)
self.subs = [sub_rgb, sub_depth, sub_ins]
sync = message_filters.TimeSynchronizer(
fs=self.subs, queue_size=100
)
sync.registerCallback(self.callback)
def unsubscribe(self):
for sub in self.subs:
sub.unregister()
def callback(self, imgmsg, depthmsg, insmsg):
bridge = cv_bridge.CvBridge()
img = bridge.imgmsg_to_cv2(imgmsg, desired_encoding='rgb8')
depth = bridge.imgmsg_to_cv2(depthmsg, desired_encoding='32FC1')
ins = bridge.imgmsg_to_cv2(insmsg, desired_encoding='32SC1')
# viz_depth = grasp_fusion_lib.image.colorize_depth(
# depth, 0, self.model.depth_max_value
# )
# viz_ins = grasp_fusion_lib.image.label2rgb(ins + 1, img)
# viz = grasp_fusion_lib.image.tile([img, viz_depth, viz_ins])
# vizmsg = bridge.cv2_to_imgmsg(viz, encoding='rgb8')
# vizmsg.header = imgmsg.header
# self.pub_viz.publish(vizmsg)
instance_ids = np.unique(ins)
instance_ids = instance_ids[instance_ids != -1]
assert (instance_ids >= 0).all()
sole_imgs = []
sole_depths = []
for ins_id in instance_ids:
mask = np.isin(ins, (-1, ins_id))
img_i = img.copy()
depth_i = depth.copy()
img_i[~mask] = 0
depth_i[~mask] = 0
sole_imgs.append(img_i.transpose(2, 0, 1))
sole_depths.append(depth_i)
probs = self.model.predict_proba(sole_imgs, sole_depths)
lbls = self.model.proba_to_lbls(probs)
del sole_imgs, sole_depths
H, W = img.shape[:2]
prob_all = np.zeros((H, W, self.out_channels), dtype=np.float32)
lbl_all = np.zeros((H, W, self.out_channels), dtype=np.int32)
for ins_id, prob, lbl in zip(instance_ids, probs, lbls):
mask = ins == ins_id
prob = prob.transpose(1, 2, 0)
lbl = lbl.transpose(1, 2, 0)
prob_all[mask] = prob[mask]
lbl_all[mask] = lbl[mask]
del probs, lbls
prob = prob_all
lbl = lbl_all
del prob_all, lbl_all
lblmsg = bridge.cv2_to_imgmsg(lbl)
lblmsg.header = imgmsg.header
self.pub_label.publish(lblmsg)
vizs = []
for c in range(lbl.shape[2]):
lbl_c = lbl[:, :, c]
viz = grasp_fusion_lib.image.label2rgb(lbl_c, img, alpha=0.7)
vizs.append(viz)
viz_lbl = grasp_fusion_lib.image.tile(vizs, boundary=True)
probmsg = bridge.cv2_to_imgmsg(prob)
probmsg.header = imgmsg.header
self.pub_prob.publish(probmsg)
vizs = []
for c in range(prob.shape[2]):
prob_c = prob[:, :, c]
viz = grasp_fusion_lib.image.colorize_heatmap(prob_c)
viz = grasp_fusion_lib.image.overlay_color_on_mono(
img_color=viz, img_mono=img, alpha=0.7
)
vizs.append(viz)
viz_prob = grasp_fusion_lib.image.tile(vizs, boundary=True)
img = grasp_fusion_lib.image.resize(img, height=viz_lbl.shape[0])
depth = grasp_fusion_lib.image.colorize_depth(
depth, min_value=0, max_value=self.model.depth_max_value
)
depth = grasp_fusion_lib.image.resize(depth, height=viz_lbl.shape[0])
viz = | np.hstack((img, depth, viz_prob, viz_lbl)) | numpy.hstack |
import matplotlib.pyplot as plt
import numpy as np
from rlkit.misc.data_processing import get_trials
from rlkit.misc.visualization_util import sliding_mean
def main():
tdm_trials = get_trials(
"/home/vitchyr/git/railrl/data/doodads3/01-03-final-ant-pos-and-vel/",
criteria={
'algorithm': 'DDPG-TDM',
'exp_id': '17',
}
)
ddpg_trials = get_trials(
"/home/vitchyr/git/railrl/data/doodads3/01-03-final-ant-pos-and-vel/",
criteria={
'algorithm': 'DDPG',
'exp_id': '5',
}
)
ddpg_sparse_trials = get_trials(
"/home/vitchyr/git/railrl/data/doodads3/01-03-final-ant-pos-and-vel/",
criteria={
'algorithm': 'DDPG-Sparse',
'exp_id': '22',
}
)
her_trials = get_trials(
"/home/vitchyr/git/railrl/data/doodads3/01-03-final-ant-pos-and-vel/",
criteria={
'algorithm': 'HER-Andrychowicz',
'exp_id': '26',
}
)
mb_trials = get_trials(
"/home/vitchyr/git/railrl/data/doodads3/01-03-final-ant-pos-and-vel/",
criteria={
'algorithm': 'Model-Based-Dagger',
'exp_id': '4',
}
)
MAX_ITERS = 300
plt.figure()
key = 'Final_Weighted_Error_Mean'
for trials, name in [
(tdm_trials, 'TDM'),
(ddpg_trials, 'DDPG'),
(her_trials, 'HER'),
(ddpg_sparse_trials, 'DDPG-Sparse'),
(mb_trials, 'Model-Based'),
]:
all_values = []
for trial in trials:
try:
values_ts = trial.data[key]
values_ts = sliding_mean(values_ts, window=5)
except:
import ipdb; ipdb.set_trace()
all_values.append(values_ts)
min_len = min(map(len, all_values))
# max_len = max(map(len, all_values))
# all_values = [
# np.pad(values, (0, max_len - len(values)), 'constant',
# constant_values=np.nan)
# for values in all_values
# ]
costs = np.vstack([
values[:min_len]
for values in all_values
])
costs = costs[:, :min(costs.shape[1], MAX_ITERS)]
mean = np.nanmean(costs, axis=0)
std = | np.nanstd(costs, axis=0) | numpy.nanstd |
# Copyright 2017 Google Inc. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Tests for tensorflow_fold.blocks.blocks."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import collections
import functools
import itertools
# import google3
import numpy as np
import six
from six.moves import xrange # pylint: disable=redefined-builtin
import tensorflow as tf
from tensorflow_fold.blocks import test_lib
import tensorflow_fold.blocks.block_compiler as tdc
import tensorflow_fold.blocks.blocks as tdb
import tensorflow_fold.blocks.layers as tdl
import tensorflow_fold.blocks.metrics as tdm
import tensorflow_fold.blocks.result_types as tdt
from tensorflow_fold.util import test_pb2
class BlocksTest(test_lib.TestCase):
def __init__(self, *args, **kwargs):
super(BlocksTest, self).__init__(*args, **kwargs)
self.longMessage = True
def _assertBuilds(self, desired, block, inp, fd, use_while_loop=True):
actual = block.eval(inp, feed_dict=fd, tolist=True,
use_while_loop=use_while_loop)
if isinstance(desired, itertools.repeat):
# itertools.repeat is not a value type
self.assertTrue(isinstance(actual, itertools.repeat))
actual = next(actual)
desired = next(desired)
msg = '\n%s vs.\n%s\n' % (desired, actual)
self.assertSameStructure(desired, actual, 'desired', 'actual', msg)
def assertBuilds(self, desired, block, inp, max_depth=1, feed_dict=None):
if max_depth is not None: self.assertEqual(max_depth, block.max_depth(inp))
with self.test_session() as sess:
# Test using a while loop.
self._assertBuilds(desired, block, inp, feed_dict)
# Test with explicit unrolling.
self._assertBuilds(desired, block, inp, feed_dict, use_while_loop=False)
# If the block can be compiled, test batching (otherwise we can't).
try:
c = tdc.Compiler.create(block)
except TypeError:
return
fd = c.build_feed_dict([inp, inp])
if feed_dict is not None: fd.update(feed_dict)
batch_out = sess.run(c.output_tensors, feed_dict=fd)
if c.metric_tensors: desired, _ = desired
desired = block.output_type.flatten(desired)
for out, desired_out in zip(batch_out, desired):
self.assertSameStructure(out[0].tolist(), out[1].tolist())
self.assertSameStructure(desired_out, out[0].tolist())
def assertBuildsConst(self, desired, block, inp):
# In this context 'const' means a block that can be evaluated
# entirely in python, without running TF at all. For example,
# (td.Map(td.Scalar()) >> td.Sum()) is const.
#
# There currently are no optimizations in Fold for const
# blocks. If/when these are implemented, code should go here for
# testing that 'block' is in fact const.
self.assertBuilds(desired, block, inp, max_depth=None)
def test_scalar(self):
self.assertBuildsConst(42., tdb.Scalar(), 42)
def test_vector(self):
self.assertBuildsConst([1., 2., 3.], tdb.Vector(3), [1, 2, 3])
def test_from_tensor(self):
t = tf.placeholder('int32', [2, 1])
block = tdb.FromTensor(t)
fd = {t: [[1], [2]]}
self.assertBuilds([[1], [2]], block, None, max_depth=0, feed_dict=fd)
def test_from_tensor_const(self):
block = tdb.FromTensor(tf.constant([1, 2, 3], 'int32'))
self.assertBuildsConst([1, 2, 3], block, None)
def test_from_tensor_const_ndarray(self):
block = tdb.FromTensor(np.zeros([2, 2], 'int32'))
self.assertBuildsConst([[0, 0], [0, 0]], block, None)
def test_from_tensor_variable(self):
v = tf.Variable( | np.ones(2) | numpy.ones |
from textwrap import dedent
import fsspec
import echopype
from echopype.testing import TEST_DATA_FOLDER
from echopype.echodata import EchoData
from echopype import open_converted
import pytest
import xarray as xr
import numpy as np
ek60_path = TEST_DATA_FOLDER / "ek60"
ek80_path = TEST_DATA_FOLDER / "ek80"
azfp_path = TEST_DATA_FOLDER / "azfp"
ad2cp_path = TEST_DATA_FOLDER / "ad2cp"
class TestEchoData:
converted_zarr = (
ek60_path / "ncei-wcsd" / "Summer2017-D20170615-T190214.zarr"
)
def test_constructor(self):
ed = EchoData(converted_raw_path=self.converted_zarr)
expected_groups = [
'top',
'environment',
'platform',
'provenance',
'sonar',
'beam',
'vendor',
]
assert ed.sonar_model == 'EK60'
assert ed.converted_raw_path == self.converted_zarr
assert ed.storage_options == {}
for group in expected_groups:
assert isinstance(getattr(ed, group), xr.Dataset)
def test_repr(self):
zarr_path_string = str(self.converted_zarr.absolute())
expected_repr = dedent(
f"""\
EchoData: standardized raw data from {zarr_path_string}
> top: (Top-level) contains metadata about the SONAR-netCDF4 file format.
> environment: (Environment) contains information relevant to acoustic propagation through water.
> platform: (Platform) contains information about the platform on which the sonar is installed.
> nmea: (Platform/NMEA) contains information specific to the NMEA protocol.
> provenance: (Provenance) contains metadata about how the SONAR-netCDF4 version of the data were obtained.
> sonar: (Sonar) contains specific metadata for the sonar system.
> beam: (Beam) contains backscatter data and other beam or channel-specific data.
> vendor: (Vendor specific) contains vendor-specific information about the sonar and the data."""
)
ed = EchoData(converted_raw_path=self.converted_zarr)
actual = "\n".join(x.rstrip() for x in repr(ed).split("\n"))
assert expected_repr == actual
def test_repr_html(self):
zarr_path_string = str(self.converted_zarr.absolute())
ed = EchoData(converted_raw_path=self.converted_zarr)
assert hasattr(ed, "_repr_html_")
html_repr = ed._repr_html_().strip()
assert f"""<div class="xr-obj-type">EchoData: standardized raw data from {zarr_path_string}</div>""" in html_repr
with xr.set_options(display_style="text"):
html_fallback = ed._repr_html_().strip()
assert html_fallback.startswith("<pre>EchoData") and html_fallback.endswith("</pre>")
@pytest.mark.parametrize(
"converted_zarr",
[
(ek60_path / "ncei-wcsd" / "Summer2017-D20170615-T190214.zarr"),
str(ek60_path / "ncei-wcsd" / "Summer2017-D20170615-T190214.zarr"),
(
ek60_path / "ncei-wcsd" / "Summer2017-D20170615-T190214.nc"
), # netcdf test
"s3://data/ek60/ncei-wcsd/Summer2017-D20170615-T190214.nc", # netcdf test
"http://localhost:8080/data/ek60/ncei-wcsd/Summer2017-D20170615-T190214.zarr",
"s3://data/ek60/ncei-wcsd/Summer2017-D20170615-T190214.zarr",
fsspec.get_mapper(
"s3://data/ek60/ncei-wcsd/Summer2017-D20170615-T190214.zarr",
**dict(
client_kwargs=dict(endpoint_url="http://localhost:9000/"),
key="minioadmin",
secret="minioadmin",
),
),
],
)
def test_open_converted(
converted_zarr,
minio_bucket # noqa
):
def _check_path(zarr_path):
storage_options = {}
if zarr_path.startswith("s3://"):
storage_options = dict(
client_kwargs=dict(endpoint_url="http://localhost:9000/"),
key="minioadmin",
secret="minioadmin",
)
return storage_options
storage_options = {}
if not isinstance(converted_zarr, fsspec.FSMap):
storage_options = _check_path(str(converted_zarr))
try:
ed = open_converted(converted_zarr, storage_options=storage_options)
assert isinstance(ed, EchoData) is True
except Exception as e:
if (
isinstance(converted_zarr, str)
and converted_zarr.startswith("s3://")
and converted_zarr.endswith(".nc")
):
assert isinstance(e, ValueError) is True
@pytest.mark.parametrize(
("filepath", "sonar_model", "azfp_xml_path", "azfp_cal_type", "ek_waveform_mode", "ek_encode_mode"),
[
(ek60_path / "ncei-wcsd" / "Summer2017-D20170615-T190214.raw", "EK60", None, None, "CW", "complex"),
(ek80_path / "D20190822-T161221.raw", "EK80", None, None, "CW", "power"),
(ek80_path / "D20170912-T234910.raw", "EK80", None, None, "BB", "complex"),
(azfp_path / "ooi" / "17032923.01A", "AZFP", azfp_path / "ooi" / "17032922.XML", "Sv", None, None),
(azfp_path / "ooi" / "17032923.01A", "AZFP", azfp_path / "ooi" / "17032922.XML", "Sp", None, None),
(ad2cp_path / "raw" / "090" / "rawtest.090.00001.ad2cp", "AD2CP", None, None, None, None)
]
)
def test_compute_range(filepath, sonar_model, azfp_xml_path, azfp_cal_type, ek_waveform_mode, ek_encode_mode):
ed = echopype.open_raw(filepath, sonar_model, azfp_xml_path)
env_params = {"sound_speed": 343}
if sonar_model == "AD2CP":
try:
ed.compute_range(env_params, ek_waveform_mode="CW", azfp_cal_type="Sv")
except ValueError:
return
else:
raise AssertionError
else:
range = ed.compute_range(env_params, azfp_cal_type, ek_waveform_mode, )
assert isinstance(range, xr.DataArray)
def test_update_platform():
saildrone_path = ek80_path / "saildrone"
raw_file = saildrone_path / "SD2019_WCS_v05-Phase0-D20190617-T125959-0.raw"
extra_platform_data_file_name = "saildrone-gen_5-fisheries-acoustics-code-sprint-sd1039-20190617T130000-20190618T125959-1_hz-v1.1595357449818.nc"
extra_platform_data_file = saildrone_path / extra_platform_data_file_name
ed = echopype.open_raw(raw_file, "EK80")
updated = ["pitch", "roll", "latitude", "longitude", "water_level"]
for variable in updated:
assert np.isnan(ed.platform[variable].values).all()
extra_platform_data = xr.open_dataset(extra_platform_data_file)
ed.update_platform(
extra_platform_data,
extra_platform_data_file_name=extra_platform_data_file_name
)
for variable in updated:
assert not | np.isnan(ed.platform[variable].values) | numpy.isnan |
import sympy as sp #math library to represent functions, we will write our own problem solving expressions
from sympy import cos, cosh, sin, sinh
import numpy as np
import matplotlib.pyplot as mplot
x = sp.Symbol('x')
s = sp.Symbol('s')
r1 = 1.87527632324985
r2 = 4.69409122046058
r3 = 7.855
#Superimpose plots
q11 = 4.29105998838015
q21 = 1.76556786
q22 = -0.83363552
q31 = 1.7774846
q32 = -0.84769887
q33 = -0.01233278
def phi(x, r):
return (sin(r*x) + sinh(r*x) + ((cos(r)+cosh(r))/(sin(r)+sinh(r)))*(cos(r*x)-cosh(r*x)))
def d2phi(x, r):
return (r**2)*(-sin(r*x) + sinh(r*x) + ((cos(r)+cosh(r))/(sin(r)+sinh(r)))*(-cos(r*x)-cosh(r*x)))
def psi_1(x):
return q11*phi(x, r1)
def d2psi_1(x):
return q11*d2phi(x, r1)
def psi_2(x):
return q21*phi(x, r1) + q22*phi(x,r2)
def d2psi_2(x):
return q21*d2phi(x, r1) + q22*d2phi(x, r2)
def psi_3(x):
return q31*phi(x, r1) + q32*phi(x,r2) + q33*phi(x,r3)
def d2psi_3(x):
return q31*d2phi(x, r1) + q32*d2phi(x, r2) + q33*d2phi(x, r3)
#governing ODE: (1)*d2phi(x) - int_{x,1}(100*cos(psi(x)-psi(s)))ds = 0
#evaluate LHS of the ODE, set RHS to zero
h_1 = 100*cos(psi_1(x) - psi_1(s))
h_2 = 100*cos(psi_2(x) - psi_2(s))
h_3 = 100*cos(psi_3(x) - psi_3(s))
def trapezoid_1(var, h, n=100, a=x, b=1):
const = (b-a)/(2*n)
dx = (b-a)/(n)
total = h.subs(var, a) + h.subs(var, b)
for i in range(1, n):
total += 2*h.subs(var, a + dx*i)
return const*total + d2psi_1(x)
def trapezoid_2(var, h, n=100, a=x, b=1):
const = (b-a)/(2*n)
dx = (b-a)/(n)
total = h.subs(var, a) + h.subs(var, b)
for i in range(1, n):
total += 2*h.subs(var, a + dx*i)
return const*total + d2psi_2(x)
def trapezoid_3(var, h, n=100, a=x, b=1):
const = (b-a)/(2*n)
dx = (b-a)/(n)
total = h.subs(var, a) + h.subs(var, b)
for i in range(1, n):
total += 2*h.subs(var, a + dx*i)
return const*total + d2psi_3(x)
ode1 = trapezoid_1(s, h_1)
ode2 = trapezoid_2(s, h_1)
ode3 = trapezoid_3(s, h_1)
xs = np.arange(0,1.01,0.01)
o1 = []
o2 = []
o3 = []
for i in xs:
o1.append(abs(ode1.subs(x, i)))
o2.append(abs(ode2.subs(x, i)))
o3.append(abs(ode3.subs(x, i)))
o1 = np.array(o1)
o2 = np.array(o2)
o3 = | np.array(o3) | numpy.array |
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from torch.distributions import Normal
import numpy as np
from datetime import datetime
import subprocess
import sys
def get_date_time_now():
return str(datetime.now().replace(microsecond=0)).replace(':', '_').replace(' ', '_')
def install_pkg(package):
subprocess.check_call([sys.executable, "-m", "pip", "install", package])
def install_req_pkgs():
subprocess.check_call([sys.executable, "-q", "pip", "install", '../../python'])
def load_checkpoint(model, path: str):
model.load_state_dict(torch.load(path))
return model
class ReplayBuffer:
def __init__(self, buffer_size=10000, batch_size=64):
self.state_mem = np.empty(shape=(buffer_size), dtype=np.ndarray)
self.action_mem = np.empty(shape=(buffer_size), dtype=np.ndarray)
self.reward_mem = np.empty(shape=(buffer_size), dtype=np.ndarray)
self.next_state_mem = np.empty(shape=(buffer_size), dtype=np.ndarray)
self.is_done_mem = np.empty(shape=(buffer_size), dtype=np.ndarray)
self.max_size = buffer_size
self.batch_size = batch_size
self._idx = 0
self.size = 0
def store(self, sample):
state, action, reward, next_state, is_done = sample
self.state_mem[self._idx] = state
self.action_mem[self._idx] = action
self.reward_mem[self._idx] = reward
self.next_state_mem[self._idx] = next_state
self.is_done_mem[self._idx] = is_done
self._idx += 1
self._idx = self._idx % self.max_size
self.size += 1
self.size = min(self.size, self.max_size)
def sample(self, batch_size=None):
if batch_size == None:
batch_size = self.batch_size
idxs = np.random.choice(
self.size, batch_size, replace=False)
experiences = np.vstack(self.state_mem[idxs]), \
np.vstack(self.action_mem[idxs]), \
np.vstack(self.reward_mem[idxs]), \
np.vstack(self.next_state_mem[idxs]), \
| np.vstack(self.is_done_mem[idxs]) | numpy.vstack |
from __future__ import print_function
import numpy as np
import os
import pickle as pk
import pyfftw
from lensit.sims.sims_generic import hash_check
from lensit.misc.misc_utils import npy_hash, Freq
from lensit.misc.rfft2_utils import udgrade_rfft2, supersample
from lensit.pbs import pbs
class ell_mat:
"""Library helping with flat-sky patch discretization and harmonic mode structure.
This handles Fourier mode structure on the flat sky, at the given resolution and size of
specified rectangular box.
Args:
lib_dir: various things might be cached there
(unlens *cache* is set to 0, in which case only a hashdict is put there at instantiation)
shape(2-tuple): pair of int defining the number of pixels on each side of the box
lsides(2-tuple): physical size (in radians) of the box sides
cache(optional): if non-zero, a bunch of matrices might be cached to speed up some calculations.
"""
def __init__(self, lib_dir, shape, lsides, cache=1):
assert len(shape) == 2 and len(lsides) == 2
assert shape[0] % 2 == 0 and shape[1] % 2 == 0
assert shape[0] < 2 ** 16 and shape[1] < 2 ** 16
self.shape = tuple(shape)
self.rshape = (shape[0], shape[1] // 2 + 1)
self.lsides = tuple(lsides)
self.lib_dir = lib_dir
self.mmap_mode = None
self.cache=cache
fn_hash = os.path.join(lib_dir, "ellmat_hash.pk")
if pbs.rank == 0 and self.cache > 0:
if not os.path.exists(lib_dir): os.makedirs(lib_dir)
if not os.path.exists(fn_hash):
pk.dump(self.hash_dict(), open(fn_hash, 'wb'), protocol=2)
pbs.barrier()
if self.cache > 0:
hash_check(pk.load(open(fn_hash, 'rb')), self.hash_dict())
if pbs.rank == 0 and self.cache > 0 and not os.path.exists(os.path.join(self.lib_dir, 'ellmat.npy')):
print('ell_mat:caching ells in ' + os.path.join(self.lib_dir, 'ellmat.npy'))
np.save(os.path.join(self.lib_dir, 'ellmat.npy'), self._build_ellmat())
pbs.barrier()
self.ellmax = int(self._get_ellmax())
self._ell_counts = self._build_ell_counts()
self._nz_counts = self._ell_counts.nonzero()
def __eq__(self, other):
return self.shape == other.shape and self.lsides == self.lsides
def _build_ellmat(self):
kmin = 2. * np.pi / np.array(self.lsides)
ky2 = Freq(np.arange(self.shape[0]), self.shape[0]) ** 2 * kmin[0] ** 2
kx2 = Freq(np.arange(self.rshape[1]), self.shape[1]) ** 2 * kmin[1] ** 2
ones = np.ones(np.max(self.shape))
return self.k2ell(np.sqrt( | np.outer(ky2, ones[0:self.rshape[1]]) | numpy.outer |
# -*- coding: utf-8 -*-
import numpy as np
def flux2photons(wave, flux):
"""
Convert flux (erg/s) to photons/s.
Parameters
----------
wave : float, array
The wavelength in Angstrom.
flux : float, array
The associated flux array in erg/s.
Returns
-------
photons : array
Number of photons/s for the given input flux
"""
# h*c = 1.98644568327e-08 erg*A; ephoton = energy(erg) per photon
ePhoton = 1.98644568327e-08 / np.array(wave)
nPhotons = | np.array(flux) | numpy.array |
# part of 2nd place solution: lightgbm model with private score 0.29124 and public lb score 0.28555
import lightgbm as lgbm
from scipy import sparse as ssp
from sklearn.model_selection import StratifiedKFold
import numpy as np
import pandas as pd
from sklearn.preprocessing import LabelEncoder
from sklearn.preprocessing import OneHotEncoder
def Gini(y_true, y_pred):
# check and get number of samples
assert y_true.shape == y_pred.shape
n_samples = y_true.shape[0]
# sort rows on prediction column
# (from largest to smallest)
arr = np.array([y_true, y_pred]).transpose()
true_order = arr[arr[:, 0].argsort()][::-1, 0]
pred_order = arr[arr[:, 1].argsort()][::-1, 0]
# get Lorenz curves
L_true = | np.cumsum(true_order) | numpy.cumsum |
"""Test the minimum spanning tree function"""
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import assert_
import numpy.testing as npt
from scipy.sparse import csr_matrix
from scipy.sparse.csgraph import minimum_spanning_tree
def test_minimum_spanning_tree():
# Create a graph with two connected components.
graph = [[0,1,0,0,0],
[1,0,0,0,0],
[0,0,0,8,5],
[0,0,8,0,1],
[0,0,5,1,0]]
graph = np.asarray(graph)
# Create the expected spanning tree.
expected = [[0,1,0,0,0],
[0,0,0,0,0],
[0,0,0,0,5],
[0,0,0,0,1],
[0,0,0,0,0]]
expected = | np.asarray(expected) | numpy.asarray |
# -*- coding: UTF-8 -*-
# File Name：linear_regression
# Author : <NAME>
# Date：2019/2/27
# Description : 线性回归 Y = WX + b
from __future__ import print_function
import matplotlib.pyplot as plt
import numpy as np
import tensorflow as tf
__author__ = '<NAME>'
# Parameters
param = {
"learning_rate": 0.01,
"training_epochs": 1000,
"display_step": 50
}
# 训练数据集
train_X = np.asarray([3.3, 4.4, 5.5, 6.71, 6.93, 4.168, 9.779, 6.182, 7.59, 2.167,
7.042, 10.791, 5.313, 7.997, 5.654, 9.27, 3.1])
train_Y = np.asarray([1.7, 2.76, 2.09, 3.19, 1.694, 1.573, 3.366, 2.596, 2.53, 1.221,
2.827, 3.465, 1.65, 2.904, 2.42, 2.94, 1.3])
n_samples = train_X.shape[0]
# 占位符
X = tf.placeholder("float")
Y = tf.placeholder("float")
# 设置参数
W = tf.Variable(initial_value=tf.random_normal([1]), name="weight")
b = tf.Variable(tf.random_normal([1, ]), name="bias")
# 模型
pred = tf.add(tf.multiply(X, W), b) # 与pred=X * W + b等价
# 损失函数：均方误差
cost = tf.reduce_sum(tf.pow(pred - Y, 2)) / (2 * n_samples)
# 定义优化器
opt = tf.train.GradientDescentOptimizer(param['learning_rate']).minimize(cost)
# 定义初始化参数函数
init = tf.global_variables_initializer()
with tf.Session() as sess:
# 使用session初始化参数
sess.run(init)
# 喂入数据
for epoch in range(param['training_epochs']):
for (x, y) in zip(train_X, train_Y):
sess.run(opt, feed_dict={X: x, Y: y})
if (epoch + 1) % param['display_step'] == 0:
c = sess.run(cost, feed_dict={X: train_X, Y: train_Y})
print("Epoch:", '%04d' % (epoch + 1), "cost=", "{:.9f}".format(c), "W=", sess.run(W), "b=", sess.run(b))
print("Optimization Finished!")
# 训练误差
training_cost = sess.run(cost, feed_dict={X: train_X, Y: train_Y})
print("Training cost=", training_cost, "W=", sess.run(W), "b=", sess.run(b), '\n')
# Graphic display
plt.plot(train_X, train_Y, 'ro', label='Original data')
plt.plot(train_X, sess.run(W) * train_X + sess.run(b), label='Fitted line')
plt.legend()
plt.show()
# 测试集数据
test_X = np.asarray([6.83, 4.668, 8.9, 7.91, 5.7, 8.7, 3.1, 2.1])
test_Y = | np.asarray([1.84, 2.273, 3.2, 2.831, 2.92, 3.24, 1.35, 1.03]) | numpy.asarray |
def projrast(Z,zv,r,p,gamma,mode = None,search = {"t": 1, "s": 1, "k": 1}, init ={"t": 1, "s": 0,"k": 1},tol = 1e-12):
"""
Projection onto the epi-graph of the scaled low-rank inducing
Frobenius and spectral norms for integer-valued r.
X,xv,final = PROJRAST(Z,zv,r,p,gamma) computes the projection onto the
epi-graph of the scaled low-rank inducing norm ||.||_{ell_p,r*}
evaluated in (Z,zv) for integer-valued r > 0, i.e.
a) (X,xv) is solution to the optimization problem:
minimize_(X,xv) ||X-Z||_{ell_2}^2+(xv-zv)^2
s.t. xv >= gamma*||X||_{ell_p,r*}
where p=2 or p='inf'.
b) final["t"] and final["s"] are the final values of parameters to the two
nested search. For p = 'inf', final["k"] is the final value of the third inner
search parameter.
If ||Z/gamma||_{ell_p^D,r} <= 1, then t = s = k = None.
... = PROJRAST(Z,zv,r,p,gamma,option) allows us to specify furhter options:
1. ... = PROJRAST(Z,zv,r,p,mode = 'vec') is used to flag that the
vector-valued problem is to be solved.
2. ... = PROJRAST(Z,zv,r,p,gamma,tol=tol_val) sets the relative
tolerance of the deciding about zeros e.g. if Z is matrix then
for all i: sigma(X)_i = 0 if |sigma(X)_i| <= tol_val*||Z||_{ell_p,r).
Default value: tol_val = 1e-12.
3. ... = PROJRAST(Z,zv,r,p,gamma,...,search = search_val) changes
from default binary search to linear search over
a) t if search_val["t"] = 0.
b) s if search_val["s"] = 0.
c) k if search_val["k"] = 0 (only for p = 'inf').
4. ... = PROJRAST(Z,zv,r,p,gamma,...,init = init_val) changes
from default binary search start values t_0 = 1, k_0 = 1, s_0 = 0
to
a) t_0 if init_val["t"] = t_0.
b) s_0 if init_val["s"] = s_0.
c) k_0 if init_val["k"] = k_0 (only for p = 'inf').
---------------
References:
- <NAME> and <NAME> and <NAME> (2018):
"Low-Rank Optimization with Convex Constraints",
IEEE Transactions on Automatic Control, DOI: 10.1109/TAC.2018.2813009.
- <NAME> and <NAME> (2016):
"Low-Rank Inducing Norms With Optimality Interpreations",
arXiv:1612.03186v1.
- <NAME> and <NAME> (2018):
"Low-Rank Inducing Norms With Optimality Interpreations",
SIAM J. Optim., 28(4), pp. 3057–3078.
- <NAME> (2017):
"Rank reduction with convex constraints", PhD Thesis,
Department of Automatic Control, Lund Institute of Technology,
Lund University, ISBN 978-91-7753-081-7.
"""
from lripy.projrnorm import projrnorm
import numpy as np
## Check if p = 2 or p = 'inf'
if p != 2 and p !='inf':
raise ValueError("p can only be equal to 2 or inf")
## Check options
dim = Z.shape
max_mn = np.max(dim)
min_mn = np.min(dim)
## Check dimensions
if mode == 'vec':
if r > max_mn:
raise ValueError("r is larger than max(Z.shape)")
elif r > min_mn:
raise ValueError("r is larger than min(Z.shape)")
if p == 'inf':
p = 1 # p for dual norm
if mode == 'vec':
## Vector valued problem
# Moreau decomposition
Y,w,final = projrnorm(Z,zv,r,p,gamma,search,init,tol)
X = Z - Y
xv = zv - w
else:
## Matrix valued problem
U,S,V = np.linalg.svd(Z,full_matrices=False)
y,w,final = projrnorm(S,zv,r,p,gamma,search,init,tol)
# Moreau decomposition
S = S - y
X = U.dot( | np.diag(S) | numpy.diag |
"""
All code & models from https://github.com/phamquiluan/ResidualMaskingNetwork
"""
import os
import glob
import json
import cv2
import numpy as np
import torch
from torchvision.transforms import transforms
from torch.hub import load_state_dict_from_url
import traceback
import torch
import torch.nn as nn
import torch.nn.functional as F
from feat.utils import get_resource_path
model_urls = {
"resnet18": "https://download.pytorch.org/models/resnet18-5c106cde.pth",
"resnet34": "https://download.pytorch.org/models/resnet34-333f7ec4.pth",
"resnet50": "https://download.pytorch.org/models/resnet50-19c8e357.pth",
"resnet101": "https://download.pytorch.org/models/resnet101-5d3b4d8f.pth",
"resnet152": "https://download.pytorch.org/models/resnet152-b121ed2d.pth",
"resnext50_32x4d": "https://download.pytorch.org/models/resnext50_32x4d-7cdf4587.pth",
"resnext101_32x8d": "https://download.pytorch.org/models/resnext101_32x8d-8ba56ff5.pth",
"wide_resnet50_2": "https://download.pytorch.org/models/wide_resnet50_2-95faca4d.pth",
"wide_resnet101_2": "https://download.pytorch.org/models/wide_resnet101_2-32ee1156.pth",
}
def conv3x3(in_planes, out_planes, stride=1, groups=1, dilation=1):
"""3x3 convolution with padding"""
return nn.Conv2d(
in_planes,
out_planes,
kernel_size=3,
stride=stride,
padding=dilation,
groups=groups,
bias=False,
dilation=dilation,
)
def conv1x1(in_planes, out_planes, stride=1):
"""1x1 convolution"""
return nn.Conv2d(in_planes, out_planes, kernel_size=1, stride=stride, bias=False)
class BasicBlock(nn.Module):
expansion = 1
__constants__ = ["downsample"]
def __init__(
self,
inplanes,
planes,
stride=1,
downsample=None,
groups=1,
base_width=64,
dilation=1,
norm_layer=None,
):
super(BasicBlock, self).__init__()
if norm_layer is None:
norm_layer = nn.BatchNorm2d
if groups != 1 or base_width != 64:
raise ValueError("BasicBlock only supports groups=1 and base_width=64")
if dilation > 1:
raise NotImplementedError("Dilation > 1 not supported in BasicBlock")
# Both self.conv1 and self.downsample layers downsample the input when stride != 1
self.conv1 = conv3x3(inplanes, planes, stride)
self.bn1 = norm_layer(planes)
self.relu = nn.ReLU(inplace=True)
self.conv2 = conv3x3(planes, planes)
self.bn2 = norm_layer(planes)
self.downsample = downsample
self.stride = stride
def forward(self, x):
identity = x
out = self.conv1(x)
out = self.bn1(out)
out = self.relu(out)
out = self.conv2(out)
out = self.bn2(out)
if self.downsample is not None:
identity = self.downsample(x)
out += identity
out = self.relu(out)
return out
class ResNet(nn.Module):
def __init__(
self,
block,
layers,
num_classes=1000,
zero_init_residual=False,
groups=1,
width_per_group=64,
replace_stride_with_dilation=None,
norm_layer=None,
in_channels=3,
):
super(ResNet, self).__init__()
if norm_layer is None:
norm_layer = nn.BatchNorm2d
self._norm_layer = norm_layer
self.inplanes = 64
self.dilation = 1
if replace_stride_with_dilation is None:
# each element in the tuple indicates if we should replace
# the 2x2 stride with a dilated convolution instead
replace_stride_with_dilation = [False, False, False]
if len(replace_stride_with_dilation) != 3:
raise ValueError(
"replace_stride_with_dilation should be None "
"or a 3-element tuple, got {}".format(replace_stride_with_dilation)
)
self.groups = groups
self.base_width = width_per_group
# NOTE: strictly set the in_channels = 3 to load the pretrained model
self.conv1 = nn.Conv2d(
3, self.inplanes, kernel_size=7, stride=2, padding=3, bias=False
)
# self.conv1 = nn.Conv2d(in_channels, self.inplanes, kernel_size=7, stride=2, padding=3, bias=False)
self.bn1 = norm_layer(self.inplanes)
self.relu = nn.ReLU(inplace=True)
self.maxpool = nn.MaxPool2d(kernel_size=3, stride=2, padding=1)
self.layer1 = self._make_layer(block, 64, layers[0])
self.layer2 = self._make_layer(
block, 128, layers[1], stride=2, dilate=replace_stride_with_dilation[0]
)
self.layer3 = self._make_layer(
block, 256, layers[2], stride=2, dilate=replace_stride_with_dilation[1]
)
self.layer4 = self._make_layer(
block, 512, layers[3], stride=2, dilate=replace_stride_with_dilation[2]
)
self.avgpool = nn.AdaptiveAvgPool2d((1, 1))
# NOTE: strictly set the num_classes = 1000 to load the pretrained model
self.fc = nn.Linear(512 * block.expansion, 1000)
for m in self.modules():
if isinstance(m, nn.Conv2d):
nn.init.kaiming_normal_(m.weight, mode="fan_out", nonlinearity="relu")
elif isinstance(m, (nn.BatchNorm2d, nn.GroupNorm)):
nn.init.constant_(m.weight, 1)
nn.init.constant_(m.bias, 0)
# Zero-initialize the last BN in each residual branch,
# so that the residual branch starts with zeros, and each residual block behaves like an identity.
# This improves the model by 0.2~0.3% according to https://arxiv.org/abs/1706.02677
if zero_init_residual:
for m in self.modules():
if isinstance(m, BasicBlock):
nn.init.constant_(m.bn2.weight, 0)
def _make_layer(self, block, planes, blocks, stride=1, dilate=False):
norm_layer = self._norm_layer
downsample = None
previous_dilation = self.dilation
if dilate:
self.dilation *= stride
stride = 1
if stride != 1 or self.inplanes != planes * block.expansion:
downsample = nn.Sequential(
conv1x1(self.inplanes, planes * block.expansion, stride),
norm_layer(planes * block.expansion),
)
layers = []
layers.append(
block(
self.inplanes,
planes,
stride,
downsample,
self.groups,
self.base_width,
previous_dilation,
norm_layer,
)
)
self.inplanes = planes * block.expansion
for _ in range(1, blocks):
layers.append(
block(
self.inplanes,
planes,
groups=self.groups,
base_width=self.base_width,
dilation=self.dilation,
norm_layer=norm_layer,
)
)
return nn.Sequential(*layers)
def forward(self, x):
x = self.conv1(x)
x = self.bn1(x)
x = self.relu(x)
x = self.maxpool(x)
x = self.layer1(x)
x = self.layer2(x)
x = self.layer3(x)
x = self.layer4(x)
x = self.avgpool(x)
x = torch.flatten(x, 1)
x = self.fc(x)
return x
###################### masking
# from .resnet import conv1x1, conv3x3, BasicBlock, Bottleneck
def up_pooling(in_channels, out_channels, kernel_size=2, stride=2):
return nn.Sequential(
nn.ConvTranspose2d(
in_channels, out_channels, kernel_size=kernel_size, stride=stride
),
nn.BatchNorm2d(out_channels),
nn.ReLU(inplace=True),
)
class Masking4(nn.Module):
def __init__(self, in_channels, out_channels, block=BasicBlock):
assert in_channels == out_channels
super(Masking4, self).__init__()
filters = [
in_channels,
in_channels * 2,
in_channels * 4,
in_channels * 8,
in_channels * 16,
]
self.downsample1 = nn.Sequential(
conv1x1(filters[0], filters[1], 1),
nn.BatchNorm2d(filters[1]),
)
self.downsample2 = nn.Sequential(
conv1x1(filters[1], filters[2], 1),
nn.BatchNorm2d(filters[2]),
)
self.downsample3 = nn.Sequential(
conv1x1(filters[2], filters[3], 1),
nn.BatchNorm2d(filters[3]),
)
self.downsample4 = nn.Sequential(
conv1x1(filters[3], filters[4], 1),
nn.BatchNorm2d(filters[4]),
)
"""
self.conv1 = block(filters[0], filters[1], downsample=conv1x1(filters[0], filters[1], 1))
self.conv2 = block(filters[1], filters[2], downsample=conv1x1(filters[1], filters[2], 1))
self.conv3 = block(filters[2], filters[3], downsample=conv1x1(filters[2], filters[3], 1))
"""
self.conv1 = block(filters[0], filters[1], downsample=self.downsample1)
self.conv2 = block(filters[1], filters[2], downsample=self.downsample2)
self.conv3 = block(filters[2], filters[3], downsample=self.downsample3)
self.conv4 = block(filters[3], filters[4], downsample=self.downsample4)
self.down_pooling = nn.MaxPool2d(kernel_size=2)
self.downsample5 = nn.Sequential(
conv1x1(filters[4], filters[3], 1),
nn.BatchNorm2d(filters[3]),
)
self.downsample6 = nn.Sequential(
conv1x1(filters[3], filters[2], 1),
nn.BatchNorm2d(filters[2]),
)
self.downsample7 = nn.Sequential(
conv1x1(filters[2], filters[1], 1),
nn.BatchNorm2d(filters[1]),
)
self.downsample8 = nn.Sequential(
conv1x1(filters[1], filters[0], 1),
nn.BatchNorm2d(filters[0]),
)
"""
self.up_pool4 = up_pooling(filters[3], filters[2])
self.conv4 = block(filters[3], filters[2], downsample=conv1x1(filters[3], filters[2], 1))
self.up_pool5 = up_pooling(filters[2], filters[1])
self.conv5 = block(filters[2], filters[1], downsample=conv1x1(filters[2], filters[1], 1))
self.conv6 = block(filters[1], filters[0], downsample=conv1x1(filters[1], filters[0], 1))
"""
self.up_pool5 = up_pooling(filters[4], filters[3])
self.conv5 = block(filters[4], filters[3], downsample=self.downsample5)
self.up_pool6 = up_pooling(filters[3], filters[2])
self.conv6 = block(filters[3], filters[2], downsample=self.downsample6)
self.up_pool7 = up_pooling(filters[2], filters[1])
self.conv7 = block(filters[2], filters[1], downsample=self.downsample7)
self.conv8 = block(filters[1], filters[0], downsample=self.downsample8)
# init weight
for m in self.modules():
if isinstance(m, nn.Conv2d):
nn.init.kaiming_normal_(m.weight, mode="fan_out", nonlinearity="relu")
elif isinstance(m, (nn.BatchNorm2d, nn.GroupNorm)):
nn.init.constant_(m.weight, 1)
nn.init.constant_(m.bias, 0)
# Zero-initialize the last BN in each residual branch,
# so that the residual branch starts with zeros, and each residual block behaves like an identity.
# This improves the model by 0.2~0.3% according to https://arxiv.org/abs/1706.02677
for m in self.modules():
if isinstance(m, BasicBlock):
nn.init.constant_(m.bn2.weight, 0)
def forward(self, x):
x1 = self.conv1(x)
p1 = self.down_pooling(x1)
x2 = self.conv2(p1)
p2 = self.down_pooling(x2)
x3 = self.conv3(p2)
p3 = self.down_pooling(x3)
x4 = self.conv4(p3)
x5 = self.up_pool5(x4)
x5 = torch.cat([x5, x3], dim=1)
x5 = self.conv5(x5)
x6 = self.up_pool6(x5)
x6 = torch.cat([x6, x2], dim=1)
x6 = self.conv6(x6)
x7 = self.up_pool7(x6)
x7 = torch.cat([x7, x1], dim=1)
x7 = self.conv7(x7)
x8 = self.conv8(x7)
output = torch.softmax(x8, dim=1)
# output = torch.sigmoid(x8)
return output
class Masking3(nn.Module):
def __init__(self, in_channels, out_channels, block=BasicBlock):
assert in_channels == out_channels
super(Masking3, self).__init__()
filters = [in_channels, in_channels * 2, in_channels * 4, in_channels * 8]
self.downsample1 = nn.Sequential(
conv1x1(filters[0], filters[1], 1),
nn.BatchNorm2d(filters[1]),
)
self.downsample2 = nn.Sequential(
conv1x1(filters[1], filters[2], 1),
nn.BatchNorm2d(filters[2]),
)
self.downsample3 = nn.Sequential(
conv1x1(filters[2], filters[3], 1),
nn.BatchNorm2d(filters[3]),
)
"""
self.conv1 = block(filters[0], filters[1], downsample=conv1x1(filters[0], filters[1], 1))
self.conv2 = block(filters[1], filters[2], downsample=conv1x1(filters[1], filters[2], 1))
self.conv3 = block(filters[2], filters[3], downsample=conv1x1(filters[2], filters[3], 1))
"""
self.conv1 = block(filters[0], filters[1], downsample=self.downsample1)
self.conv2 = block(filters[1], filters[2], downsample=self.downsample2)
self.conv3 = block(filters[2], filters[3], downsample=self.downsample3)
self.down_pooling = nn.MaxPool2d(kernel_size=2)
self.downsample4 = nn.Sequential(
conv1x1(filters[3], filters[2], 1),
nn.BatchNorm2d(filters[2]),
)
self.downsample5 = nn.Sequential(
conv1x1(filters[2], filters[1], 1),
nn.BatchNorm2d(filters[1]),
)
self.downsample6 = nn.Sequential(
conv1x1(filters[1], filters[0], 1),
nn.BatchNorm2d(filters[0]),
)
"""
self.up_pool4 = up_pooling(filters[3], filters[2])
self.conv4 = block(filters[3], filters[2], downsample=conv1x1(filters[3], filters[2], 1))
self.up_pool5 = up_pooling(filters[2], filters[1])
self.conv5 = block(filters[2], filters[1], downsample=conv1x1(filters[2], filters[1], 1))
self.conv6 = block(filters[1], filters[0], downsample=conv1x1(filters[1], filters[0], 1))
"""
self.up_pool4 = up_pooling(filters[3], filters[2])
self.conv4 = block(filters[3], filters[2], downsample=self.downsample4)
self.up_pool5 = up_pooling(filters[2], filters[1])
self.conv5 = block(filters[2], filters[1], downsample=self.downsample5)
self.conv6 = block(filters[1], filters[0], downsample=self.downsample6)
# init weight
for m in self.modules():
if isinstance(m, nn.Conv2d):
nn.init.kaiming_normal_(m.weight, mode="fan_out", nonlinearity="relu")
elif isinstance(m, (nn.BatchNorm2d, nn.GroupNorm)):
nn.init.constant_(m.weight, 1)
nn.init.constant_(m.bias, 0)
# Zero-initialize the last BN in each residual branch,
# so that the residual branch starts with zeros, and each residual block behaves like an identity.
# This improves the model by 0.2~0.3% according to https://arxiv.org/abs/1706.02677
for m in self.modules():
if isinstance(m, BasicBlock):
nn.init.constant_(m.bn2.weight, 0)
def forward(self, x):
x1 = self.conv1(x)
p1 = self.down_pooling(x1)
x2 = self.conv2(p1)
p2 = self.down_pooling(x2)
x3 = self.conv3(p2)
x4 = self.up_pool4(x3)
x4 = torch.cat([x4, x2], dim=1)
x4 = self.conv4(x4)
x5 = self.up_pool5(x4)
x5 = torch.cat([x5, x1], dim=1)
x5 = self.conv5(x5)
x6 = self.conv6(x5)
output = torch.softmax(x6, dim=1)
# output = torch.sigmoid(x6)
return output
class Masking2(nn.Module):
def __init__(self, in_channels, out_channels, block=BasicBlock):
assert in_channels == out_channels
super(Masking2, self).__init__()
filters = [in_channels, in_channels * 2, in_channels * 4, in_channels * 8]
self.downsample1 = nn.Sequential(
conv1x1(filters[0], filters[1], 1),
nn.BatchNorm2d(filters[1]),
)
self.downsample2 = nn.Sequential(
conv1x1(filters[1], filters[2], 1),
nn.BatchNorm2d(filters[2]),
)
"""
self.conv1 = block(filters[0], filters[1], downsample=conv1x1(filters[0], filters[1], 1))
self.conv2 = block(filters[1], filters[2], downsample=conv1x1(filters[1], filters[2], 1))
"""
self.conv1 = block(filters[0], filters[1], downsample=self.downsample1)
self.conv2 = block(filters[1], filters[2], downsample=self.downsample2)
self.down_pooling = nn.MaxPool2d(kernel_size=2)
self.downsample3 = nn.Sequential(
conv1x1(filters[2], filters[1], 1),
nn.BatchNorm2d(filters[1]),
)
self.downsample4 = nn.Sequential(
conv1x1(filters[1], filters[0], 1),
nn.BatchNorm2d(filters[0]),
)
"""
self.up_pool3 = up_pooling(filters[2], filters[1])
self.conv3 = block(filters[2], filters[1], downsample=conv1x1(filters[2], filters[1], 1))
self.conv4 = block(filters[1], filters[0], downsample=conv1x1(filters[1], filters[0], 1))
"""
self.up_pool3 = up_pooling(filters[2], filters[1])
self.conv3 = block(filters[2], filters[1], downsample=self.downsample3)
self.conv4 = block(filters[1], filters[0], downsample=self.downsample4)
# init weight
for m in self.modules():
if isinstance(m, nn.Conv2d):
nn.init.kaiming_normal_(m.weight, mode="fan_out", nonlinearity="relu")
elif isinstance(m, (nn.BatchNorm2d, nn.GroupNorm)):
nn.init.constant_(m.weight, 1)
nn.init.constant_(m.bias, 0)
# Zero-initialize the last BN in each residual branch,
# so that the residual branch starts with zeros, and each residual block behaves like an identity.
# This improves the model by 0.2~0.3% according to https://arxiv.org/abs/1706.02677
for m in self.modules():
if isinstance(m, BasicBlock):
nn.init.constant_(m.bn2.weight, 0)
def forward(self, x):
x1 = self.conv1(x)
p1 = self.down_pooling(x1)
x2 = self.conv2(p1)
x3 = self.up_pool3(x2)
x3 = torch.cat([x3, x1], dim=1)
x3 = self.conv3(x3)
x4 = self.conv4(x3)
output = torch.softmax(x4, dim=1)
# output = torch.sigmoid(x4)
return output
class Masking1(nn.Module):
def __init__(self, in_channels, out_channels, block=BasicBlock):
assert in_channels == out_channels
super(Masking1, self).__init__()
filters = [in_channels, in_channels * 2, in_channels * 4, in_channels * 8]
self.downsample1 = nn.Sequential(
conv1x1(filters[0], filters[1], 1),
nn.BatchNorm2d(filters[1]),
)
self.conv1 = block(filters[0], filters[1], downsample=self.downsample1)
self.downsample2 = nn.Sequential(
conv1x1(filters[1], filters[0], 1),
nn.BatchNorm2d(filters[0]),
)
self.conv2 = block(filters[1], filters[0], downsample=self.downsample2)
# init weight
for m in self.modules():
if isinstance(m, nn.Conv2d):
nn.init.kaiming_normal_(m.weight, mode="fan_out", nonlinearity="relu")
elif isinstance(m, (nn.BatchNorm2d, nn.GroupNorm)):
nn.init.constant_(m.weight, 1)
nn.init.constant_(m.bias, 0)
# Zero-initialize the last BN in each residual branch,
# so that the residual branch starts with zeros, and each residual block behaves like an identity.
# This improves the model by 0.2~0.3% according to https://arxiv.org/abs/1706.02677
for m in self.modules():
if isinstance(m, BasicBlock):
nn.init.constant_(m.bn2.weight, 0)
def forward(self, x):
x1 = self.conv1(x)
x2 = self.conv2(x1)
output = torch.softmax(x2, dim=1)
# output = torch.sigmoid(x2)
return output
def masking(in_channels, out_channels, depth, block=BasicBlock):
if depth == 1:
return Masking1(in_channels, out_channels, block)
elif depth == 2:
return Masking2(in_channels, out_channels, block)
elif depth == 3:
return Masking3(in_channels, out_channels, block)
elif depth == 4:
return Masking4(in_channels, out_channels, block)
else:
traceback.print_exc()
raise Exception("depth need to be from 0-3")
#######################
# from .resnet import conv1x1, conv3x3, BasicBlock, Bottleneck
class ResMasking(ResNet):
def __init__(self, weight_path):
super(ResMasking, self).__init__(
block=BasicBlock, layers=[3, 4, 6, 3], in_channels=3, num_classes=1000
)
# state_dict = torch.load('saved/checkpoints/resnet18_rot30_2019Nov05_17.44')['net']
# state_dict = load_state_dict_from_url(model_urls['resnet34'], progress=True)
# self.load_state_dict(state_dict)
self.fc = nn.Linear(512, 7)
"""
# freeze all net
for m in self.parameters():
m.requires_grad = False
"""
self.mask1 = masking(64, 64, depth=4)
self.mask2 = masking(128, 128, depth=3)
self.mask3 = masking(256, 256, depth=2)
self.mask4 = masking(512, 512, depth=1)
def forward(self, x): # 224
x = self.conv1(x) # 112
x = self.bn1(x)
x = self.relu(x)
x = self.maxpool(x) # 56
x = self.layer1(x) # 56
m = self.mask1(x)
x = x * (1 + m)
# x = x * m
x = self.layer2(x) # 28
m = self.mask2(x)
x = x * (1 + m)
# x = x * m
x = self.layer3(x) # 14
m = self.mask3(x)
x = x * (1 + m)
# x = x * m
x = self.layer4(x) # 7
m = self.mask4(x)
x = x * (1 + m)
# x = x * m
x = self.avgpool(x)
x = torch.flatten(x, 1)
x = self.fc(x)
return x
def resmasking(in_channels, num_classes, weight_path=""):
return ResMasking(weight_path)
def resmasking_dropout1(in_channels=3, num_classes=7, weight_path=""):
model = ResMasking(weight_path)
model.fc = nn.Sequential(
nn.Dropout(0.4),
nn.Linear(512, 7)
# nn.Linear(512, num_classes)
)
return model
###########################
def ensure_color(image):
if len(image.shape) == 2:
return | np.dstack([image] * 3) | numpy.dstack |
# pylint: disable=no-member, invalid-name, too-many-instance-attributes
"""
load raw EWD into memory
"""
# Copyright (c) <NAME>. All Rights Reserved.
# Distributed under the (new) BSD License. See LICENSE.txt for more info.
import os
from struct import unpack
import numpy as np
class EWD:
"""EIT raw/waveform data"""
def __init__(self, file_name):
"""
RAW data (.EWD) contains only data
"""
self.file_name = file_name
self.file_size = os.path.getsize(file_name)
# 256 measurement waveforms, 128 points per wave, 2 bytes per point
self.n_wave = 256
self.n_point = 128
self.n_data = self.n_wave * self.n_point
self.frame_size = self.n_data * 2 # signed short
self.n_frame = int(self.file_size / self.frame_size)
self.tot_data = int(self.file_size / 2)
raw = self.load_raw()
self.wave = self.demodulate(raw)
scale = 4096 / 65536 / 29.9 * 1000 / 1250
self.data = (self.wave[:, :256] + 1j * self.wave[:, 256:]) * scale
def load_raw(self):
"""load raw data"""
raw = np.zeros((self.n_frame, self.n_data), dtype=np.int)
with open(self.file_name, "rb") as fh:
for i in range(self.n_frame):
d = fh.read(self.frame_size)
raw[i] = unpack("{}h".format(self.n_data), d)
return raw
def demodulate(self, raw):
"""demodulate raw data into [re, im]"""
wave = np.zeros((self.n_frame, 2 * self.n_wave), dtype=np.double)
sin_rom = np.sin(2.0 * np.pi * np.arange(self.n_point) / self.n_point)
cos_rom = np.cos(2.0 * np.pi * np.arange(self.n_point) / self.n_point)
for i in range(self.n_frame):
dw = raw[i].reshape(self.n_wave, -1)
wave_re = np.sum(dw * sin_rom, axis=1)
wave_im = | np.sum(dw * cos_rom, axis=1) | numpy.sum |
import ast
import math
import numpy as np
import pandas as pd
from imblearn.combine import SMOTEENN
from imblearn.over_sampling import SMOTE
def Change_Label(label):
if label == "Sitting":
return 1
if label == "Standing":
return 2
if label == "Upstairs":
return 3
if label == "Downstairs":
return 4
if label == "Walking":
return 5
if label == "Jogging":
return 6
def kurt(arr, mean, std, Seg):
mean = float(mean)
std = float(std)
Seg = int(Seg)
sum = 0
for i in arr:
sum = sum + math.pow((i - mean), 4)
frac = (Seg - 1) * math.pow(std, 4) + 1
return sum / frac
def skew(arr, mean, std, Seg):
mean = float(mean)
std = float(std)
Seg = int(Seg)
sum = 0
for i in arr:
sum = sum + math.pow((i - mean), 3)
frac = (Seg - 1) * math.pow(std, 3) + 1
return sum / frac
def rms(arr, Seg):
Seg = int(Seg)
sum = 0
for i in arr:
sum = sum + math.pow(i, 2)
return math.sqrt(sum / Seg)
def max(statistics_data, tag):
max = ast.literal_eval(statistics_data[0][tag])
for data in statistics_data:
temp = ast.literal_eval(data[tag])
if(temp > max):
max = temp
return max
def min(statistics_data, tag):
min = ast.literal_eval(statistics_data[0][tag])
for data in statistics_data:
temp = ast.literal_eval(data[tag])
if(temp < min):
min = temp
return min
def scale(value, max, min):
diff = max - ast.literal_eval(value)
range = max - min
return int((1 - diff / range) * 255)
def Calculate_Gravity(file_dir, list):
print("Now, Calculate Gravity ... ")
acc_data = []
with open(file_dir) as f:
index = 0
for line in f:
clear_line = line.strip().lstrip().rstrip(';')
raw_list = clear_line.split(',')
index = index + 1
if len(raw_list) < 5:
continue
id = int(raw_list[0])
status = raw_list[1]
acc_x = float(raw_list[3])
acc_y = float(raw_list[4])
acc_z = float(raw_list[5])
if id in list:
gravity = math.sqrt(math.pow(acc_x, 2) + math.pow(acc_y, 2) + math.pow(acc_z, 2))
acc_tuple = {"gravity": gravity, "acc_x":acc_x, "acc_y":acc_y, "acc_z":acc_z, "status": status}
acc_data.append(acc_tuple)
print("Acc_Data Length: ", len(acc_data))
return acc_data
def Low_Pass(acc_data, k):
print("Now, Low_Pass Filter ... ")
index_range = len(acc_data)
for index in range(1, index_range):
x = acc_data[index]["acc_x"] * k + acc_data[index - 1]["acc_x"] * (1 - k)
y = acc_data[index]["acc_y"] * k + acc_data[index - 1]["acc_y"] * (1 - k)
z = acc_data[index]["acc_z"] * k + acc_data[index - 1]["acc_z"] * (1 - k)
acc_data[index]["acc_x"] = acc_data[index]["acc_x"] - x
acc_data[index]["acc_y"] = acc_data[index]["acc_y"] - y
acc_data[index]["acc_z"] = acc_data[index]["acc_z"] - z
print("After Low_Pass Filter, Acc_Data Length: ", len(acc_data))
return acc_data
def Split_Data(acc_data, Seg_granularity):
print("Now, Split Data ... ")
splited_data = []
gravity_cluster = []
acc_x_cluster = []
acc_y_cluster = []
acc_z_cluster = []
counter = 0
last_status = acc_data[0]["status"]
for acc_tuple in acc_data:
if not (counter < Seg_granularity and acc_tuple["status"] == last_status):
seg_data = {"status": last_status, "gravity_cluster": gravity_cluster, "acc_x_cluster": acc_x_cluster, "acc_y_cluster": acc_y_cluster, "acc_z_cluster": acc_z_cluster}
splited_data.append(seg_data)
gravity_cluster = []
acc_x_cluster = []
acc_y_cluster = []
acc_z_cluster = []
counter = 0
gravity_cluster.append(acc_tuple["gravity"])
acc_x_cluster.append(acc_tuple["acc_x"])
acc_y_cluster.append(acc_tuple["acc_y"])
acc_z_cluster.append(acc_tuple["acc_z"])
last_status = acc_tuple["status"]
counter += 1
print("Splited_Data Length: ", len(splited_data))
return splited_data
def Calculate_Statistic_Feature(splited_data, Seg_granularity):
print("Now, Calculate Statistic Feature ... ")
statistics_data = []
for seg_data in splited_data:
gravity_values = np.array(seg_data.pop("gravity_cluster"))
acc_x_values = np.array(seg_data.pop("acc_x_cluster"))
acc_y_values = np.array(seg_data.pop("acc_y_cluster"))
acc_z_values = np.array(seg_data.pop("acc_z_cluster"))
t_g_mean = ("%.2f" % np.mean(gravity_values))
t_g_var = ("%.2f" % | np.var(gravity_values) | numpy.var |
import argparse
import csv
import os
import random
import string
import numpy as np
import skimage.measure
from os.path import join
from image_class import image_class
# Returns a dictionary with new names like aa.jpg
def rename(shuffled_keys):
# Create the dictionary
# key is real image name (e.g. "real/no_alk_123.jpg")
# the value is the new name to use (e.g. aa.png)
result = {key: str(i) for i, key in enumerate(shuffled_keys, 1)}
return result
# Returns a list of shuffled keys of a dictionary
def get_shuffled_keys(dictionary):
keys = list(dictionary.keys())
random.shuffle(keys)
return keys
# Outputs a folder of renamed images, csv's for pathologists to fill out and for real labels
def generate_turing_test(real_image_folder, synthetic_images_folder, output_folder,
control_image_folder, baseline_1, baseline_2):
# Dictionaries to record data
# the key is real image name (e.g. "real/no_alk_123.jpg")
# the value is "R" or "F" or "C"
real_or_fake_dictionary = {}
# the key is real image name (e.g. "real/no_alk_123.jpg")
# the value is the new name to use (e.g. aa.png)
original_and_renamed_dictionary = {}
# Loop through real images and register them as real
for image in os.listdir(real_image_folder):
image_path = join(real_image_folder, image)
real_or_fake_dictionary[image_path] = "R"
# Loop through fake images and register them as fake
for image in os.listdir(synthetic_images_folder):
image_path = join(synthetic_images_folder, image)
real_or_fake_dictionary[image_path] = "F"
# Loop through control images folder and register them as control
for image in os.listdir(control_image_folder):
image_path = join(control_image_folder, image)
real_or_fake_dictionary[image_path] = "C"
# Get shuffled keys
shuffled_keys = get_shuffled_keys(real_or_fake_dictionary)
# Update to some new names
original_and_renamed_dictionary = rename(shuffled_keys)
# Write master csv
with open('master_file.csv', mode='w') as file:
# Prepare to write out file
writer = csv.writer(file, delimiter=',', quoting=csv.QUOTE_MINIMAL)
writer.writerow(['Original Image Name', 'New Name', 'Real or Model it came from'])
# Write out each image
for each in shuffled_keys:
if '.DS_Store' in each:
continue
writer.writerow([each, original_and_renamed_dictionary.get(each) + '.png', real_or_fake_dictionary.get(each)])
# Create output folder
os.makedirs(output_folder, exist_ok=True)
# Write pathologist csv
with open('pathologist_file.csv', mode='w') as file:
# Prepare to write out file
writer = csv.writer(file, delimiter=',', quoting=csv.QUOTE_MINIMAL)
writer.writerow(['Image Name', 'Authenticity (R = Real or F = Fake)', 'Notes'])
# Write out each image and save it to the output folder
for each in shuffled_keys:
writer.writerow([original_and_renamed_dictionary.get(each) + '.png', '', ''])
# Save the image
if '.DS_Store' in each:
continue
os.system("cp -r {} {}.png".format(
each, join(output_folder, original_and_renamed_dictionary.get(each))))
# Whether an image is mostly whitespace, takes in np array
def is_whitespace(crop):
pooled = skimage.measure.block_reduce(
crop, (int(crop.shape[0]/10), int(crop.shape[1]/10), 3), np.average)
pooled = np.mean(pooled, axis=2)
pooled = | np.rint(pooled[:9, :9]) | numpy.rint |
# Python libraries
import cv2
import numpy as np
import math
# Global Variable
COLORS = dict()
def __add_color(label):
if label not in COLORS.keys():
COLORS[label] = np.random.uniform(0, 255, size=(1, 3)).flatten()
def draw_keypoints(image, kp):
"""
Function to draw keypoints on the image.
INPUT
image(numpy.ndarray): Numpy image. This is the complete image with object to be detected.
kp : Keypoints to be plotted on the image
RETURN
Returns the image with the keypoints plotted on the image.
"""
# Draw Key points
return cv2.drawKeypoints(image,kp ,image, flags=cv2.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS)
def draw_detections(image, bbox, **kwargs):
"""
Function to draw the rectangle, label and mask on the image.
INPUT
image(numpy.ndarray): Image on which the info is drawn.
bbox(numpy.array) : 4 corners of the bounding box on the image
KWARGS Elements
obj_label(str) : Label to put on the top of the image.
confidence(float) : Detection confidence from the object detection model.
mask(numpy.array) : Array of the mask
directions(float) : heading direction of the object
id(int): : object ID used for tracking
color(tuple) : color of the box
RETURN
<numpy.ndarray>
Image with the bbox and label on the image
"""
clone = image.copy()
# Choose a random color
if "obj_label" not in kwargs:
obj_label= "_"
else:
obj_label = kwargs["obj_label"]
__add_color(obj_label)
# Detection parameters
(startX, startY, endX, endY) = bbox
# Put rectangle around the objects detected
if "color" not in kwargs:
cv2.rectangle(clone, (startX, startY), (endX, endY), COLORS[obj_label], 2)
else:
cv2.rectangle(clone, (startX, startY), (endX, endY), kwargs["color"], 2)
# Put label and confidence
y = startY - 10 if startY - 10 > 10 else startY + 10
label = "{}".format(obj_label)
if "confidence" in kwargs:
label += " {:.2f}%".format(kwargs["confidence"])
if "direction" in kwargs:
label += " {}".format(kwargs["directions"]) + u"\N{DEGREE SIGN}"
cv2.putText(clone, label, (startX, y), cv2.FONT_HERSHEY_SIMPLEX, 0.5, (0, 255, 0), 2)
# If mask is there then put mask also in the image
if "mask" in kwargs:
mask = kwargs["mask"]
# Put mask around the detection
roi = clone[startY:endY, startX:endX]
roi = roi[mask]
# Color for the mask
blended = ((0.4 * COLORS[obj_label]) + (0.6 * roi)).astype("uint8")
clone[startY:endY, startX:endX][mask] = blended
return clone
def draw_compare_features(image1, image2, kp1, kp2, goodmatches):
"""
Function to draw matching keypoints on the two images.
INPUT
image1(numpy.ndarray): First Image on which the info is drawn.
image2(numpy.ndarray): Second Image on which the info is drawn.
kp1(list) : List of Keypoints for image 1
kp2(list) : List of Keypoints for image 2.
goodmatches(list) : List of good matches of keypoints between the two images.
RETURN
<numpy.ndarray>
2 images, stiched together with mathces marked.
"""
# Drawing parameters
draw_params = dict(matchColor = (0,255,0),
singlePointColor = (255,0,0),
flags = cv2.DrawMatchesFlags_DEFAULT)
return cv2.drawMatchesKnn(image1,kp1,image2,kp2,goodmatches,None,**draw_params)
def get_videotimestamp(cameraCapture, ret_type="str"):
"""
Function to get the timestamps of the video.
INPUT
cameraCapture(<class 'cv2.VideoCapture'>): Video capture object for the video currenty read.
ret_type(str): Return Type. Defines the type of return ("str", "datetime")
RETURN
<str> or <datetime.datetime>
Current timestamp of the video either in string or datetime format, based on the type.
"""
import datetime
seconds = 0
minutes = 0
hours = 0
milliseconds = cameraCapture.get(cv2.CAP_PROP_POS_MSEC)
seconds = milliseconds//1000
milliseconds = milliseconds%1000
if seconds >= 60:
minutes = seconds//60
seconds = seconds % 60
if minutes >= 60:
hours = minutes//60
minutes = minutes % 60
if milliseconds < 10:
ts = "{}:{}:{}.00{}".format(int(hours), int(minutes), int(seconds), int(milliseconds))
elif milliseconds < 100:
ts = "{}:{}:{}.0{}".format(int(hours), int(minutes), int(seconds), int(milliseconds))
else:
ts = "{}:{}:{}.{}".format(int(hours), int(minutes), int(seconds), int(milliseconds))
if ret_type=="str":
return ts
elif ret_type=="datetime":
return datetime.datetime.strptime(ts, "%H:%M:%S.%f")
else:
raise ValueError("Choose either str or datetime as ret_type")
def pp_detectionlist(dectList):
"""
Function to Pretty Print (PP) detection from single image.
INPUT
dectList(list): Output the list of dictonary with {label, confidence, box}
"""
for detection in dectList:
obj = detection["label"]
confidence = detection["confidence"]
print("[DETECTED] {}: {:.2f}".format(obj, confidence))
def draw_metadata(image, **kwargs):
"""
Function to put textual data on the bottom of the screen
INPUT
image(numpy.ndarray): Image on which the info is drawn.
kwargs(dict): Data on the image
"""
(height, width, channel) = image.shape
# loop over the info tuples and draw them on our frame
itr = 0
for k, v in kwargs.items():
text = "{}: {}".format(k, v)
cv2.putText(image, text, (10, height - ((itr * 30) + 20)),
cv2.FONT_HERSHEY_SIMPLEX, 1, (0, 0, 255), 2)
itr += 1
def draw_marker(image):
"""
Function to draw XY-axis in image plane on the image.
INPUT
image(numpy.ndarray): Image on which the info is drawn.
"""
height, width, channel = image.shape
# Center of image
cx = int(width/2)
cy = int(height/2)
# Draw Center of the Image
cv2.circle(image, (cx, cy),
5, (0, 0, 255), -1)
# Draw line
cv2.line(image, (cx, 0), (cx, height),
(255, 0, 0), 1)
cv2.line(image, (0, cy), (width, cy),
(255, 0, 0), 1)
# Put Coordinates
cv2.putText(image, "+X", (cx-50, 30),
cv2.FONT_HERSHEY_SIMPLEX, 1, (255, 0, 0), 1)
cv2.putText(image, "+Y", (10, cy),
cv2.FONT_HERSHEY_SIMPLEX, 1, (255, 0, 0), 1)
def read_srt(filepath: str) -> list:
"""Function to read the meta data from OpenCamera .srt files
with location and timestamp data
INPUT:
filepath(str): Path for file to read.
RETURN:
List of dictonary with keys
start_time: Start time of the data acq for video
end_time: Start time of the data acq for video
date: Timestamp of video
lat: Latitude in degree
lng: Longitude in degree
alt: Altitude above sea-level in meters
heading: Heading angle from North in degree
"""
import datetime
import re
# Return list
metaData = list()
# Check if the file exits
import os
if os.path.isfile(filepath):
pass
else:
raise Exception("File does not exits!")
with open(filepath, "r") as f:
data = f.readlines()
counter = 1
for itr, line in enumerate(data):
try:
if int(line) == counter:
counter += 1
loc = re.split('[°\'\"\,\ ]', data[itr+3])
s_time = data[itr+1].split("-->")[0].split(" ")[0]
e_time = data[itr+1].split("-->")[1].split("\n")[0]
metaData.append(dict(start_time= datetime.datetime.strptime(s_time, "%H:%M:%S,%f"),
end_time = datetime.datetime.strptime(e_time, " %H:%M:%S,%f"),
date = data[itr+2].split("\n")[0],
lat = float(int(loc[:3][0]) + int(loc[:3][1])/60 + int(loc[:3][2])/3600),
lng = float(int(loc[5:8][0]) + int(loc[5:8][1])/60 + int(loc[5:8][2])/3600),
alt = loc[10],
heading = loc[12]
)
)
except ValueError:
pass
return metaData
# Malisiewicz et al.
def non_max_suppression_fast(detections, overlapThresh):
boxes = list()
for detect in detections:
boxes.append(detect["bbox"])
boxes = np.array(boxes, dtype="float")
# if there are no boxes, return an empty list
if len(boxes) == 0:
return []
# initialize the list of picked indexes
pick = []
# grab the coordinates of the bounding boxes
x1 = boxes[:,0]
y1 = boxes[:,1]
x2 = boxes[:,2]
y2 = boxes[:,3]
# compute the area of the bounding boxes and sort the bounding
# boxes by the bottom-right y-coordinate of the bounding box
area = (x2 - x1 + 1) * (y2 - y1 + 1)
idxs = np.argsort(y2)
# keep looping while some indexes still remain in the indexes
# list
while len(idxs) > 0:
# grab the last index in the indexes list and add the
# index value to the list of picked indexes
last = len(idxs) - 1
i = idxs[last]
pick.append(i)
# find the largest (x, y) coordinates for the start of
# the bounding box and the smallest (x, y) coordinates
# for the end of the bounding box
xx1 = np.maximum(x1[i], x1[idxs[:last]])
yy1 = np.maximum(y1[i], y1[idxs[:last]])
xx2 = np.minimum(x2[i], x2[idxs[:last]])
yy2 = np.minimum(y2[i], y2[idxs[:last]])
# compute the width and height of the bounding box
w = np.maximum(0, xx2 - xx1 + 1)
h = np.maximum(0, yy2 - yy1 + 1)
# compute the ratio of overlap
overlap = (w * h) / area[idxs[:last]]
# delete all indexes from the index list that have
idxs = np.delete(idxs, np.concatenate(([last],
np.where(overlap > overlapThresh)[0])))
# return only the bounding boxes that were picked using the
return [detections[i] for i in pick]
def draw_polygon(frame, pts, color=None): # Polygon Box
bbox = np.array(pts, np.int32)
bbox = bbox.reshape((-1,1,2))
if color is None:
cv2.polylines(frame, [bbox], True, (0, 0, 255), 1)
else:
cv2.polylines(frame, [bbox], True, color ,1)
def draw_line(frame, pts): # Line
point1 = pts[0]
point2 = pts[1]
cv2.line(frame, point1, point2, (0, 0, 255), 1)
def get_fps(video):
# Find OpenCV version
(major_ver, minor_ver, subminor_ver) = (cv2.__version__).split('.')
# With webcam get(CV_CAP_PROP_FPS) does not work.
if int(major_ver) < 3 :
return video.get(cv2.cv.CV_CAP_PROP_FPS)
else :
return video.get(cv2.CAP_PROP_FPS)
def get_number_of_frames(video):
video.set(cv2.CAP_PROP_POS_AVI_RATIO,1)
num_of_frames = video.get(cv2.CAP_PROP_POS_FRAMES)
video.set(cv2.CAP_PROP_POS_AVI_RATIO,0)
assert video.get(cv2.CAP_PROP_POS_FRAMES) == float(0); "Some error in getting number of frames!"
return num_of_frames
def distance_from_camera(bbox, image_shape, real_life_size):
"""
Calculates the distance of the object from the camera.
PARMS
bbox: Bounding box [px]
image_shape: Size of the image (width, height) [px]
real_life_size: Height of the object in real world [cms]
"""
## REFERENCE FOR GOPRO
# Focal Length and Image Size
# https://clicklikethis.com/gopro-sensor-size/
# https://gethypoxic.com/blogs/technical/gopro-hero9-teardown
# https://www.sony-semicon.co.jp/products/common/pdf/IMX677-AAPH5_AAPJ_Flyer.pdf
# http://photoseek.com/2013/compare-digital-camera-sensor-sizes-full-frame-35mm-aps-c-micro-four-thirds-1-inch-type/
# https://www.gophotonics.com/products/cmos-image-sensors/sony-corporation/21-209-imx677
# Camera Sensor: Sony IMX677
# Camera Sensor array pixel size: 1.12[um] X 1.12[um]
# Camera Resolution: 5663(H) X 4223(V)
# Camera Sensor dimensions: 6.343[mm/H] X 4.730[mm/V]
# Camera Focal Length: 2.92 mm
# 5633(px)
# 4 -------------------
# 2 - -
# 2 - -
# 3 - -
# (p - -
# x) - -
# -------------------
# REFERNCE FOR CALCULATION
# https://www.scantips.com/lights/subjectdistance.html
# GoPro Intrensic Camera Settings #
###################################
focal_length_mm = 5.21
unit_pixel_length = 1.12
sen_res = (5663, 4223)
sensor_height_mm = (unit_pixel_length*sen_res[1])/1000
sensor_width_mm = (unit_pixel_length*sen_res[0])/1000
###################################
# Calculation
image_height_px = image_shape[0]
image_width_px = image_shape[1]
(startX, startY, endX, endY) = bbox
height_of_object_px = endY - startY
width_of_object_px = endX - startX
obj_height_on_sensor_mm = (sensor_height_mm * height_of_object_px) / image_height_px
return (real_life_size * focal_length_mm)/obj_height_on_sensor_mm
def lat_lng_from_camera(origin, heading_angle, distance,
EARTH_RADIUS_KMS = 6378.1):
"""
Calculates the latitude and longitude (in degree) of the object from the camera.
PARMS
origin: Origin point in (lat, lng)
heading_angle: Heading angle of the object from the camera
distance: Distance of the object from camera [kms]
EARTH_RADIUS_KMS: Radius of earth in kms
"""
lat1 = math.radians(origin[0])
lng1 = math.radians(origin[1])
brng = math.radians(heading_angle)
lat2 = math.asin(math.sin(lat1)*math.cos(distance/EARTH_RADIUS_KMS) + math.cos(lat1)*math.sin(distance/EARTH_RADIUS_KMS)*math.cos(brng))
lng2 = lng1 + math.atan2(math.sin(brng)*math.sin(distance/EARTH_RADIUS_KMS)*math.cos(lat1), math.cos(distance/EARTH_RADIUS_KMS)-math.sin(lat1)*math.sin(lat2))
lat2 = math.degrees(lat2)
lng2 = math.degrees(lng2)
return (lat2, lng2)
def get_latlon(image, detection, origin, heading_angle,
real_life_size=150):
# Distance in cms
distance = distance_from_camera(detection["bbox"], image.shape, real_life_size)
# Latitude and logitude of object
return lat_lng_from_camera(origin, heading_angle, distance/100000)
def heading(start_point, end_point):
# Reference:
# https://www.igismap.com/formula-to-find-bearing-or-heading-angle-between-two-points-latitude-longitude/
# https://www.movable-type.co.uk/scripts/latlong.html
# Convert all the points to
start_point["lat"] = math.radians(start_point["lat"])
start_point["lon"] = math.radians(start_point["lon"])
end_point["lat"] = math.radians(end_point["lat"])
end_point["lon"] = math.radians(end_point["lon"])
dL = end_point["lon"]-start_point["lon"]
Y = (math.cos(start_point["lat"])*math.sin(end_point["lat"])) - (math.sin(start_point["lat"])*math.cos(end_point["lat"])*math.cos(dL))
X = math.cos(end_point["lat"])*math.sin(dL)
return math.degrees(math.atan2(X, Y)) # in degrees
def heading_from_camera(bbox, image_shape):
"""
Calculates the heading angle (in degree) of the object from the camera.
PARMS
bbox: Bounding box [px]
image_shape: Size of the image (width, height) [px]
"""
# GoPro Intrensic Camera Settings #
###################################
focal_length_mm = 5.21
unit_pixel_length = 1.12
sen_res = (5663, 4223)
sensor_height_mm = (unit_pixel_length*sen_res[1])/1000
sensor_width_mm = (unit_pixel_length*sen_res[0])/1000
###################################
# Image Center
(cX, cY) = image_shape[1]/2, image_shape[0]/2
# Object Center
(startX, startY, endX, endY) = bbox
(centerX, centerY) = (startX+endX)/2, (startY+endY)/2
# Distance between the two points
distance = math.sqrt((centerX - cX)**2 + (centerY - cY)**2)
# Focal Length in px
img_width_px = image_shape[1]
f_px = (focal_length_mm * img_width_px)/ (sensor_width_mm)
# Heading Angle
angle = math.degrees(math.asin(distance/f_px))
if centerX > cX:
return angle
else:
return -angle
def distance_btw_lalon_points(lat1, lon1, lat2, lon2):
# Distance between two lat/long points
# Using Haversine formula
# https://stackoverflow.com/questions/27928/calculate-distance-between-two-latitude-longitude-points-haversine-formula
lat1, lon1 = np.radians(lat1), np.radians(lon1)
lat2, lon2 = np.radians(lat2), np.radians(lon2)
R = 6371
dLat = lat2-lat1
dLon = lon2-lon1
a = np.sin(dLat/2) *np.sin(dLat/2) + np.cos(lat1)*np.cos(lat2) * np.sin(dLon/2) *np.sin(dLon/2)
c = 2 * np.arctan2( | np.sqrt(a) | numpy.sqrt |
import numpy as np
import sys
import warnings
warnings.filterwarnings('ignore')
import george
from george import kernels
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF,WhiteKernel, ConstantKernel as C, DotProduct, RationalQuadratic, Matern
from scipy.optimize import minimize
from scipy.interpolate import PchipInterpolator, interp1d
import scipy.io as sio
from .priors import *
import pkg_resources
def get_file(folder, filename):
resource_package = __name__
resource_path = '/'.join((folder, filename)) # Do not use os.path.join()
template = pkg_resources.resource_stream(resource_package, resource_path)
return template
fsps_mlc = sio.loadmat(get_file('train_data','fsps_mass_loss_curve.mat'))
#fsps_mlc = sio.loadmat('dense_basis/train_data/fsps_mass_loss_curve.mat')
fsps_time = fsps_mlc['timeax_fsps'].ravel()
fsps_massloss = fsps_mlc['mass_loss_fsps'].ravel()
# basic SFH tuples
rising_sfh = np.array([10.0,1.0,3,0.5,0.7,0.9])
regular_sfg_sfh = np.array([10.0,0.3,3,0.25,0.5,0.75])
young_quenched_sfh = np.array([10.0,-1.0,3,0.3,0.6,0.8])
old_quenched_sfh = np.array([10.0,-1.0,3,0.1,0.2,0.4])
old_very_quenched_sfh = np.array([10.0,-10.0,3,0.1,0.2,0.4])
double_peaked_SF_sfh = np.array([10.0,0.5,3,0.25,0.4,0.7])
double_peaked_Q_sfh = np.array([10.0,-1.0,3,0.2,0.4,0.8])
# functions:
def neg_ln_like(p, gp, y):
gp.set_parameter_vector(p)
return -gp.log_likelihood(y)
def grad_neg_ln_like(p, gp, y):
gp.set_parameter_vector(p)
return -gp.grad_log_likelihood(y)
def correct_for_mass_loss(sfh, time, mass_loss_curve_time, mass_loss_curve):
correction_factors = np.interp(time, mass_loss_curve_time, mass_loss_curve)
return sfh * correction_factors
def gp_interpolator(x,y,res = 1000, Nparam = 3):
yerr = np.zeros_like(y)
yerr[2:(2+Nparam)] = 0.001/np.sqrt(Nparam)
if len(yerr) > 26:
yerr[2:(2+Nparam)] = 0.1/np.sqrt(Nparam)
#kernel = np.var(yax) * kernels.ExpSquaredKernel(np.median(yax)+np.std(yax))
#k2 = np.var(yax) * kernels.LinearKernel(np.median(yax),order=1)
#kernel = np.var(y) * kernels.Matern32Kernel(np.median(y)) #+ k2
kernel = np.var(y) * (kernels.Matern32Kernel(np.median(y)) + kernels.LinearKernel(np.median(y), order=2))
gp = george.GP(kernel)
#print(xax.shape, yerr.shape)
gp.compute(x.ravel(), yerr.ravel())
x_pred = np.linspace(np.amin(x), np.amax(x), res)
y_pred, pred_var = gp.predict(y.ravel(), x_pred, return_var=True)
return x_pred, y_pred
def gp_sklearn_interpolator(x,y,res = 1000):
kernel = DotProduct(10.0, (1e-2,1e2)) *RationalQuadratic(0.1)
gp = GaussianProcessRegressor(kernel=kernel, n_restarts_optimizer=9)
gp.fit(x.reshape(-1,1),(y-x).reshape(-1,1))
x_pred = np.linspace(0,1,1000)
y_pred, sigma = gp.predict(x_pred[:,np.newaxis], return_std=True)
y_pred = y_pred.ravel() + x_pred
return x_pred, y_pred
def linear_interpolator(x,y,res = 1000):
interpolator = interp1d(x,y)
x_pred = np.linspace(np.amin(x), np.amax(x), res)
y_pred = interpolator(x_pred)
return x_pred, y_pred
def Pchip_interpolator(x,y,res = 1000):
interpolator = PchipInterpolator(x,y)
x_pred = np.linspace(np.amin(x), np.amax(x), res)
y_pred = interpolator(x_pred)
return x_pred, y_pred
def tuple_to_sfh(sfh_tuple, zval, interpolator = 'gp_george', set_sfr_100Myr = False, vb = False):
# generate an SFH from an input tuple (Mass, SFR, {tx}) at a specified redshift
Nparam = int(sfh_tuple[2])
mass_quantiles = np.linspace(0,1,Nparam+2)
time_quantiles = np.zeros_like(mass_quantiles)
time_quantiles[-1] = 1
time_quantiles[1:-1] = sfh_tuple[3:]
# now add SFR constraints
# SFR smoothly increasing from 0 at the big bang
mass_quantiles = np.insert(mass_quantiles,1,[0.00])
time_quantiles = np.insert(time_quantiles,1,[0.01])
# SFR constrained to SFR_inst at the time of observation
SFH_constraint_percentiles = np.array([0.96,0.97,0.98,0.99])
for const_vals in SFH_constraint_percentiles:
delta_mstar = 10**(sfh_tuple[0]) *(1-const_vals)
delta_t = 1 - delta_mstar/(10**sfh_tuple[1])/(cosmo.age(zval).value*1e9)
if (delta_t > time_quantiles[-2]) & (delta_t > 0.9):
mass_quantiles = np.insert(mass_quantiles, -1, [const_vals], )
time_quantiles = np.insert(time_quantiles, -1, [delta_t],)
else:
delta_m = 1 - ((cosmo.age(zval).value*1e9)*(1-const_vals)*(10**sfh_tuple[1]))/(10**sfh_tuple[0])
time_quantiles = np.insert(time_quantiles, -1, [const_vals])
mass_quantiles= np.insert(mass_quantiles, -1, [delta_m])
if interpolator == 'gp_george':
time_arr_interp, mass_arr_interp = gp_interpolator(time_quantiles, mass_quantiles, Nparam = int(Nparam))
elif interpolator == 'gp_sklearn':
time_arr_interp, mass_arr_interp = gp_sklearn_interpolator(time_quantiles, mass_quantiles)
elif interpolator == 'linear':
time_arr_interp, mass_arr_interp = linear_interpolator(time_quantiles, mass_quantiles)
elif interpolator == 'pchip':
time_arr_interp, mass_arr_interp = Pchip_interpolator(time_quantiles, mass_quantiles)
else:
raise Exception('specified interpolator does not exist: {}. \n use one of the following: gp_george, gp_sklearn, linear, and pchip '.format(interpolator))
sfh_scale = 10**(sfh_tuple[0])/(cosmo.age(zval).value*1e9/1000)
sfh = np.diff(mass_arr_interp)*sfh_scale
sfh[sfh<0] = 0
sfh = np.insert(sfh,0,[0])
if set_sfr_100Myr == True:
time_100Myr = np.argmin(np.abs(time_arr_interp*cosmo.age(zval).value - 0.1))
sfh[-time_100Myr:] = 10**sfh_tuple[1]
timeax = time_arr_interp * cosmo.age(zval).value
if vb == True:
print('time and mass quantiles:')
print(time_quantiles, mass_quantiles)
plt.plot(time_quantiles, mass_quantiles,'--o')
plt.plot(time_arr_interp, mass_arr_interp)
plt.axis([0,1,0,1])
#plt.axis([0.9,1.05,0.9,1.05])
plt.show()
print('instantaneous SFR: %.1f' %sfh[-1])
plt.plot(np.amax(time_arr_interp) - time_arr_interp, sfh)
#plt.xscale('log')
plt.show()
return sfh, timeax
def calctimes(timeax,sfh,nparams):
massint = np.cumsum(sfh)
massint_normed = massint/np.amax(massint)
tx = np.zeros((nparams,))
for i in range(nparams):
tx[i] = timeax[np.argmin(np.abs(massint_normed - 1*(i+1)/(nparams+1)))]
#tx[i] = (np.argmin(np.abs(massint_normed - 1*(i+1)/(nparams+1))))
#print(1*(i+1)/(nparams+1))
#mass = np.log10(np.sum(sfh)*1e9)
mass = np.log10(np.trapz(sfh,timeax*1e9))
sfr = np.log10(sfh[-1])
return mass, sfr, tx/ | np.amax(timeax) | numpy.amax |
import os
import glob
import pickle
import pcl
import torch
import torch.utils.data
import torch.nn as nn
import numpy as np
# global configurations:
from autolab_core import YamlConfig
from dexnet.grasping import GpgGraspSampler
from dexnet.grasping import RobotGripper
home_dir = os.environ['HOME']
yaml_config = YamlConfig(home_dir + "/Projects/PointNetGPD/dex-net/test/config.yaml")
gripper_name = 'robotiq_85'
gripper = RobotGripper.load(gripper_name, home_dir + "/Projects/PointNetGPD/dex-net/data/grippers")
ags = GpgGraspSampler(gripper, yaml_config)
class PointGraspDataset(torch.utils.data.Dataset):
def __init__(self, obj_points_num, grasp_points_num, pc_file_used_num, grasp_amount_per_file, thresh_good,
thresh_bad, path, tag, with_obj=False, projection=False, project_chann=3, project_size=60):
self.obj_points_num = obj_points_num
self.grasp_points_num = grasp_points_num
self.pc_file_used_num = pc_file_used_num
self.grasp_amount_per_file = grasp_amount_per_file
self.path = path
self.tag = tag
self.thresh_good = thresh_good
self.thresh_bad = thresh_bad
self.with_obj = with_obj
self.min_point_limit = 50
# projection related
self.projection = projection
self.project_chann = project_chann
if self.project_chann not in [3, 12]:
raise NotImplementedError
self.project_size = project_size
if self.project_size != 60:
raise NotImplementedError
self.normal_K = 10
self.voxel_point_num = 50
self.projection_margin = 1
self.transform = pickle.load(open(os.path.join(self.path, 'google2cloud.pkl'), 'rb'))
fl_grasp = glob.glob(os.path.join(path, 'ycb_grasp', self.tag, '*.npy'))
fl_pc = glob.glob(os.path.join(path, 'ycb_rgbd', '*', 'clouds', '*.npy'))
self.d_pc, self.d_grasp = {}, {}
for i in fl_pc:
k = i.split('/')[-3]
if k in self.d_pc.keys():
self.d_pc[k].append(i)
else:
self.d_pc[k] = [i]
for i in fl_grasp:
k = i.split('/')[-1].split('.')[0]
self.d_grasp[k] = i
object1 = set(self.d_grasp.keys())
object2 = set(self.transform.keys())
self.object = list(object1.intersection(object2))
self.amount = len(self.object) * self.grasp_amount_per_file
def collect_pc(self, grasp, pc, transform):
center = grasp[0:3]
axis = grasp[3:6] # binormal
width = grasp[6]
angle = grasp[7]
axis = axis/np.linalg.norm(axis)
binormal = axis
# cal approach
cos_t = np.cos(angle)
sin_t = np.sin(angle)
R1 = np.c_[[cos_t, 0, sin_t],[0, 1, 0],[-sin_t, 0, cos_t]]
axis_y = axis
axis_x = np.array([axis_y[1], -axis_y[0], 0])
if np.linalg.norm(axis_x) == 0:
axis_x = np.array([1, 0, 0])
axis_x = axis_x / np.linalg.norm(axis_x)
axis_y = axis_y / np.linalg.norm(axis_y)
axis_z = np.cross(axis_x, axis_y)
R2 = np.c_[axis_x, np.c_[axis_y, axis_z]]
approach = R2.dot(R1)[:, 0]
approach = approach / np.linalg.norm(approach)
minor_normal = np.cross(axis, approach)
left = center - width*axis/2
right = center + width*axis/2
# bottom = center - width*approach
left = (np.dot(transform, np.array([left[0], left[1], left[2], 1])))[:3]
right = (np.dot(transform, np.array([right[0], right[1], right[2], 1])))[:3]
# bottom = (transform @ np.array([bottom[0], bottom[1], bottom[2], 1]))[:3]
center = (np.dot(transform, np.array([center[0], center[1], center[2], 1])))[:3]
binormal = (np.dot(transform, np.array([binormal[0], binormal[1], binormal[2], 1])))[:3].reshape(3, 1)
approach = (np.dot(transform, np.array([approach[0], approach[1], approach[2], 1])))[:3].reshape(3, 1)
minor_normal = (np.dot(transform, np.array([minor_normal[0], minor_normal[1], minor_normal[2], 1])))[:3].reshape(3, 1)
matrix = np.hstack([approach, binormal, minor_normal]).T
# pc_p2c/left_t/right_t is in local coordinate(with center as origin)
# other(include pc) are in pc coordinate
pc_p2c = (np.dot(matrix, (pc-center).T)).T
left_t = (-width * np.array([0,1,0]) / 2).squeeze()
right_t = (width * np.array([0,1,0]) / 2).squeeze()
x_limit = width/4
z_limit = width/4
y_limit = width/2
x1 = pc_p2c[:, 0] > -x_limit
x2 = pc_p2c[:, 0] < x_limit
y1 = pc_p2c[:, 1] > -y_limit
y2 = pc_p2c[:, 1] < y_limit
z1 = pc_p2c[:, 2] > -z_limit
z2 = pc_p2c[:, 2] < z_limit
a = np.vstack([x1, x2, y1, y2, z1, z2])
self.in_ind = np.where(np.sum(a, axis=0) == len(a))[0]
if len(self.in_ind) < self.min_point_limit:
return None
if self.projection:
return self.project_pc(pc_p2c, width)
else:
return pc_p2c[self.in_ind]
def check_square(self, point, points_g):
dirs = np.array([[-1, 1, 1], [1, 1, 1], [-1, -1, 1], [1, -1, 1],
[-1, 1, -1], [1, 1, -1], [-1, -1, -1], [1, -1, -1]])
p = dirs * 0.5 + point # here res * 0.5 means get half of a pixel width
a1 = p[2][1] < points_g[:, 1]
a2 = p[0][1] > points_g[:, 1]
a3 = p[0][2] > points_g[:, 2]
a4 = p[4][2] < points_g[:, 2]
a5 = p[1][0] > points_g[:, 0]
a6 = p[0][0] < points_g[:, 0]
a = np.vstack([a1, a2, a3, a4, a5, a6])
points_in_area = np.where(np.sum(a, axis=0) == len(a))[0]
if len(points_in_area) == 0:
has_p = False
else:
has_p = True
return points_in_area
def cal_projection(self, point_cloud_voxel, m_width_of_pic, margin, surface_normal, order, gripper_width):
occupy_pic = np.zeros([m_width_of_pic, m_width_of_pic, 1])
norm_pic = np.zeros([m_width_of_pic, m_width_of_pic, 3])
norm_pic_num = np.zeros([m_width_of_pic, m_width_of_pic, 1])
max_x = point_cloud_voxel[:, order[0]].max()
min_x = point_cloud_voxel[:, order[0]].min()
max_y = point_cloud_voxel[:, order[1]].max()
min_y = point_cloud_voxel[:, order[1]].min()
min_z = point_cloud_voxel[:, order[2]].min()
tmp = max((max_x - min_x), (max_y - min_y))
if tmp == 0:
print("WARNING : the num of input points seems only have one, no possilbe to do learning on"
"such data, please throw it away. -- Hongzhuo")
return occupy_pic, norm_pic
# Here, we use the gripper width to cal the res:
res = gripper_width / (m_width_of_pic-margin)
voxel_points_square_norm = []
x_coord_r = ((point_cloud_voxel[:, order[0]]) / res + m_width_of_pic / 2)
y_coord_r = ((point_cloud_voxel[:, order[1]]) / res + m_width_of_pic / 2)
z_coord_r = ((point_cloud_voxel[:, order[2]]) / res + m_width_of_pic / 2)
x_coord_r = np.floor(x_coord_r).astype(int)
y_coord_r = np.floor(y_coord_r).astype(int)
z_coord_r = np.floor(z_coord_r).astype(int)
voxel_index = np.array([x_coord_r, y_coord_r, z_coord_r]).T # all point in grid
coordinate_buffer = np.unique(voxel_index, axis=0) # get a list of points without duplication
K = len(coordinate_buffer)
# [K, 1] store number of points in each voxel grid
number_buffer = np.zeros(shape=K, dtype=np.int64)
feature_buffer = np.zeros(shape=(K, self.voxel_point_num, 6), dtype=np.float32)
index_buffer = {}
for i in range(K):
index_buffer[tuple(coordinate_buffer[i])] = i # got index of coordinate
for voxel, point, normal in zip(voxel_index, point_cloud_voxel, surface_normal):
index = index_buffer[tuple(voxel)]
number = number_buffer[index]
if number < self.voxel_point_num:
feature_buffer[index, number, :3] = point
feature_buffer[index, number, 3:6] = normal
number_buffer[index] += 1
voxel_points_square_norm = np.sum(feature_buffer[..., -3:], axis=1)/number_buffer[:, np.newaxis]
voxel_points_square = coordinate_buffer
if len(voxel_points_square) == 0:
return occupy_pic, norm_pic
x_coord_square = voxel_points_square[:, 0]
y_coord_square = voxel_points_square[:, 1]
norm_pic[x_coord_square, y_coord_square, :] = voxel_points_square_norm
occupy_pic[x_coord_square, y_coord_square] = number_buffer[:, np.newaxis]
occupy_max = occupy_pic.max()
assert(occupy_max > 0)
occupy_pic = occupy_pic / occupy_max
return occupy_pic, norm_pic
def project_pc(self, pc, gripper_width):
"""
for gpd baseline, only support input_chann == [3, 12]
"""
pc = pc.astype(np.float32)
pc = pcl.PointCloud(pc)
norm = pc.make_NormalEstimation()
norm.set_KSearch(self.normal_K)
normals = norm.compute()
surface_normal = normals.to_array()
surface_normal = surface_normal[:, 0:3]
pc = pc.to_array()
grasp_pc = pc[self.in_ind]
grasp_pc_norm = surface_normal[self.in_ind]
bad_check = (grasp_pc_norm != grasp_pc_norm)
if np.sum(bad_check)!=0:
bad_ind = np.where(bad_check == True)
grasp_pc = np.delete(grasp_pc, bad_ind[0], axis=0)
grasp_pc_norm = np.delete(grasp_pc_norm, bad_ind[0], axis=0)
assert(np.sum(grasp_pc_norm != grasp_pc_norm) == 0)
m_width_of_pic = self.project_size
margin = self.projection_margin
order = np.array([0, 1, 2])
occupy_pic1, norm_pic1 = self.cal_projection(grasp_pc, m_width_of_pic, margin, grasp_pc_norm,
order, gripper_width)
if self.project_chann == 3:
output = norm_pic1
elif self.project_chann == 12:
order = np.array([1, 2, 0])
occupy_pic2, norm_pic2 = self.cal_projection(grasp_pc, m_width_of_pic, margin, grasp_pc_norm,
order, gripper_width)
order = np.array([0, 2, 1])
occupy_pic3, norm_pic3 = self.cal_projection(grasp_pc, m_width_of_pic, margin, grasp_pc_norm,
order, gripper_width)
output = np.dstack([occupy_pic1, norm_pic1, occupy_pic2, norm_pic2, occupy_pic3, norm_pic3])
else:
raise NotImplementedError
return output
def __getitem__(self, index):
# try:
obj_ind, grasp_ind = np.unravel_index(index, (len(self.object), self.grasp_amount_per_file))
obj_grasp = self.object[obj_ind]
obj_pc = self.transform[obj_grasp][0]
f_grasp = self.d_grasp[obj_grasp]
fl_pc = np.array(self.d_pc[obj_pc])
fl_pc = fl_pc[np.random.choice(len(fl_pc), size=self.pc_file_used_num)]
grasp = np.load(f_grasp)[grasp_ind]
pc = np.vstack([np.load(i) for i in fl_pc])
pc = pc[np.random.choice(len(pc), size=self.obj_points_num)]
t = self.transform[obj_grasp][1]
grasp_pc = self.collect_pc(grasp, pc, t)
if grasp_pc is None:
return None
level_score, refine_score = grasp[-2:]
if not self.projection:
if len(grasp_pc) > self.grasp_points_num:
grasp_pc = grasp_pc[np.random.choice(len(grasp_pc), size=self.grasp_points_num,
replace=False)].T
else:
grasp_pc = grasp_pc[np.random.choice(len(grasp_pc), size=self.grasp_points_num,
replace=True)].T
else:
grasp_pc = grasp_pc.transpose((2, 1, 0))
score = level_score + refine_score*0.01
if score >= self.thresh_bad:
label = 0
elif score <= self.thresh_good:
label = 1
else:
return None
if self.with_obj:
return grasp_pc, label, obj_grasp
else:
return grasp_pc, label
def __len__(self):
return self.amount
class PointGraspMultiClassDataset(torch.utils.data.Dataset):
def __init__(self, obj_points_num, grasp_points_num, pc_file_used_num, grasp_amount_per_file, thresh_good,
thresh_bad, path, tag, with_obj=False, projection=False, project_chann=3, project_size=60):
self.obj_points_num = obj_points_num
self.grasp_points_num = grasp_points_num
self.pc_file_used_num = pc_file_used_num
self.grasp_amount_per_file = grasp_amount_per_file
self.path = path
self.tag = tag
self.thresh_good = thresh_good
self.thresh_bad = thresh_bad
self.with_obj = with_obj
self.min_point_limit = 50
# projection related
self.projection = projection
self.project_chann = project_chann
if self.project_chann not in [3, 12]:
raise NotImplementedError
self.project_size = project_size
if self.project_size != 60:
raise NotImplementedError
self.normal_K = 10
self.voxel_point_num = 50
self.projection_margin = 1
self.transform = pickle.load(open(os.path.join(self.path, 'google2cloud.pkl'), 'rb'))
fl_grasp = glob.glob(os.path.join(path, 'ycb_grasp', self.tag, '*.npy'))
fl_pc = glob.glob(os.path.join(path, 'ycb_rgbd', '*', 'clouds', '*.npy'))
self.d_pc, self.d_grasp = {}, {}
for i in fl_pc:
k = i.split('/')[-3]
if k in self.d_pc.keys():
self.d_pc[k].append(i)
else:
self.d_pc[k] = [i]
for i in fl_grasp:
k = i.split('/')[-1].split('.')[0]
self.d_grasp[k] = i
object1 = set(self.d_grasp.keys())
object2 = set(self.transform.keys())
self.object = list(object1.intersection(object2))
self.amount = len(self.object) * self.grasp_amount_per_file
def collect_pc(self, grasp, pc, transform):
center = grasp[0:3]
axis = grasp[3:6] # binormal
width = grasp[6]
angle = grasp[7]
axis = axis/np.linalg.norm(axis)
binormal = axis
# cal approach
cos_t = np.cos(angle)
sin_t = np.sin(angle)
R1 = np.c_[[cos_t, 0, sin_t],[0, 1, 0],[-sin_t, 0, cos_t]]
axis_y = axis
axis_x = np.array([axis_y[1], -axis_y[0], 0])
if np.linalg.norm(axis_x) == 0:
axis_x = np.array([1, 0, 0])
axis_x = axis_x / np.linalg.norm(axis_x)
axis_y = axis_y / np.linalg.norm(axis_y)
axis_z = np.cross(axis_x, axis_y)
R2 = np.c_[axis_x, np.c_[axis_y, axis_z]]
approach = R2.dot(R1)[:, 0]
approach = approach / np.linalg.norm(approach)
minor_normal = np.cross(axis, approach)
left = center - width*axis/2
right = center + width*axis/2
# bottom = center - width*approach
left = (np.dot(transform, np.array([left[0], left[1], left[2], 1])))[:3]
right = (np.dot(transform, np.array([right[0], right[1], right[2], 1])))[:3]
# bottom = (transform @ np.array([bottom[0], bottom[1], bottom[2], 1]))[:3]
center = (np.dot(transform, np.array([center[0], center[1], center[2], 1])))[:3]
binormal = (np.dot(transform, np.array([binormal[0], binormal[1], binormal[2], 1])))[:3].reshape(3, 1)
approach = (np.dot(transform, np.array([approach[0], approach[1], approach[2], 1])))[:3].reshape(3, 1)
minor_normal = (np.dot(transform, np.array([minor_normal[0], minor_normal[1], minor_normal[2], 1])))[:3].reshape(3, 1)
matrix = np.hstack([approach, binormal, minor_normal]).T
# pc_p2c/left_t/right_t is in local coordinate(with center as origin)
# other(include pc) are in pc coordinate
pc_p2c = (np.dot(matrix, (pc-center).T)).T
left_t = (-width * np.array([0,1,0]) / 2).squeeze()
right_t = (width * np.array([0,1,0]) / 2).squeeze()
x_limit = width/4
z_limit = width/4
y_limit = width/2
x1 = pc_p2c[:, 0] > -x_limit
x2 = pc_p2c[:, 0] < x_limit
y1 = pc_p2c[:, 1] > -y_limit
y2 = pc_p2c[:, 1] < y_limit
z1 = pc_p2c[:, 2] > -z_limit
z2 = pc_p2c[:, 2] < z_limit
a = np.vstack([x1, x2, y1, y2, z1, z2])
self.in_ind = np.where(np.sum(a, axis=0) == len(a))[0]
if len(self.in_ind) < self.min_point_limit:
return None
if self.projection:
return self.project_pc(pc_p2c, width)
else:
return pc_p2c[self.in_ind]
def check_square(self, point, points_g):
dirs = np.array([[-1, 1, 1], [1, 1, 1], [-1, -1, 1], [1, -1, 1],
[-1, 1, -1], [1, 1, -1], [-1, -1, -1], [1, -1, -1]])
p = dirs * 0.5 + point # here res * 0.5 means get half of a pixel width
a1 = p[2][1] < points_g[:, 1]
a2 = p[0][1] > points_g[:, 1]
a3 = p[0][2] > points_g[:, 2]
a4 = p[4][2] < points_g[:, 2]
a5 = p[1][0] > points_g[:, 0]
a6 = p[0][0] < points_g[:, 0]
a = np.vstack([a1, a2, a3, a4, a5, a6])
points_in_area = np.where(np.sum(a, axis=0) == len(a))[0]
if len(points_in_area) == 0:
has_p = False
else:
has_p = True
return points_in_area
def cal_projection(self, point_cloud_voxel, m_width_of_pic, margin, surface_normal, order, gripper_width):
occupy_pic = np.zeros([m_width_of_pic, m_width_of_pic, 1])
norm_pic = np.zeros([m_width_of_pic, m_width_of_pic, 3])
norm_pic_num = np.zeros([m_width_of_pic, m_width_of_pic, 1])
max_x = point_cloud_voxel[:, order[0]].max()
min_x = point_cloud_voxel[:, order[0]].min()
max_y = point_cloud_voxel[:, order[1]].max()
min_y = point_cloud_voxel[:, order[1]].min()
min_z = point_cloud_voxel[:, order[2]].min()
tmp = max((max_x - min_x), (max_y - min_y))
if tmp == 0:
print("WARNING : the num of input points seems only have one, no possilbe to do learning on"
"such data, please throw it away. -- Hongzhuo")
return occupy_pic, norm_pic
# Here, we use the gripper width to cal the res:
res = gripper_width / (m_width_of_pic-margin)
voxel_points_square_norm = []
x_coord_r = ((point_cloud_voxel[:, order[0]]) / res + m_width_of_pic / 2)
y_coord_r = ((point_cloud_voxel[:, order[1]]) / res + m_width_of_pic / 2)
z_coord_r = ((point_cloud_voxel[:, order[2]]) / res + m_width_of_pic / 2)
x_coord_r = np.floor(x_coord_r).astype(int)
y_coord_r = np.floor(y_coord_r).astype(int)
z_coord_r = np.floor(z_coord_r).astype(int)
voxel_index = np.array([x_coord_r, y_coord_r, z_coord_r]).T # all point in grid
coordinate_buffer = np.unique(voxel_index, axis=0) # get a list of points without duplication
K = len(coordinate_buffer)
# [K, 1] store number of points in each voxel grid
number_buffer = np.zeros(shape=K, dtype=np.int64)
feature_buffer = np.zeros(shape=(K, self.voxel_point_num, 6), dtype=np.float32)
index_buffer = {}
for i in range(K):
index_buffer[tuple(coordinate_buffer[i])] = i # got index of coordinate
for voxel, point, normal in zip(voxel_index, point_cloud_voxel, surface_normal):
index = index_buffer[tuple(voxel)]
number = number_buffer[index]
if number < self.voxel_point_num:
feature_buffer[index, number, :3] = point
feature_buffer[index, number, 3:6] = normal
number_buffer[index] += 1
voxel_points_square_norm = np.sum(feature_buffer[..., -3:], axis=1)/number_buffer[:, np.newaxis]
voxel_points_square = coordinate_buffer
if len(voxel_points_square) == 0:
return occupy_pic, norm_pic
x_coord_square = voxel_points_square[:, 0]
y_coord_square = voxel_points_square[:, 1]
norm_pic[x_coord_square, y_coord_square, :] = voxel_points_square_norm
occupy_pic[x_coord_square, y_coord_square] = number_buffer[:, np.newaxis]
occupy_max = occupy_pic.max()
assert(occupy_max > 0)
occupy_pic = occupy_pic / occupy_max
return occupy_pic, norm_pic
def project_pc(self, pc, gripper_width):
"""
for gpd baseline, only support input_chann == [3, 12]
"""
pc = pc.astype(np.float32)
pc = pcl.PointCloud(pc)
norm = pc.make_NormalEstimation()
norm.set_KSearch(self.normal_K)
normals = norm.compute()
surface_normal = normals.to_array()
surface_normal = surface_normal[:, 0:3]
pc = pc.to_array()
grasp_pc = pc[self.in_ind]
grasp_pc_norm = surface_normal[self.in_ind]
bad_check = (grasp_pc_norm != grasp_pc_norm)
if np.sum(bad_check)!=0:
bad_ind = np.where(bad_check == True)
grasp_pc = np.delete(grasp_pc, bad_ind[0], axis=0)
grasp_pc_norm = np.delete(grasp_pc_norm, bad_ind[0], axis=0)
assert(np.sum(grasp_pc_norm != grasp_pc_norm) == 0)
m_width_of_pic = self.project_size
margin = self.projection_margin
order = np.array([0, 1, 2])
occupy_pic1, norm_pic1 = self.cal_projection(grasp_pc, m_width_of_pic, margin, grasp_pc_norm,
order, gripper_width)
if self.project_chann == 3:
output = norm_pic1
elif self.project_chann == 12:
order = np.array([1, 2, 0])
occupy_pic2, norm_pic2 = self.cal_projection(grasp_pc, m_width_of_pic, margin, grasp_pc_norm,
order, gripper_width)
order = np.array([0, 2, 1])
occupy_pic3, norm_pic3 = self.cal_projection(grasp_pc, m_width_of_pic, margin, grasp_pc_norm,
order, gripper_width)
output = np.dstack([occupy_pic1, norm_pic1, occupy_pic2, norm_pic2, occupy_pic3, norm_pic3])
else:
raise NotImplementedError
return output
def __getitem__(self, index):
# try:
obj_ind, grasp_ind = np.unravel_index(index, (len(self.object), self.grasp_amount_per_file))
obj_grasp = self.object[obj_ind]
obj_pc = self.transform[obj_grasp][0]
f_grasp = self.d_grasp[obj_grasp]
fl_pc = np.array(self.d_pc[obj_pc])
fl_pc = fl_pc[np.random.choice(len(fl_pc), size=self.pc_file_used_num)]
grasp = np.load(f_grasp)[grasp_ind]
pc = np.vstack([np.load(i) for i in fl_pc])
pc = pc[np.random.choice(len(pc), size=self.obj_points_num)]
t = self.transform[obj_grasp][1]
grasp_pc = self.collect_pc(grasp, pc, t)
if grasp_pc is None:
return None
level_score, refine_score = grasp[-2:]
if not self.projection:
if len(grasp_pc) > self.grasp_points_num:
grasp_pc = grasp_pc[np.random.choice(len(grasp_pc), size=self.grasp_points_num,
replace=False)].T
else:
grasp_pc = grasp_pc[np.random.choice(len(grasp_pc), size=self.grasp_points_num,
replace=True)].T
else:
grasp_pc = grasp_pc.transpose((2, 1, 0))
score = level_score + refine_score*0.01
if score >= self.thresh_bad:
label = 0
elif score <= self.thresh_good:
label = 2
else:
label = 1
if self.with_obj:
return grasp_pc, label, obj_grasp
else:
return grasp_pc, label
def __len__(self):
return self.amount
class PointGraspOneViewDataset(torch.utils.data.Dataset):
def __init__(self, grasp_points_num, grasp_amount_per_file, thresh_good,
thresh_bad, path, tag, with_obj=False, projection=False, project_chann=3, project_size=60):
self.grasp_points_num = grasp_points_num
self.grasp_amount_per_file = grasp_amount_per_file
self.path = path
self.tag = tag
self.thresh_good = thresh_good
self.thresh_bad = thresh_bad
self.with_obj = with_obj
self.min_point_limit = 150 # 最低点数限制
# projection related 投影相关参数
self.projection = projection
self.project_chann = project_chann
if self.project_chann not in [3, 12]:
raise NotImplementedError
self.project_size = project_size
if self.project_size != 60:
raise NotImplementedError
self.normal_K = 10
self.voxel_point_num = 50
self.projection_margin = 1
self.minimum_point_amount = 150
# google扫描仪到点云的转换矩阵
self.transform = pickle.load(open(os.path.join(self.path, 'google2cloud.pkl'), 'rb'))
fl_grasp = glob.glob(os.path.join(path, 'ycb_grasp', self.tag, '*.npy')) # grasp pose file
# 仅获取相机NP3采集的点云
fl_pc = glob.glob(os.path.join(path, 'ycb_rgbd', '*', 'clouds', 'pc_NP3_NP5*.npy')) # point cloud file
self.d_pc, self.d_grasp = {}, {}
for i in fl_pc: # 获取点云文件列表
k = i.split('/')[-3]
if k in self.d_pc.keys():
self.d_pc[k].append(i)
else:
self.d_pc[k] = [i]
for k in self.d_pc.keys():
self.d_pc[k].sort()
for i in fl_grasp: # 获取已生成的抓取姿态列表
grasp_fl_name = i.split('/')[-1].split('.')[0] # grasp文件名
cnt = grasp_fl_name.split('_')[-1] # grasp文件尾
head = grasp_fl_name.split('_')[0] # grasp文件头
k = grasp_fl_name[len(head)+1:-(len(cnt)+1)] # 标准物品名称
self.d_grasp[k] = i
object1 = set(self.d_grasp.keys()) # objects to deal with
# print("object1", object1)
object2 = set(self.transform.keys()) # all ycb objects name
# print("object2", object2)
self.object = list(object1)
# self.object = list(object1.intersection(object2)) # 取交集
print("objects to deal with", self.object)
self.amount = len(self.object) * self.grasp_amount_per_file
def collect_pc(self, grasp, pc, transform):
"""
获取手抓闭合区域中的点云
:param grasp: 扫描仪获取的mesh坐标系下抓取姿态 (grasp_center, grasp_axis, grasp_angle, grasp_width, jaw_width)
:param pc: 点云
:param transform: 扫描仪mesh到点云的转换矩阵
:param vis: 可视化选项
:return: 手抓闭合区域中的点云, 或其投影
"""
# 轴角表示
center = grasp[0:3] # 抓取姿态中心点
axis = grasp[3:6] # binormal 副法线
width = grasp[6] # 抓取姿态宽度
angle = grasp[7] # 旋转角
axis = axis/np.linalg.norm(axis) # (3,)
binormal = axis
# cal approach
cos_t = np.cos(angle)
sin_t = np.sin(angle)
R1 = np.c_[[cos_t, 0, sin_t], [0, 1, 0], [-sin_t, 0, cos_t]] # 旋转矩阵
axis_y = axis
axis_x = np.array([axis_y[1], -axis_y[0], 0])
if np.linalg.norm(axis_x) == 0:
axis_x = np.array([1, 0, 0])
# 各轴单位方向向量
axis_x = axis_x / np.linalg.norm(axis_x)
axis_y = axis_y / np.linalg.norm(axis_y)
axis_z = np.cross(axis_x, axis_y)
R2 = np.c_[axis_x, np.c_[axis_y, axis_z]] # 旋转矩阵
approach = R2.dot(R1)[:, 0]
approach = approach / np.linalg.norm(approach) # 手抓朝向
minor_normal = -np.cross(axis, approach) # 次曲率方向 NOTE: 添加了负号调整为右手坐标系
# 碰撞检测
# grasp_bottom_center = -ags.gripper.hand_depth * approach + center
# hand_points = ags.get_hand_points(grasp_bottom_center, approach, binormal)
# local_hand_points = ags.get_hand_points(np.array([0, 0, 0]), np.array([1, 0, 0]), np.array([0, 1, 0]))
# if_collide = ags.check_collide(grasp_bottom_center, approach,
# binormal, minor_normal, graspable, local_hand_points)
vis = False
if vis: # NOTE：此处获得的抓取姿态可能与点云存在碰撞(影响不是很大)！！！ TODO：碰撞检查
mlab.figure(bgcolor=(1, 1, 1), size=(1000, 800))
mlab.pipeline.surface(mlab.pipeline.open("/home/sdhm/Projects/PointNetGPD/PointNetGPD/data/"
"ycb_meshes_google/003_cracker_box/google_512k/nontextured.ply"))
# ---扫描仪坐标系下---：
# 世界坐标系
show_line([0, 0, 0], [0.1, 0, 0], color='r', scale_factor=.0015)
show_line([0, 0, 0], [0, 0.1, 0], color='g', scale_factor=.0015)
show_line([0, 0, 0], [0, 0, 0.1], color='b', scale_factor=.0015)
show_points(pc, color='b', scale_factor=.002) # 原始点云
show_points(center, color='r', scale_factor=.008)
# 显示手抓坐标系
show_line(center, (center + binormal * 0.05).reshape(3), color='g', scale_factor=.0015)
show_line(center, (center + approach * 0.05).reshape(3), color='r', scale_factor=.0015)
show_line(center, (center + minor_normal * 0.05).reshape(3), color='b', scale_factor=.0015)
grasp_bottom_center = -ags.gripper.hand_depth * approach + center
hand_points = ags.get_hand_points(grasp_bottom_center, approach, binormal)
ags.show_grasp_3d(hand_points, color=(0.4, 0.6, 0.0))
mlab.title("google", size=0.3, color=(0, 0, 0))
mlab.show()
left = center - width*axis/2 # 手抓最左侧点
right = center + width*axis/2 # 手抓最右侧点
# bottom = center - width*approach
left = (np.dot(transform, np.array([left[0], left[1], left[2], 1])))[:3]
right = (np.dot(transform, np.array([right[0], right[1], right[2], 1])))[:3]
# bottom = (transform @ np.array([bottom[0], bottom[1], bottom[2], 1]))[:3]
# NOTE: m:mesh c:center p:point cloud
matrix_m2c = np.array([approach, binormal, minor_normal]) # 旋转矩阵: 扫描仪坐标系->中心点坐标系
matrix_p2m = transform[:3, :3] # 旋转矩阵: 点云坐标系->扫描仪坐标系
trans_p2m = transform[:, 3:][:3].reshape(3,) # 平移矩阵: 点云坐标系->扫描仪坐标系
trans_p2m = np.array([trans_p2m[0], trans_p2m[1], trans_p2m[2] + 0.02]) # 微调
pc_p2m = np.dot(matrix_p2m.T, (pc - trans_p2m).T).T # 配准到扫描仪坐标系下的点云
pc_m2c = (np.dot(matrix_m2c, (pc_p2m-center).T)).T # 扫描仪坐标系下点云转换到中心点坐标系下
# pc_c2m = (np.dot(matrix_m2c.T, pc_m2c.T)).T + center # 中心点坐标系下点云转换到扫描仪坐标系下
left_t = (-width * np.array([0, 1, 0]) / 2).squeeze()
right_t = (width * np.array([0, 1, 0]) / 2).squeeze()
# 获取手抓闭合区域中的点
x_limit = ags.gripper.hand_depth
z_limit = ags.gripper.hand_height
y_limit = width
x1 = pc_m2c[:, 0] > -x_limit
x2 = pc_m2c[:, 0] < 0
y1 = pc_m2c[:, 1] > -y_limit/2
y2 = pc_m2c[:, 1] < y_limit/2
z1 = pc_m2c[:, 2] > -z_limit/2
z2 = pc_m2c[:, 2] < z_limit/2
a = np.vstack([x1, x2, y1, y2, z1, z2])
self.in_ind = np.where(np.sum(a, axis=0) == len(a))[0] # 手抓闭合区域中点的索引
if len(self.in_ind) < self.min_point_limit: # 手抓闭合区域内点数太少
# print("\033[0;32m%s\033[0m" % "[INFO] points num", len(self.in_ind))
return None
vis = False
if vis: # 显示手抓闭合区域内点云
mlab.figure(bgcolor=(1, 1, 1), size=(1000, 800))
mlab.pipeline.surface(mlab.pipeline.open("/home/sdhm/Projects/PointNetGPD/PointNetGPD/data/"
"ycb_meshes_google/003_cracker_box/google_512k/nontextured.ply"))
# 世界坐标系
show_line([0, 0, 0], [0.1, 0, 0], color='r', scale_factor=.0015)
show_line([0, 0, 0], [0, 0.1, 0], color='g', scale_factor=.0015)
show_line([0, 0, 0], [0, 0, 0.1], color='b', scale_factor=.0015)
# show_points(pc, color='b', scale_factor=.002) # 原始点云
show_points(pc_p2m, color='g', scale_factor=.002) # 配准到扫描仪坐标系下点云
show_points(pc_m2c, color='b', scale_factor=.002) # 手抓中心坐标系下点云
# show_points(pc_c2m, color='r', scale_factor=.002) # 手抓中心坐标系转换到扫描仪坐标系下点云
# 显示扫描仪坐标系下手抓
grasp_bottom_center = -ags.gripper.hand_depth * approach + center
hand_points = ags.get_hand_points(grasp_bottom_center, approach, binormal)
ags.show_grasp_3d(hand_points, color=(0.0, 1.0, 0.0))
# 中心点坐标系下手抓(应在世界坐标系原点)
hand_points = (np.dot(matrix_m2c, (hand_points - center).T)).T # 手抓关键点转换到中心点坐标系
ags.show_grasp_3d(hand_points, color=(0.5, 0.5, 0.5)) # 显示手抓
# 扫描仪坐标系下抓取坐标系
show_points(center, color='r', scale_factor=.008) # 扫描仪坐标系下中心点
show_line(center, (center + binormal * 0.05).reshape(3), color='g', scale_factor=.0015)
show_line(center, (center + approach * 0.05).reshape(3), color='r', scale_factor=.0015)
show_line(center, (center + minor_normal * 0.05).reshape(3), color='b', scale_factor=.0015)
show_points(pc_m2c, color='c', scale_factor=.002) # 手抓中心坐标系下点云
show_points(pc_m2c[self.in_ind], color='b', scale_factor=.002) # 中心点坐标系下手抓闭合区域中的点云
pc_c2m_region = (np.dot(matrix_m2c.T, pc_m2c[self.in_ind].T)).T + center # 扫描仪坐标系下手抓闭合区域中的点云
show_points(pc_c2m_region, color='r', scale_factor=.002)
# 显示手抓闭合区域
# x = (np.array([[-1, 1, 1, -1, -1], [-1, 1, 1, -1, -1]]) - 1) * x_limit/2
# y = np.array([[-1, -1, -1, -1, -1], [1, 1, 1, 1, 1]]) * y_limit
# z = np.array([[1, 1, -1, -1, 1], [1, 1, -1, -1, 1]]) * z_limit
# mlab.mesh(x, y, z, color=(1, 0, 0), opacity=0.4)
# 体积为1的正方体的八个顶点
x_arr = np.array([-1, 1, 1, -1, -1, 1, 1, -1])/2
y_arr = np.array([-1, -1, 1, 1, -1, -1, 1, 1])/2
z_arr = np.array([-1, -1, -1, -1, 1, 1, 1, 1])/2
x = (x_arr - 0.5) * ags.gripper.hand_depth # 平移半个单位
y = y_arr * (ags.gripper.hand_outer_diameter-2*ags.gripper.finger_width)
z = z_arr * ags.gripper.hand_height
triangles = [(0, 1, 2), (0, 2, 3), (4, 5, 6), (4, 6, 7), (1, 5, 6), (1, 2, 6),
(0, 4, 7), (0, 3, 7), (2, 3, 6), (3, 6, 7), (0, 1, 5), (0, 4, 5)]
mlab.triangular_mesh(x, y, z, triangles, color=(1, 0, 1), opacity=0.2)
mlab.title("cloud", size=0.3, color=(0, 0, 0))
mlab.show()
if self.projection:
return self.project_pc(pc_m2c, width) # 返回投影后的点云
else:
return pc_m2c[self.in_ind] # 返回手抓闭合区域中的点云
def check_square(self, point, points_g):
dirs = np.array([[-1, 1, 1], [1, 1, 1], [-1, -1, 1], [1, -1, 1],
[-1, 1, -1], [1, 1, -1], [-1, -1, -1], [1, -1, -1]])
p = dirs * 0.5 + point # here res * 0.5 means get half of a pixel width
a1 = p[2][1] < points_g[:, 1]
a2 = p[0][1] > points_g[:, 1]
a3 = p[0][2] > points_g[:, 2]
a4 = p[4][2] < points_g[:, 2]
a5 = p[1][0] > points_g[:, 0]
a6 = p[0][0] < points_g[:, 0]
a = np.vstack([a1, a2, a3, a4, a5, a6])
points_in_area = np.where(np.sum(a, axis=0) == len(a))[0]
if len(points_in_area) == 0:
has_p = False
else:
has_p = True
return points_in_area
def cal_projection(self, point_cloud_voxel, m_width_of_pic, margin, surface_normal, order, gripper_width):
"""
计算点云投影
:param point_cloud_voxel:
:param m_width_of_pic:
:param margin:
:param surface_normal:
:param order:
:param gripper_width:
:return:
"""
occupy_pic = np.zeros([m_width_of_pic, m_width_of_pic, 1])
norm_pic = np.zeros([m_width_of_pic, m_width_of_pic, 3])
norm_pic_num = np.zeros([m_width_of_pic, m_width_of_pic, 1])
max_x = point_cloud_voxel[:, order[0]].max()
min_x = point_cloud_voxel[:, order[0]].min()
max_y = point_cloud_voxel[:, order[1]].max()
min_y = point_cloud_voxel[:, order[1]].min()
min_z = point_cloud_voxel[:, order[2]].min()
tmp = max((max_x - min_x), (max_y - min_y))
if tmp == 0:
print("WARNING : the num of input points seems only have one, no possilbe to do learning on"
"such data, please throw it away. -- Hongzhuo")
return occupy_pic, norm_pic
# Here, we use the gripper width to cal the res:
res = gripper_width / (m_width_of_pic-margin)
voxel_points_square_norm = []
x_coord_r = ((point_cloud_voxel[:, order[0]]) / res + m_width_of_pic / 2)
y_coord_r = ((point_cloud_voxel[:, order[1]]) / res + m_width_of_pic / 2)
z_coord_r = ((point_cloud_voxel[:, order[2]]) / res + m_width_of_pic / 2)
x_coord_r = np.floor(x_coord_r).astype(int)
y_coord_r = np.floor(y_coord_r).astype(int)
z_coord_r = np.floor(z_coord_r).astype(int)
voxel_index = np.array([x_coord_r, y_coord_r, z_coord_r]).T # all point in grid
coordinate_buffer = np.unique(voxel_index, axis=0) # get a list of points without duplication
K = len(coordinate_buffer)
# [K, 1] store number of points in each voxel grid
number_buffer = np.zeros(shape=K, dtype=np.int64)
feature_buffer = np.zeros(shape=(K, self.voxel_point_num, 6), dtype=np.float32)
index_buffer = {}
for i in range(K):
index_buffer[tuple(coordinate_buffer[i])] = i # got index of coordinate
for voxel, point, normal in zip(voxel_index, point_cloud_voxel, surface_normal):
index = index_buffer[tuple(voxel)]
number = number_buffer[index]
if number < self.voxel_point_num:
feature_buffer[index, number, :3] = point
feature_buffer[index, number, 3:6] = normal
number_buffer[index] += 1
voxel_points_square_norm = | np.sum(feature_buffer[..., -3:], axis=1) | numpy.sum |
from sklearn.metrics import confusion_matrix, roc_auc_score, auc
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import FuncFormatter
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits import mplot3d
from datetime import datetime
from common.config import *
import warnings
"""
Read OpticalFLow uint16 images
flow_u(u,v) = ((float)I(u,v,1)-2^15)/64.0;
flow_v(u,v) = ((float)I(u,v,2)-2^15)/64.0;
valid(u,v) = (bool)I(u,v,3);
"""
def ReadOpticalFlow(image):
assert (len(image.shape) == 3)
image_f64 = np.zeros(image.shape, dtype=np.float)
image_u16 = image.astype(np.uint16) #unsigned 16bits
# b g r
u_comp = image_u16[:,:,2]
v_comp = image_u16[:,:,1]
valid_comp = image_u16[:,:,0]
flow_u = ((u_comp - np.float_power(2,15))/64.0)
flow_v = ((v_comp - np.float_power(2,15))/64.0)
valid = (valid_comp == 1) # boolean valid
# just fot assure only valid pixels
flow_u[valid_comp == 0] = 0
flow_v[valid_comp == 0] = 0
image_f64[:,:,0] = flow_u
image_f64[:,:,1] = flow_v
image_f64[:,:,2] = flow_u
return flow_u, flow_v, valid, image_f64
"""
MeanSquareError and Percentage of Erroneous Pixels in Non-Occluded Areas
"""
def MSEN_PEPN(y_gt, y_pred, of_from_dataset=False, show_error=False, th=3):
padd_y, padd_x = np.array(y_gt.shape[:2]) - np.array(y_pred.shape[:2])
flow_pred_image = np.zeros((y_gt.shape))
if padd_x or padd_y:
flow_pred_image[padd_y//2:-padd_y//2, padd_x//2:-padd_x//2,:2] = y_pred
else:
flow_pred_image[... ,:2] = y_pred
flow_u_gt , flow_v_gt, valid_gt, flow_gt_image = ReadOpticalFlow(y_gt)
if of_from_dataset:
flow_u_pred, flow_v_pred, valid_pred, flow_pred_image = ReadOpticalFlow(y_pred)
assert (y_gt.shape[0:2] == flow_pred_image.shape)
else:
flow_u_pred, flow_v_pred = flow_pred_image[:,:,0], flow_pred_image[:,:,1] # vx, vy
assert (y_gt.shape[0:2] == flow_pred_image.shape[:2])
# Errors (mean-square error)
E_u = np.float_power((flow_u_gt - flow_u_pred), 2)
E_v = np.float_power((flow_v_gt - flow_v_pred), 2)
E = np.sqrt(E_u + E_v)
E[valid_gt==0] = 0
error_mse = E[valid_gt==1]
pepn_error = len(E[E > th]) / len(E[valid_gt])
if show_error:
plt.figure()
plt.imshow(np.reshape(E, y_gt.shape[:-1]), cmap='viridis')
plt.colorbar(orientation='horizontal')
plotHistogram(error_mse, pepn_error, "Optical Flow")
print("Error MSEN {:.4f}%".format(np.mean(error_mse)))
print("Error PEPN {:.4f}%".format(pepn_error * 100))
return flow_gt_image, flow_pred_image, error_mse, pepn_error
"""
Plot Histogram for the MSE
"""
def plotHistogram(error, pepn_error, name_seq):
E = error.flatten() if len(error.shape) > 1 else error
plt.figure()
cm = plt.cm.get_cmap('viridis')
n, bins, patches = plt.hist(E, bins=25, normed=True, color='green')
col = (n - n.min()) / (n.max() - n.min())
for c, p in zip(np.flip(col,0), patches):
plt.setp(p, 'facecolor', cm(c))
plt.gca().yaxis.set_major_formatter(FuncFormatter(lambda y, _: '{:.0%}'.format(y))) # add %
plt.xlabel("MSEN values")
plt.ylabel("Number of Pixels")
plt.title("Histogram '{}' with a PEPN {:1f}%".format(name_seq, pepn_error * 100))
plt.show()
"""
Show the OPtical Flow using quiver
"""
def ShowOpticalFlow(image):
u_flow, v_flow, _, _ = ReadOpticalFlow(image)
rows, cols = u_flow.shape
x, y = np.meshgrid(np.arange(0, cols, 1), np.arange(0, rows, 1))
plt.quiver(x, y, np.abs(u_flow), np.abs(v_flow), scale=1, hatch=' ', alpha=0.3, linewidth=0.001)
plt.show()
"""
Return Precision, Recall, F1-Score and Accuracy
"""
def metrics(TP, FP, TN, FN, y_test, array_params=None):
precision_list = []
recall_list = []
fscore_list = []
accuracy_list = []
dim = 1
if np.array(y_test).ndim > 3:
dim = len(y_test)
for m in range(dim):
precision = float(TP[m])/float(TP[m]+FP[m])
recall = float(TP[m])/float(TP[m] + FN[m])
fscore = 2*(float(precision*recall)/float(precision+recall))
accuracy = float(TP[m] + TN[m])/float(TP[m] + TN[m] + FP[m] + FN[m])
precision_list.append(precision)
recall_list.append(recall)
fscore_list.append(fscore)
accuracy_list.append(accuracy)
print("\nSummary: Precision, Recall, F1-Score, Accuracy for each alpha")
print("------------------------------------------------------------")
if array_params is None:
print("Precision: {:.4f} \tRecall: {:.4f} \tF1-Score: {:.4f} \tAccuracy: {:.4f}".format(precision_list[0],recall_list[0],fscore_list[0],accuracy_list[0]))
else:
for id, alpha in enumerate(array_params):
print("For alpha = {} - Precision: {:.4f} \tRecall: {:.4f} \tF1-Score: {:.4f} \tAccuracy: {:.4f}".format(alpha, precision_list[id], recall_list[id], fscore_list[id], accuracy_list[id]))
print("AUC: {}".format(getAUC(recall_list, precision_list, reorder=True)))
print("Best F1-Score is {:.4f} with alpha {:.4f}".format(np.max(fscore_list),array_params[np.argmax(fscore_list)]))
print("------------------------------------------------------------")
return precision_list, recall_list, fscore_list, accuracy_list
def metrics_2Params(TP, FP, TN, FN, array_params_a, array_params_b):
precision_list = []
recall_list = []
fscore_list = []
accuracy_list = []
total_id = 0
for a in range(len(array_params_a)):
for b in range(len(array_params_b)):
precision = float(TP[total_id])/float(TP[total_id]+FP[total_id]) if TP[total_id]+FP[total_id] > 0 else 0
recall = float(TP[total_id])/float(TP[total_id] + FN[total_id])
fscore = 2*(float(precision*recall)/float(precision+recall)) if precision > 0 else 0
accuracy = float(TP[total_id] + TN[total_id])/float(TP[total_id] + TN[total_id] + FP[total_id] + FN[total_id])
precision_list.append(precision)
recall_list.append(recall)
fscore_list.append(fscore)
accuracy_list.append(accuracy)
total_id += 1
precision_all = np.array(precision_list).reshape(len(array_params_a), len(array_params_b))
recall_all = np.array(recall_list).reshape(len(array_params_a), len(array_params_b))
accuracy_all = np.array(accuracy_list).reshape(len(array_params_a), len(array_params_b))
print("\nSummary: Precision, Recall, F1-Score, Accuracy for each alpha")
print(":::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::")
total_id = 0
for id_a, param_a in enumerate(array_params_a):
for id_b, param_b in enumerate(array_params_b):
print("For params = {:.4f} | {:.4f} - Precision: {:.4f} \tRecall: {:.4f} \tF1-Score: {:.4f} \tAccuracy: {:.4f}".format(param_a, param_b, precision_list[total_id], recall_list[total_id], fscore_list[total_id], accuracy_list[total_id]))
total_id += 1
print("AUC: {}".format(getAUC(recall_all[id_a], precision_all[id_a], reorder=True)))
print("------------------------------------------------------------")
print("Best F1-Score is {:.4f} with params = {:.4f} | {:.4f}".format(np.max(fscore_list),array_params_a[np.argmax(fscore_list)//len(array_params_b)], array_params_b[np.argmax(fscore_list)%len(array_params_b)]))
print("Worst F1-Score is {:.4f} with params = {:.4f} | {:.4f}".format(np.min(fscore_list), array_params_a[
np.argmin(fscore_list) // len(array_params_b)], array_params_b[np.argmin(fscore_list) % len(array_params_b)]))
print(":::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::")
return precision_all, recall_all, fscore_list, accuracy_all
"""
Return the value of the parameter given the index. Useful to depict the desire GIF o plot
"""
def findParams(data, index):
if index < len(data):
warnings.warn("index < len(data)")
return -1
else:
return data[index]
"""
Return the AUC (Area Under Curve)
"""
def getAUC(a,b, reorder=False):
return np.trapz(a, b)
# return auc(a, b, reorder=reorder)
def plot2D(x_axis, y_axis, x_label='', y_label='', legend_label=DATABASE):
plt.figure()
plt.plot(x_axis, y_axis, 'b', label=legend_label)
plt.legend(loc="lower right")
plt.xlabel(x_label)
plt.ylabel(y_label)
# plt.ylim([0, 1])
plt.savefig("plot2d_{}.png".format(datetime.now().strftime('%d%m%y_%H-%M-%S')), bbox_inches='tight', frameon=False)
plt.show()
def plotF1Score2D(x_axis, y_axis):
plt.figure()
plt.plot(x_axis, y_axis, 'b', label=DATABASE)
plt.legend(loc="lower right")
plt.xlabel("Alpha")
plt.ylabel("F1-score")
plt.axis([0, 1, 0, 1]) # [xmin, xmax, ymin, ymax]
plt.savefig("f1score2d_{}.png".format(datetime.now().strftime('%d%m%y_%H-%M-%S')), bbox_inches='tight', frameon=False)
# plt.show()
def plotF1Score3D(x_axis, y_axis, z_axis, x_label='', y_label='', z_label='', name=''):
name = "f1score3d_{}_{}.png".format(datetime.now().strftime('%d%m%y_%H-%M-%S'), DATABASE) if name == '' else name
if isinstance(x_axis, (list,)):
x_axis = np.array(x_axis)
if isinstance(y_axis, (list,)):
y_axis = np.array(y_axis)
if isinstance(z_axis, (list,)):
z_axis = np.array(z_axis)
X, Y = np.meshgrid(x_axis, y_axis, indexing='ij')
Z = z_axis.reshape(X.shape)
plt.figure()
ax = plt.axes(projection='3d')
surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap='viridis', edgecolor='none')
ax.contour3D(X, Y, Z, 50, cmap='viridis')
ax.set_xlabel(x_label)
ax.set_ylabel(y_label)
ax.set_zlabel(z_label)
plt.colorbar(surf)
plt.savefig(name, bbox_inches='tight', frameon=False)
plt.show()
def plotPrecisionRecall(recall_axis, precision_axis):
plt.figure()
plt.plot(recall_axis, precision_axis, 'r', label=DATABASE)
plt.legend(loc='upper right')
plt.title("Precision-Recall")
plt.xlabel("Recall")
plt.ylabel("Precision")
plt.ylim([0, 1])
# plt.xlim([0, 1])
plt.savefig("precision_recall_{}_{}_a.png".format(DATABASE, datetime.now().strftime('%d%m%y_%H-%M-%S')), bbox_inches='tight', frameon=False)
# plt.show()
plt.figure()
# plt.step(recall_axis, precision_axis, color='b', alpha=0.2, where='post')
# plt.fill_between(recall_axis, precision_axis, step='post', alpha=0.2, color='b')
plt.plot(recall_axis, precision_axis, '-.g')
plt.fill_between(recall_axis, precision_axis, alpha=0.2, color='g')
plt.xlabel("Recall")
plt.ylabel("Precision")
plt.ylim([ | np.min(precision_axis) | numpy.min |
"""
3D plots helpers
"""
import numpy as np
import matplotlib.pyplot as plt
def set_equal_axis(ax, xlims, ylims, zlims, scale=1.0, dim3=True):
"""Helper function to set equal axis
Args:
ax (Axes3DSubplot): matplotlib 3D axis, created by `ax = fig.add_subplot(projection='3d')`
xlims (list): 2-element list containing min and max value of x
ylims (list): 2-element list containing min and max value of y
zlims (list): 2-element list containing min and max value of z
scale (float): scaling factor along x,y,z
dim3 (bool): whether to also set z-limits (True for 3D plots)
"""
# compute max required range
max_range = np.array([max(xlims)-min(xlims), max(ylims)-min(ylims), max(zlims)-min(zlims)]).max() / 2.0
# compute mid-point along each axis
mid_x = (max(xlims) + min(xlims)) * 0.5
mid_y = (max(ylims) + min(ylims)) * 0.5
mid_z = (max(zlims) + min(zlims)) * 0.5
# set limits to axis
if dim3==True:
ax.set_box_aspect((max_range, max_range, max_range))
ax.set_xlim(mid_x - max_range*scale, mid_x + max_range*scale)
ax.set_ylim(mid_y - max_range*scale, mid_y + max_range*scale)
if dim3==True:
ax.set_zlim(mid_z - max_range*scale, mid_z + max_range*scale)
return
def get_sphere_coordinates(radius, center=None):
"""Get x,y,z coordinates for sphere
Args:
radius (float): sphere radius
center (list): x,y,z coordinates of center; if None, set to [0.0, 0.0, 0.0]
Returns:
(tuple): x, y, z coordinates of sphere
"""
# check if center is provided
if center is None:
center = [0.0, 0.0, 0.0]
# construct reference sphere
u, v = np.mgrid[0:2*np.pi:20j, 0:np.pi:10j]
#u, v = np.mgrid[0:2*np.pi:20j, 0:np.pi:10j]
x_sphere = center[0] + radius*np.cos(u)*np.sin(v)
y_sphere = center[1] + radius*np.sin(u)*np.sin(v)
z_sphere = center[2] + radius* | np.cos(v) | numpy.cos |
import os
import numpy as np
import torch
from torch.utils.data.dataloader import DataLoader
from torch.utils.data.sampler import SequentialSampler
from tqdm import tqdm
from LibVQ.dataset.dataset import DatasetForEncoding
from LibVQ.models import Encoder
def inference_dataset(encoder: Encoder,
dataset: DatasetForEncoding,
is_query: bool,
output_file: str,
batch_size: int,
enable_rewrite: bool = True,
dataparallel: bool = True,
return_vecs: bool = False,
save_to_memmap: bool = True):
if output_file is not None:
if os.path.exists(output_file) and not enable_rewrite:
print(f"{output_file} exists ! Please save to another path.")
return
output_memmap = None
if return_vecs or not save_to_memmap: vecs = []
dataloader = DataLoader(
dataset,
sampler=SequentialSampler(dataset),
batch_size=batch_size,
drop_last=False,
)
device = torch.device("cuda" if torch.cuda.is_available() else 'cpu')
encoder = encoder.to(device)
if dataparallel and torch.cuda.is_available():
encoder = torch.nn.DataParallel(encoder)
encoder.eval()
write_index = 0
for step, data in enumerate(tqdm(dataloader, total=len(dataloader))):
input_ids, attention_mask = data
input_ids = input_ids.to(device)
attention_mask = attention_mask.to(device)
with torch.no_grad():
batch_vecs = encoder(input_ids=input_ids, attention_mask=attention_mask,
is_query=is_query).detach().cpu().numpy()
if output_file is not None:
if save_to_memmap:
if output_memmap is None: output_memmap = np.memmap(output_file, dtype=np.float32, mode="w+",
shape=(len(dataset), | np.shape(batch_vecs) | numpy.shape |
from typing import Callable
from aoc21 import utils
import numpy as np
def gamma_and_epsilon(array: np.ndarray) -> tuple[int, int]:
"""Calculate gamma and epsilon for a submarine diagnostic report."""
if len(array) == 0:
raise ValueError("Empty array")
diff = np.sum(array == 1, axis=0) - np.sum(array == 0, axis=0)
g_bits = list(diff >= 0)
e_bits = list(diff < 0)
return bools_to_int(g_bits), bools_to_int(e_bits)
def bools_to_int(xs: list[bool]) -> int:
"""Convert a boolean list into the corresponding integer using base 2."""
return int("".join("1" if x else "0" for x in xs), base=2)
def o2_and_co2(array: np.ndarray) -> tuple[int, int]:
"""Calculate o2 and co2 ratings for a submarine diagnostic report."""
o2 = life_support(array, o2_criteria)
co2 = life_support(array, co2_criteria)
return o2, co2
def o2_criteria(column: np.ndarray) -> int:
"""The criteria for o2: the most common value in the column."""
return 1 if np.sum(column == 1) >= np.sum(column == 0) else 0
def co2_criteria(column: np.ndarray) -> int:
"""The criteria for co2: the least common value in the column."""
return 0 if np.sum(column == 0) <= | np.sum(column == 1) | numpy.sum |
import iris
import iris.plot as iplt
import iris.quickplot as qplt
import numpy as np
import matplotlib.pyplot as plt
import fnmatch
import os
import matplotlib.dates as mdates
import sys
reload(sys)
sys.getdefaultencoding()
import numpy.ma as ma
import cartopy.crs as ccrs
import matplotlib
from tools import rotate_data
def load_files(case):
if case == 'CS1':
os.chdir('/data/clivarm/wip/ellgil82/May_2016/Re-runs/CS1/') # path to data
filepath = '/data/clivarm/wip/ellgil82/May_2016/Re-runs/CS1/'
case_date = '20160507T1200Z'
elif case == 'CS2':
os.chdir('/data/clivarm/wip/ellgil82/May_2016/Re-runs/CS2/')
filepath = '/data/clivarm/wip/ellgil82/May_2016/Re-runs/CS2/'
case_date = '20160522T1200Z'
os.chdir(filepath)
surf = filepath+case_date+'_Peninsula_km4p0_ctrl_pa000.pp'
print ('importing cubes...')
T_air = iris.load_cube(surf, 'air_temperature')
T_surf = iris.load_cube(surf, 'surface_temperature')
lsm = iris.load_cube(surf, 'land_binary_mask')
orog = iris.load_cube(surf, 'surface_altitude')
P = iris.load_cube(surf, 'surface_air_pressure')
P.convert_units('hPa')
T_air.convert_units('celsius')
T_surf.convert_units('celsius')
## Iris v1.11 version
u_wind = iris.load_cube(surf, 'x_wind')
v_wind = iris.load_cube(surf, 'y_wind')
v_wind = v_wind[:,1:,:]
## Rotate projection
for var in [T_air, T_surf, u_wind, v_wind, P]:
real_lon, real_lat = rotate_data(var,1,2)
for var in [lsm, orog]:
real_lon, real_lat = rotate_data(var, 0, 1)
P_ma = np.ma.masked_where(lsm.data == 1, P[0,:,:].data) #orog.data > 0 &
return u_wind[0,:,:], v_wind[0,:,:], T_air[0,:,:], T_surf[0,:,:], P_ma, lsm, real_lat, real_lon, orog
u_wind, v_wind, T_air, T_surf, P, lsm, real_lat, real_lon, orog = load_files('CS1')
def shiftedColorMap(cmap, min_val, max_val, name, var):
epsilon = 0.001
start, stop = 0.00, 1.0 #0.15, 0.85
min_val, max_val = min(0.0, min_val), max(0.0, max_val)
midpoint = 1.0 - max_val / (max_val + abs(min_val))
cdict = {'red': [], 'green': [], 'blue': [], 'alpha': []}
# regular index to compute the colors
reg_index = np.linspace(start, stop, 257)
# shifted index to match the data
shift_index = np.hstack([np.linspace(0.0, midpoint, 128, endpoint=False), np.linspace(midpoint, 1.0, 129, endpoint=True)])
for ri, si in zip(reg_index, shift_index):
if abs(si - midpoint) < epsilon:
r, g, b, a = cmap(0.5) # 0.5 = original midpoint.
else:
r, g, b, a = cmap(ri)
cdict['red'].append((si, r, r))
cdict['green'].append((si, g, g))
cdict['blue'].append((si, b, b))
cdict['alpha'].append((si, a, a))
newcmap = matplotlib.colors.LinearSegmentedColormap(name, cdict)
plt.register_cmap(cmap=newcmap)
return newcmap
## Caption:
def plot_synop():
fig = plt.figure(figsize=(10, 12))
ax = fig.add_axes([0.18, 0.25, 0.75, 0.63], frameon=False)#, projection=ccrs.PlateCarree())#
ax.tick_params(which='both', axis='both', labelsize=34, labelcolor='dimgrey', pad=10, size=0, tick1On=False, tick2On=False)
PlotLonMin = np.min(real_lon)
PlotLonMax = np.max(real_lon)
PlotLatMin = np.min(real_lat)
PlotLatMax = np.max(real_lat)
XTicks = np.linspace(PlotLonMin, PlotLonMax, 3)
XTickLabels = [None] * len(XTicks)
for i, XTick in enumerate(XTicks):
if XTick < 0:
XTickLabels[i] = '{:.0f}{:s}'.format(np.abs(XTick), '$^{\circ}$W')
else:
XTickLabels[i] = '{:.0f}{:s}'.format( | np.abs(XTick) | numpy.abs |
import preprocessor
import sys
import numpy as np
from multiprocessing import Pool
from random import shuffle
def process_all(filenames):
with Pool() as p:
res_temp = p.map(process_file, filenames)
res = | np.concatenate(res_temp) | numpy.concatenate |
"""
Implements the Azran-Ghahramani clustering algorithm outlined in the
paper "A New Approach to Data Driven Clustering", which we refer to as
"the paper".
"""
import itertools
import numpy as np
import random
from regimedetection.src.metrics import kl_divergence
from typing import Any
from typing import Callable
from typing import List
from typing import Optional
from typing import Tuple
def get_space_distances(points: np.ndarray, metric: Callable[[Any, Any], np.float]) -> np.ndarray:
"""
Compute all non-trivial distances between all points in a metric
space. I.e. all distances except those of the form d(x,x) which is 0
by definition
Args:
points: array of points in the metric space. These can be of any type
as long as the metric is suitably defined to expect this type
metric: a distance function between points in the space. Expected to
take two points of the same type as in the points array and return
a float
Returns:
A one-dimensional array of all distances between all non-trivial
combinations of points in the array. Order of the distances is
inherited from the order returned by itertools.combinations(points, 2),
i.e. of the form [(x1, x2), (x1, x3), ..., (x2, x3), ...]
Length of the returned array is n(n-1)/2 where n = len(points)
"""
return np.fromiter(
(metric(*comb) for comb in itertools.combinations(points, 2)),
dtype=np.float,
count=len(points) * (len(points) - 1) // 2,
)
def get_space_similarities(
points: np.ndarray,
metric: Callable[[Any, Any], np.float],
similarity: Callable[[np.float], np.float],
) -> np.ndarray:
"""
Compute all similarities between all points in a metric space apart
from the self-similarities
This function provides access to a the array of similarities without
needing to compute the distances array in memory if not separately required
or already computed
Args:
points: array of points in the metric space. These can be of any type
as long as the metric is suitably defined to expect this type
metric: a distance function between points in the space. Expected to
take two points of the same type as in the points array and return
a float
similarity: a unary function from np.float to np.float. Expected to be
a monotonically decreasing function such that larger distances
correspond to smaller similarities
Returns:
A one-dimensional array of all similarities between all non-trivial
combinations of points in the array. Order of the distances is inherited
from the order returned by itertools.combinations(points, 2), i.e. of the
form [(x1, x2), (x1, x3), ..., (x2, x3), ...].
Length of the returned array is n(n-1)/2 where n = len(points)
"""
return np.fromiter(
(similarity(metric(*comb)) for comb in itertools.combinations(points, 2)),
dtype=np.float,
count=len(points) * (len(points) - 1) // 2,
)
def get_similarities_matrix(
points: np.ndarray,
metric: Callable[[Any, Any], np.float],
similarity: Callable[[np.float], np.float],
distances: Optional[np.ndarray] = None,
self_similarity_multiplier: Optional[float] = 0.1,
) -> np.array:
"""
Compute the matrix of similarities between points in a metric space.
Args:
points: array of points in the metric space. These can be of any type
as long as the metric is suitably defined to expect this type
metric: a distance function between points in the space. Expected to
take two points of the same type as in the points array and return
a float
similarity: a unary function from np.float to np.float. Expected to be
a monotonically decreasing function such that larger distances
correspond to smaller similarities
distances: allows the specification of the distances between
points in the space. Expected to be a np.ndarray of length n(n-1)/2
where n = len(points), the form returned by get_space_distances
self_similarity_multiplier: the similarity of a particle with itself is
set to self_similarity_multplier * min(similarities). Smaller values
encourage exploration away from self.
Returns:
2-dimensional np.ndarray which has (i,j)-entry equal to the similarity
of the distance between point i and point j.
"""
if distances is None:
similarities = get_space_similarities(points, metric, similarity)
else:
similarities = np.vectorize(similarity)(distances)
# the similarity of a particle with itself is set to a multiple of
# the smallest similarity observed, specified by self_similarity_multiplier
self_similarity = min(similarities) * self_similarity_multiplier
similarities_matrix = np.zeros(shape=(len(points), len(points)))
upper_indices = np.triu_indices(len(points), 1)
diag_indices = np.diag_indices(len(points))
similarities_matrix[upper_indices] = similarities
similarities_matrix += similarities_matrix.T
similarities_matrix[diag_indices] = self_similarity
# W is assumed to be full rank
if np.linalg.matrix_rank(similarities_matrix) != len(points):
print("WARN: Similarities matrix is not full rank")
return similarities_matrix
def get_transition_matrix_from_similarities_matrix(
similarities_matrix: np.array,
) -> np.array:
"""
Compute a transition matrix from a matrix of similarities.
Divide each row of the similarities matrix by the row sum to give
a transition matrix with each row representing a probability
distribution.
Implements equation (2) of the paper.
Args:
similarities_matrix: a 2-dimensional np.ndarray which has (i,j)-entry
equal to the similarity of the distance between point i and point j.
Of the form returned by get_similarities_matrix
Returns:
A 2-dimensional np.ndarray which has (i,j)-entry equal to the
transition probability from point X_i to X_j
"""
row_sums = similarities_matrix.sum(axis=1)
transition_matrix = similarities_matrix / row_sums[:, np.newaxis]
return transition_matrix
def k_prototypes(transition_matrix: np.array, prototypes_init: np.array):
"""
Finds the K-clustering of the points evolving under the specified
transition matrix, with initial prototypes prototypes_init. K is
inferred from the length of the prototypes_init parameter
Args:
transition_matrix: a 2-dimensional np.ndarray which has (i,j)-entry
equal to the probability of transitioning from particle X_i to
particle X_j in the next time step
prototypes_init: a list of lists. The ith list is the indexes of
points which begin in partition i
Returns:
A list of lists representing the converged partition. The ith
element contains indices of the points which belong to the ith
partition
Implements Algorithm 1 of the paper
"""
n_points = len(transition_matrix)
n_clusters = len(prototypes_init)
prototypes = prototypes_init
previous_partition = list()
while True:
partition = [[] for _ in range(n_clusters)]
# Compute KL-divergence from each row to each cluster centre
divergences = kl_divergence(
np.repeat(transition_matrix, len(prototypes), axis=0),
np.tile(prototypes, reps=(len(transition_matrix), 1)),
)
divergences = np.split(divergences, len(transition_matrix))
closest_clusters = np.argmin(divergences, axis=1)
new_prototypes = np.empty((n_clusters, n_points))
for k in range(n_clusters):
partition[k] = list(np.where(closest_clusters == k)[0])
if partition[k]:
new_prototypes[k] = | np.average(transition_matrix[partition[k]], axis=0) | numpy.average |
import os
import sys
from openbabel import openbabel as ob
from openbabel import pybel as pb
import gen3D
import numpy as np
from statistics import mean
import props
ELEMENT_TABLE = props.ElementData()
class FILTER(object):
def __init__(self, reactant_file, cluster_bond_file = None, fixed_atoms = None):
self.reactant_file = reactant_file
self.cluster_bond_file = cluster_bond_file
self.fixed_atoms = fixed_atoms
if self.fixed_atoms:
with open(self.fixed_atoms, 'r') as f:
lines = f.read()
self.fixed_atoms = eval(lines)
def initialization(self):
mol = next(pb.readfile('xyz', self.reactant_file))
if self.cluster_bond_file:
m = pb.ob.OBMol()
m.BeginModify()
for atom in mol:
coords = [coord for coord in atom.coords]
atomno = atom.atomicnum
obatom = ob.OBAtom()
obatom.thisown = 0
obatom.SetAtomicNum(atomno)
obatom.SetVector(*coords)
m.AddAtom(obatom)
del obatom
with open(self.cluster_bond_file, 'r') as f:
lines = f.read()
cluster_bond = eval(lines)
bonds = [(bond.GetBeginAtomIdx(), bond.GetEndAtomIdx(), bond.GetBondOrder())
for bond in pb.ob.OBMolBondIter(mol.OBMol)]
bonds.extend(cluster_bond)
for bond in bonds:
m.AddBond(bond[0], bond[1], bond[2])
# m.ConnectTheDots()
m.PerceiveBondOrders()
# m.SetTotalSpinMultiplicity(1)
m.SetTotalCharge(int(mol.charge))
m.Center()
m.EndModify()
self.mol = gen3D.Molecule(m)
else:
self.mol = gen3D.Molecule(mol.OBMol)
self.atoms = tuple(atom.atomicnum for atom in self.mol)
for frag in self.mol.write('can').split()[0].split('.'):
if '[OH]' in frag and 'Sn' not in frag:
return 'job_fail', 'non-bonded OH group'
return 'pass', 'pass'
def check_feasible_rxn(self, check_mm_overlap = True, qmmm = None, qm_atoms = 23, threshold_ratio = 0.6):
status, msg = self.initialization()
if status == 'job_fail':
return 'job_fail', msg
if check_mm_overlap:
status, msg = self.check_overlap_mm_region_v2(qmmm = qmmm, qm_atoms = qm_atoms, threshold_ratio = threshold_ratio)
else:
status = True
if status:
status, msg = self.check_reactant_bonds()
if status:
status, msg = self.check_unreasonable_connection()
if status:
return 'job_success', msg
else:
return 'job_fail', msg
else:
return 'job_fail', msg
else:
return 'job_fail', msg
def check_reactant_bonds(self):
# extract reactant bonds
reactant_bonds = [tuple(sorted((bond.GetBeginAtomIdx() - 1, bond.GetEndAtomIdx() - 1)) + [bond.GetBondOrder()])
for bond in pb.ob.OBMolBondIter(self.mol.OBMol)]
self.reactant_bonds = tuple(sorted(reactant_bonds))
# check the bond order and save in a dict
bond_type = {}
for i in range(len(self.atoms)):
num = 0
for j in reactant_bonds:
if j[0] == i or j[1] == i:
num += j[2]
bond_type[i] = num
if 0 in bond_type.values(): # The dissociated atom
return False, 'Have dissociated atom.'
else:
for idx, i in enumerate(self.atoms):
# use != or > need test
if i == 6 and idx not in self.fixed_atoms:
if bond_type[idx] < 3 or bond_type[idx] > 4: # remove only C=O
return False, 'reactant carbon bond type is invalid.({})'.format(bond_type[idx])
# use != or > need test
elif i == 8 and bond_type[idx] > 2 and idx not in self.fixed_atoms: # Here we can't use !=2 because some time reactant O don't detect bind on Sn
return False, 'reactant oxygen bond type is invalid.({})'.format(bond_type[idx])
# use != or > need test
elif i == 14 and bond_type[idx] != 4 and idx not in self.fixed_atoms:
return False, 'reactant silicon bond type is invalid.({})'.format(bond_type[idx])
# While the bronsted acid already have proton on the active site, then aborted.
elif i == 8 and bond_type[idx] > 3:
return False, 'oxygen have more than 4 connection.({})'.format(bond_type[idx])
return True, 'bond type check is pass.'
def check_unreasonable_connection(self):
# Use generator is more efficient
reactant_carbon = [idx for idx, reactant_atoms in enumerate(self.atoms) if idx not in self.fixed_atoms and reactant_atoms == 6]
reactant_oxygen = [idx for idx, reactant_atoms in enumerate(self.atoms) if idx not in self.fixed_atoms and reactant_atoms == 8]
active_site_oxygen = [active_site_atom for active_site_atom in self.fixed_atoms if self.atoms[active_site_atom] == 8]
active_site_silicon = [active_site_atom for active_site_atom in self.fixed_atoms if self.atoms[active_site_atom] == 14]
active_site_metal = [active_site_atom for active_site_atom in self.fixed_atoms if self.atoms[active_site_atom] in [42, 50, 74]]
hcap = [active_site_atom for active_site_atom in self.fixed_atoms if self.atoms[active_site_atom] == 1]
for bond in self.reactant_bonds:
if (bond[0] in reactant_oxygen and bond[1] in active_site_silicon) or (bond[1] in reactant_oxygen and bond[0] in active_site_silicon):
return False, 'reactant oxygen have connection with active site silicon.'
elif (bond[0] not in self.fixed_atoms and bond[1] in hcap) or (bond[1] not in self.fixed_atoms and bond[0] in hcap):
return False, 'reactant have connection with hcap.'
elif (bond[0] in reactant_carbon and bond[1] in active_site_oxygen) or (bond[1] in reactant_carbon and bond[0] in active_site_oxygen):
return False, 'reactant carbon have connection with active site oxygen.'
elif (bond[0] in reactant_oxygen and bond[1] in active_site_oxygen) or (bond[1] in reactant_oxygen and bond[0] in active_site_oxygen):
return False, 'reactant oxygen have connection with active site oxygen.'
return True, 'check_unreasonable_connection is pass.'
def check_overlap_mm_region(self, qm_silicon = [], threshold = 5.4):
# mm silicon index start from 0
# Choose the silicon in cluster model which is in mm region
self.mol.gen3D(self.fixed_atoms, make3D=False)
if len(self.mol.mols) == 1:
return True, 'pass'
else:
nodes_1 = [mol.toNode() for mol in self.mol.mols]
fd1 = [node.getCentroid() for node in nodes_1]
tmps, dist2 = [], []
for idx, i in enumerate(self.mol.mols):
if all(idx2 not in self.fixed_atoms for idx2 in i.mols_indices[idx]):
if any(self.atoms[idx2] == 6 or self.atoms[idx2] == 8 for idx2 in i.mols_indices[idx]):
tmps.append(idx)
for tmp in tmps:
for qm_si in qm_silicon:
diff2 = self.mol[qm_si].coords - fd1[tmp]
dist2.append(np.linalg.norm(diff2))
# print(max(dist2))
# print(mean(dist2))
if max(dist2) > 6.5 and mean(dist2) > 5.4:
# print(max(dist2))
# print(mean(dist2))
return False, 'Overlap with the mm region'
else:
return True, 'pass'
def check_overlap_mm_region_v2(self, qmmm = None, qm_atoms = 23, threshold_ratio = 0.6):
"""
The distance between qm atoms and mm atoms should greater than 0.6 vdw radius.
"""
dist2 = []
for idx1, qm_atom in enumerate(self.mol):
if idx1 >= qm_atoms:
continue
for idx2, mm_atom in enumerate(qmmm):
if idx2 < qm_atoms:
continue
diff2 = np.array(qm_atom.coords) - | np.array(mm_atom.coords) | numpy.array |
import numpy as np
import pandas as pd
import pytest
from scipy import stats
from locan import LocData
from locan.analysis import BlinkStatistics
from locan.analysis.blinking import _blink_statistics, _DistributionFits
def test__blink_statistics_0():
# frame with on and off periods up to three frames and starting with one-frame on-period.
frames = np.array([0, 4, 6, 7, 8, 12, 13])
results = _blink_statistics(frames, memory=0, remove_heading_off_periods=False)
assert len(results["on_periods"]) == len(results["on_periods_frame"])
assert len(results["off_periods"]) == len(results["off_periods_frame"])
assert np.array_equal(results["on_periods"], [1, 1, 3, 2])
assert np.array_equal(results["off_periods"], [3, 1, 3])
assert | np.array_equal(results["on_periods_frame"], [0, 4, 6, 12]) | numpy.array_equal |
# ============================================================================
# 输入格式为已经过提取的光流或rgb的.npy文件
# i3d网络，rgb和光流分别计算，再进行模型融合
# 预加载模型为imagenet_pretrained和rgb_imagenet，
# 未添加数据增强
# ============================================================================
# -*- coding: utf-8 -*-
"""Loads a sample video and classifies using a trained Kinetics checkpoint."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
import tensorflow as tf
import i3d
import sonnet as snt
import time
from math import isnan
from tensorflow.python import debug as tf_debug
import os
import logging
from sklearn.metrics import accuracy_score, precision_score, recall_score, f1_score
import cv2
_IMAGE_SIZE = 224
frameHeight = 224#480
frameWidth = 224#640
dropout_keep_prob = 0.8
batch_size = 16 #8
epoch = 200
_LEARNING_RATE = 0.01
videolabel_dict = {}
flag = False
_NUM_PARALLEL_CALLS = 10
_PREFETCH_BUFFER_SIZE = 30
_MOMENTUM = 0.9
rgb_or_flow = 'flow'
_SAVER_MAX_TO_KEEP = 3
_SAMPLE_VIDEO_FRAMES = 15
_SAMPLE_PATHS = {
'rgb': '/data2/ye/data/rgb',
'flow': '/data2/ye/data/flow',
}
_CHECKPOINT_PATHS = {
'rgb': 'data/checkpoints/rgb_scratch/model.ckpt',
'rgb600': 'data/checkpoints/rgb_scratch_kin600/model.ckpt',
'flow': 'data/checkpoints/flow_scratch/model.ckpt',
'rgb_imagenet': 'data/checkpoints/rgb_imagenet/model.ckpt',
'flow_imagenet': 'data/checkpoints/flow_imagenet/model.ckpt',
}
_LABEL_MAP_PATH = 'preprocess/label_kugou.txt'
_LABEL_MAP_PATH_600 = 'data/label_map_600.txt'
train_path = 'preprocess/video_9k_train_list_v2.txt'
test_path = 'preprocess/video_9k_test_list_v2.txt'
log_dir = 'preprocess/log-joint/'
FLAGS = tf.flags.FLAGS
tf.flags.DEFINE_string('eval_type', rgb_or_flow, 'rgb, rgb600, flow, or joint') #'joint'
tf.flags.DEFINE_boolean('imagenet_pretrained', True, '')
_CHANNEL = {
'rgb': 3,
'flow': 2,
}
_SCOPE = {
'rgb': 'RGB',
'flow': 'Flow',
}
_CLASS_NUM = {
'ucf101': 101,
'hmdb51': 51,
'kugou': 15
}
def main(unused_argv):
# def main(dataset='kugou'):
tf.logging.set_verbosity(tf.logging.INFO)
eval_type = FLAGS.eval_type
imagenet_pretrained = FLAGS.imagenet_pretrained
NUM_CLASSES = 15 #400
if eval_type == 'rgb600':
NUM_CLASSES = 600
if eval_type not in ['rgb', 'rgb600', 'flow', 'joint']:
raise ValueError('Bad `eval_type`, must be one of rgb, rgb600, flow, joint')
if eval_type == 'rgb600':
f1 = open(_LABEL_MAP_PATH_600)
kinetics_classes = [x.strip() for x in f1]
f1.close()
else:
f2 = open(_LABEL_MAP_PATH, 'r', encoding='utf8')
kinetics_classes = [x.strip().split(' ')[0] for x in f2 if x.strip() != '']
f2.close()
logging.basicConfig(level=logging.INFO, filename=os.path.join(log_dir, 'log.txt'),
filemode='a', format='%(message)s')
trainpathlist = split_data(train_path)
testpathlist = split_data(test_path)
print(len(trainpathlist))
print(len(testpathlist))
train_info_tensor = tf.constant(trainpathlist)
test_info_tensor = tf.constant(testpathlist)
train_info_dataset = tf.data.Dataset.from_tensor_slices(train_info_tensor).shuffle(len(trainpathlist))
train_dataset = train_info_dataset.map(lambda x: _get_data_label_from_info(x,eval_type), num_parallel_calls=_NUM_PARALLEL_CALLS)
train_dataset = train_dataset.repeat().batch(batch_size)
train_dataset = train_dataset.prefetch(buffer_size=_PREFETCH_BUFFER_SIZE)
# Phase 2 Testing
# one element in this dataset is (train_info list)
test_info_dataset = tf.data.Dataset.from_tensor_slices(test_info_tensor).shuffle(len(testpathlist))
# one element in this dataset is (single image_postprocess, single label)
test_dataset = test_info_dataset.map(lambda x: _get_data_label_from_info(
x, eval_type), num_parallel_calls=_NUM_PARALLEL_CALLS)
# one element in this dataset is (batch image_postprocess, batch label)
test_dataset = test_dataset.batch(batch_size).repeat()#1
test_dataset = test_dataset.prefetch(buffer_size=_PREFETCH_BUFFER_SIZE)
iterator = tf.data.Iterator.from_structure(
train_dataset.output_types, train_dataset.output_shapes)
train_init_op = iterator.make_initializer(train_dataset)
test_init_op = iterator.make_initializer(test_dataset)
clip_holder, label_holder = iterator.get_next()
clip_holder = tf.squeeze(clip_holder, [1])
# label_holder = tf.squeeze(label_holder, [1])
clip_holder.set_shape(
[None, _SAMPLE_VIDEO_FRAMES, _IMAGE_SIZE, _IMAGE_SIZE, _CHANNEL[eval_type]])
dropout_holder = tf.placeholder(tf.float32)
is_train_holder = tf.placeholder(tf.bool)
if eval_type in ['rgb', 'rgb600', 'joint']:
# RGB input has 3 channels.
with tf.variable_scope('RGB'):
rgb_model = i3d.InceptionI3d(
NUM_CLASSES, spatial_squeeze=True, final_endpoint= 'Mixed_5c') #'Logits'
rgb_logits, _ = rgb_model(
clip_holder, is_training= True, dropout_keep_prob=dropout_holder) #is_train_holder
with tf.variable_scope('Logits_ye_rgb'):
netrgb = tf.nn.avg_pool3d(rgb_logits, ksize=[1, 2, 7, 7, 1],
strides=[1, 1, 1, 1, 1], padding=snt.VALID)
netrgb = tf.nn.dropout(netrgb, dropout_keep_prob)
logits = i3d.Unit3D(output_channels=NUM_CLASSES,
kernel_shape=[1, 1, 1],
activation_fn=None, # tf.nn.relu,#
use_batch_norm=False, # ,True
use_bias=True,
name='Conv3d_0c_1x1_ye_rgb')(netrgb, is_training=is_train_holder) # True
rgb_logits = tf.squeeze(logits, [2, 3], name='SpatialSqueeze')
rgb_logits = tf.reduce_mean(rgb_logits, axis=1)
rgb_variable_map = [v for v in tf.global_variables() if 'Logits_ye_rgb' not in v.name]
rgb_saver = tf.train.Saver(var_list=rgb_variable_map, reshape=True)
if eval_type in ['flow', 'joint']:
# Flow input has only 2 channels.
with tf.variable_scope('Flow'):#Flow
flow_model = i3d.InceptionI3d(
NUM_CLASSES, spatial_squeeze=True, final_endpoint= 'Mixed_5c')
flow_logits, _ = flow_model(
clip_holder, is_training=True, dropout_keep_prob=dropout_holder)#is_train_holder
with tf.variable_scope('Logits_ye'):
netflow = tf.nn.avg_pool3d(flow_logits, ksize=[1, 2, 7, 7, 1],
strides=[1, 1, 1, 1, 1], padding=snt.VALID)
netflow = tf.nn.dropout(netflow, dropout_keep_prob)
logits = i3d.Unit3D(output_channels=NUM_CLASSES,
kernel_shape=[1, 1, 1],
activation_fn= None,#tf.nn.relu,#
use_batch_norm= False,#,True
use_bias=True,
name='Conv3d_0c_1x1_ye')(netflow, is_training=is_train_holder) # True
flow_logits = tf.squeeze(logits, [2, 3], name='SpatialSqueeze')
flow_logits = tf.reduce_mean(flow_logits, axis=1)
flow_variable_map = [v for v in tf.global_variables() if 'Logits_ye' not in v.name]
flow_saver = tf.train.Saver(var_list=flow_variable_map, reshape=True)
if eval_type == 'rgb':
fc_out = rgb_logits
elif eval_type == 'flow':
fc_out = flow_logits
else:
fc_out = rgb_logits + flow_logits
model_predictions = tf.nn.softmax(fc_out)
is_in_top_1_op = tf.nn.in_top_k(fc_out, label_holder, 1)
varlist = [i for i in tf.trainable_variables()]
# varlist1 = [i for i in tf.global_variables() if ('Conv3d_0c_1x1' in i.name)]#Conv3d_0c_1x1 Logits_ye
cost = tf.reduce_mean(tf.nn.sparse_softmax_cross_entropy_with_logits(logits= fc_out, labels=label_holder)) #+ 7e-7*tf.nn.l2_loss(varlist1[0])
global_step = tf.Variable(0, trainable=False)
# learning_rate = tf.train.exponential_decay(0.001, global_step, 100, 0.95, staircase= True) #100000
# Set learning rate schedule by hand, also you can use an auto way
boundaries = [20000, 30000, 50000] #[10000, 20000, 30000, 40000, 50000]
values = [_LEARNING_RATE, 0.005, 0.001, 0.0001]#0.0008, 0.0005, 0.0003, 0.0001, 5e-5]
learning_rate = tf.train.piecewise_constant(
global_step, boundaries, values)
# learning_rate = 0.1
update_ops = tf.get_collection(tf.GraphKeys.UPDATE_OPS)
with tf.control_dependencies(update_ops):
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate, epsilon=1e-08).minimize(cost, var_list=varlist, global_step=global_step)#
# optimizer = tf.train.MomentumOptimizer(learning_rate,
# _MOMENTUM).minimize(cost, var_list=varlist, global_step=global_step)
# max_gradient_norm = 5
init = tf.global_variables_initializer()
saver2 = tf.train.Saver(max_to_keep=_SAVER_MAX_TO_KEEP)
with tf.Session() as sess:
sess.run(init)
sess.run(train_init_op)
# sess = tf_debug.LocalCLIDebugWrapperSession(sess)
# sess.add_tensor_filter("has_inf_or_nan", tf_debug.has_inf_or_nan)
# print(sess.run(variable1))
if eval_type in ['rgb', 'rgb600', 'joint']:
if imagenet_pretrained:
rgb_saver.restore(sess, _CHECKPOINT_PATHS['rgb_imagenet'])
else:
rgb_saver.restore(sess, _CHECKPOINT_PATHS[eval_type])
tf.logging.info('RGB checkpoint restored')
if eval_type in ['flow', 'joint']:
if imagenet_pretrained:
flow_saver.restore(sess, _CHECKPOINT_PATHS['flow_imagenet'])
else:
flow_saver.restore(sess, _CHECKPOINT_PATHS['flow'])
tf.logging.info('Flow checkpoint restored')
batch_num = (int)(np.ceil(len(trainpathlist) / batch_size))
step = 0
count = 0
tmp_count = 0
true_count = 0
accuracy_tmp = 0
logging.info(train_path)
time1 = time.time()
while step < epoch * batch_num:
time2 = time.time()
step += 1
_, out_logits, out_predictions, cost1, is_in_top_1, input, label, learning_rate_c \
= sess.run([optimizer,fc_out, model_predictions,cost, is_in_top_1_op, clip_holder, label_holder, learning_rate],
feed_dict={dropout_holder: dropout_keep_prob, is_train_holder: True})#False
tmp = np.sum(is_in_top_1)
tmp_count = tmp
true_count += tmp
accuracy = tmp_count /batch_size
duration = time.time() - time2
# for i in range(input.shape[0]):
# for j in np.arange(0,input.shape[1],5):
# cv2.imshow('label_'+ str(label[i])+"frame_"+ str(j), input[i][j])
# cv2.waitKey(0)
print("(%.2f sec/batch) epoch:%d, step:%d/%d, learning_rate:%f, loss: %-.4f, accuracy: %.3f "
% (duration, count, step % batch_num, batch_num-1,learning_rate_c, cost1, accuracy))
logging.info("(%.2f sec/batch) epoch:%d, step:%d/%d, learning_rate:%f, loss: %-.4f, accuracy: %.3f "
% (duration, count, step % batch_num, batch_num-1,learning_rate_c, cost1, accuracy))
if step % batch_num == 0:
accuracy = true_count / (batch_num * batch_size)
print('Epoch%d, train accuracy: %.3f' %
(count, accuracy))
logging.info('Epoch%d, train accuracy: %.3f' %
(count, accuracy))
true_count = 0
test_count = 0
test_output = []
test_label = []
step_test = 0
if accuracy > 0.1:
sess.run(test_init_op) # new iterator
test_batch_num = int(np.ceil(len(testpathlist)/batch_size))#最后一个batch的数目不满一个batch_size
while step_test < test_batch_num:
step_test += 1
test_predictions, is_in_top_1, input, label \
= sess.run([model_predictions,is_in_top_1_op, clip_holder, label_holder],
feed_dict={dropout_holder: 1, is_train_holder: False}) # False
test_label.extend(label)
test_output.extend(np.argmax(test_predictions, axis=1))
tmp = | np.sum(is_in_top_1) | numpy.sum |
#!/usr/bin/env python
# vim: set fileencoding=utf-8 :
# <NAME> <<EMAIL>>
#
# Copyright (C) 2011-2014 Idiap Research Institute, Martigny, Switzerland
"""Tests the I-Vector trainer
"""
import numpy
import numpy.linalg
import numpy.random
import nose.tools
from bob.learn.em import GMMMachine, GMMStats, IVectorMachine, IVectorTrainer
import bob.learn.em
### Test class inspired by an implementation of Chris McCool
### <NAME> (<EMAIL>)
class IVectorTrainerPy():
"""An IVector extractor"""
def __init__(self, convergence_threshold=0.001, max_iterations=10,
compute_likelihood=False, sigma_update=False, variance_floor=1e-5):
self.m_convergence_threshold = convergence_threshold
self.m_max_iterations = max_iterations
self.m_compute_likelihood = compute_likelihood
self.m_sigma_update = sigma_update
self.m_variance_floor = variance_floor
def initialize(self, machine, data):
ubm = machine.ubm
self.m_dim_c = ubm.shape[0]
self.m_dim_d = ubm.shape[1]
self.m_dim_t = machine.t.shape[1]
self.m_meansupervector = ubm.mean_supervector
t = numpy.random.randn(self.m_dim_c*self.m_dim_d, self.m_dim_t)
machine.t = t
machine.sigma = machine.ubm.variance_supervector
def e_step(self, machine, data):
n_samples = len(data)
self.m_acc_Nij_Sigma_wij2 = {}
self.m_acc_Fnorm_Sigma_wij = {}
self.m_acc_Snorm = numpy.zeros(shape=(self.m_dim_c*self.m_dim_d,), dtype=numpy.float64)
self.m_N = numpy.zeros(shape=(self.m_dim_c,), dtype=numpy.float64)
for c in range(self.m_dim_c):
self.m_acc_Nij_Sigma_wij2[c] = numpy.zeros(shape=(self.m_dim_t,self.m_dim_t), dtype=numpy.float64)
self.m_acc_Fnorm_Sigma_wij[c] = numpy.zeros(shape=(self.m_dim_d,self.m_dim_t), dtype=numpy.float64)
for n in range(n_samples):
Nij = data[n].n
Fij = data[n].sum_px
Sij = data[n].sum_pxx
# Estimate latent variables
TtSigmaInv_Fnorm = machine.__compute_TtSigmaInvFnorm__(data[n])
I_TtSigmaInvNT = machine.__compute_Id_TtSigmaInvT__(data[n])
Fnorm = numpy.zeros(shape=(self.m_dim_c*self.m_dim_d,), dtype=numpy.float64)
Snorm = numpy.zeros(shape=(self.m_dim_c*self.m_dim_d,), dtype=numpy.float64)
# Compute normalized statistics
for c in range(self.m_dim_c):
start = c*self.m_dim_d
end = (c+1)*self.m_dim_d
Fc = Fij[c,:]
Sc = Sij[c,:]
mc = self.m_meansupervector[start:end]
Fc_mc = Fc * mc
Nc_mc_mcT = Nij[c] * mc * mc
Fnorm[start:end] = Fc - Nij[c] * mc
Snorm[start:end] = Sc - (2 * Fc_mc) + Nc_mc_mcT
# Latent variables
I_TtSigmaInvNT_inv = numpy.linalg.inv(I_TtSigmaInvNT)
E_w_ij = numpy.dot(I_TtSigmaInvNT_inv, TtSigmaInv_Fnorm)
E_w_ij2 = I_TtSigmaInvNT_inv + numpy.outer(E_w_ij, E_w_ij)
# Do the accumulation for each component
self.m_acc_Snorm = self.m_acc_Snorm + Snorm # (dim_c*dim_d)
for c in range(self.m_dim_c):
start = c*self.m_dim_d
end = (c+1)*self.m_dim_d
current_Fnorm = Fnorm[start:end] # (dim_d)
self.m_acc_Nij_Sigma_wij2[c] = self.m_acc_Nij_Sigma_wij2[c] + Nij[c] * E_w_ij2 # (dim_t, dim_t)
self.m_acc_Fnorm_Sigma_wij[c] = self.m_acc_Fnorm_Sigma_wij[c] + numpy.outer(current_Fnorm, E_w_ij) # (dim_d, dim_t)
self.m_N[c] = self.m_N[c] + Nij[c]
def m_step(self, machine, data):
A = self.m_acc_Nij_Sigma_wij2
T = numpy.zeros(shape=(self.m_dim_c*self.m_dim_d,self.m_dim_t), dtype=numpy.float64)
Told = machine.t
if self.m_sigma_update:
sigma = numpy.zeros(shape=self.m_acc_Snorm.shape, dtype=numpy.float64)
for c in range(self.m_dim_c):
start = c*self.m_dim_d;
end = (c+1)*self.m_dim_d;
# T update
A = self.m_acc_Nij_Sigma_wij2[c].transpose()
B = self.m_acc_Fnorm_Sigma_wij[c].transpose()
if numpy.array_equal(A, numpy.zeros(A.shape)):
X = numpy.zeros(shape=(self.m_dim_t,self.m_dim_d), dtype=numpy.float64)
else:
X = numpy.linalg.solve(A, B)
T[start:end,:] = X.transpose()
# Sigma update
if self.m_sigma_update:
Told_c = Told[start:end,:].transpose()
# warning: Use of the new T estimate! (revert second next line if you don't want that)
Fnorm_Ewij_Tt = numpy.diag(numpy.dot(self.m_acc_Fnorm_Sigma_wij[c], X))
#Fnorm_Ewij_Tt = numpy.diag(numpy.dot(self.m_acc_Fnorm_Sigma_wij[c], Told_c))
sigma[start:end] = (self.m_acc_Snorm[start:end] - Fnorm_Ewij_Tt) / self.m_N[c]
machine.t = T
if self.m_sigma_update:
sigma[sigma < self.m_variance_floor] = self.m_variance_floor
machine.sigma = sigma
def finalize(self, machine, data):
pass
def train(self, machine, data):
self.initialize(machine, data)
average_output_previous = -sys.maxsize
average_output = -sys.maxsize
self.e_step(machine, data)
i = 0
while True:
average_output_previous = average_output
self.m_step(machine, data)
self.e_step(machine, data)
if(self.m_max_iterations > 0 and i+1 >= self.m_max_iterations):
break
i += 1
def test_trainer_nosigma():
# Ubm
ubm = GMMMachine(2,3)
ubm.weights = numpy.array([0.4,0.6])
ubm.means = numpy.array([[1.,7,4],[4,5,3]])
ubm.variances = numpy.array([[0.5,1.,1.5],[1.,1.5,2.]])
# Defines GMMStats
gs1 = GMMStats(2,3)
log_likelihood1 = -3.
T1 = 1
n1 = numpy.array([0.4, 0.6], numpy.float64)
sumpx1 = numpy.array([[1., 2., 3.], [2., 4., 3.]], numpy.float64)
sumpxx1 = | numpy.array([[10., 20., 30.], [40., 50., 60.]], numpy.float64) | numpy.array |
from controller import Supervisor, Keyboard, Node
import rospy
from geometry_msgs.msg import Quaternion, Pose, Point, Twist
from gazebo_msgs.msg import ModelStates
from bitbots_msgs.srv import SetObjectPose, SetObjectPoseResponse, SetObjectPosition, SetObjectPositionResponse
from rosgraph_msgs.msg import Clock
from std_srvs.srv import Empty, EmptyResponse
import transforms3d
import numpy as np
G = 9.81
class SupervisorController:
def __init__(self, ros_active=False, mode='normal', do_ros_init=True, base_ns='', model_states_active=True):
"""
The SupervisorController, a Webots controller that can control the world.
Set the environment variable WEBOTS_ROBOT_NAME to "supervisor_robot" if used with 1_bot.wbt or 4_bots.wbt.
:param ros_active: Whether to publish ROS messages
:param mode: Webots mode, one of 'normal', 'paused', or 'fast'
:param do_ros_init: Whether rospy.init_node should be called
:param base_ns: The namespace of this node, can normally be left empty
"""
# requires WEBOTS_ROBOT_NAME to be set to "supervisor_robot"
self.ros_active = ros_active
self.model_states_active = model_states_active
self.time = 0
self.clock_msg = Clock()
self.supervisor = Supervisor()
self.keyboard_activated = False
if mode == 'normal':
self.supervisor.simulationSetMode(Supervisor.SIMULATION_MODE_REAL_TIME)
elif mode == 'paused':
self.supervisor.simulationSetMode(Supervisor.SIMULATION_MODE_PAUSE)
elif mode == 'fast':
self.supervisor.simulationSetMode(Supervisor.SIMULATION_MODE_FAST)
else:
self.supervisor.simulationSetMode(Supervisor.SIMULATION_MODE_REAL_TIME)
self.motors = []
self.sensors = []
self.timestep = int(self.supervisor.getBasicTimeStep())
self.robot_nodes = {}
self.translation_fields = {}
self.rotation_fields = {}
self.joint_nodes = {}
self.link_nodes = {}
root = self.supervisor.getRoot()
children_field = root.getField('children')
children_count = children_field.getCount()
for i in range(children_count):
node = children_field.getMFNode(i)
name_field = node.getField('name')
if name_field is not None and node.getType() == Node.ROBOT:
# this is a robot
name = name_field.getSFString()
if name == "supervisor_robot":
continue
self.robot_nodes[name] = node
self.translation_fields[name] = node.getField("translation")
self.rotation_fields[name] = node.getField("rotation")
self.joint_nodes[name], self.link_nodes[name] = self.collect_joint_and_link_node_references(node, {},
{})
if self.ros_active:
# need to handle these topics differently or we will end up having a double //
if base_ns == "":
clock_topic = "/clock"
model_topic = "/model_states"
else:
clock_topic = base_ns + "clock"
model_topic = base_ns + "model_states"
if do_ros_init:
rospy.init_node("webots_ros_supervisor", argv=['clock:=' + clock_topic])
self.clock_publisher = rospy.Publisher(clock_topic, Clock, queue_size=1)
self.model_state_publisher = rospy.Publisher(model_topic, ModelStates, queue_size=1)
self.reset_service = rospy.Service(base_ns + "reset", Empty, self.reset)
self.reset_pose_service = rospy.Service(base_ns + "reset_pose", Empty, self.set_initial_poses)
self.set_robot_pose_service = rospy.Service(base_ns + "set_robot_pose", SetObjectPose,
self.robot_pose_callback)
self.reset_ball_service = rospy.Service(base_ns + "reset_ball", Empty, self.reset_ball)
self.set_ball_position_service = rospy.Service(base_ns + "set_ball_position", SetObjectPosition,
self.ball_pos_callback)
self.world_info = self.supervisor.getFromDef("world_info")
self.ball = self.supervisor.getFromDef("ball")
def collect_joint_and_link_node_references(self, node, joint_dict, link_dict):
# this is a recursive function that iterates through the whole robot as this seems to be the only way to
# get all joints
# add node if it is a joint
if node.getType() == Node.SOLID:
name = node.getDef()
link_dict[name] = node
if node.getType() == Node.HINGE_JOINT:
name = node.getDef()
# substract the "Joint" keyword due to naming convention
name = name[:-5]
joint_dict[name] = node
# the joints dont have children but an "endpoint" that we need to search through
if node.isProto():
endpoint_field = node.getProtoField('endPoint')
else:
endpoint_field = node.getField('endPoint')
endpoint_node = endpoint_field.getSFNode()
self.collect_joint_and_link_node_references(endpoint_node, joint_dict, link_dict)
# needs to be done because Webots has two different getField functions for proto nodes and normal nodes
if node.isProto():
children_field = node.getProtoField('children')
else:
children_field = node.getField('children')
if children_field is not None:
for i in range(children_field.getCount()):
child = children_field.getMFNode(i)
self.collect_joint_and_link_node_references(child, joint_dict, link_dict)
return joint_dict, link_dict
def step_sim(self):
self.time += self.timestep / 1000
self.supervisor.step(self.timestep)
def step(self):
self.step_sim()
if self.ros_active:
self.publish_clock()
if self.model_states_active:
self.publish_model_states()
def handle_gui(self):
if not self.keyboard_activated:
self.keyboard = Keyboard()
self.keyboard.enable(100)
self.keyboard_activated = True
key = self.keyboard.getKey()
if key == ord('R'):
self.reset()
elif key == ord('P'):
self.set_initial_poses()
elif key == Keyboard.SHIFT + ord('R'):
try:
self.reset_ball()
except AttributeError:
print("No ball in simulation that can be reset")
return key
def publish_clock(self):
self.clock_msg.clock = rospy.Time.from_seconds(self.time)
self.clock_publisher.publish(self.clock_msg)
def set_gravity(self, active):
if active:
self.world_info.getField("gravity").setSFFloat(9.81)
else:
self.world_info.getField("gravity").setSFFloat(0)
def set_self_collision(self, active, name="amy"):
self.robot_nodes[name].getField("selfCollision").setSFBool(active)
def reset_robot_pose(self, pos, quat, name="amy"):
self.set_robot_pose_quat(pos, quat, name)
if name in self.robot_nodes:
self.robot_nodes[name].resetPhysics()
def reset_robot_pose_rpy(self, pos, rpy, name="amy"):
self.set_robot_pose_rpy(pos, rpy, name)
if name in self.robot_nodes:
self.robot_nodes[name].resetPhysics()
def reset(self, req=None):
self.supervisor.simulationReset()
self.supervisor.simulationResetPhysics()
return EmptyResponse()
def reset_robot_init(self, name="amy"):
self.robot_nodes[name].loadState('__init__')
self.robot_nodes[name].resetPhysics()
def set_initial_poses(self, req=None):
self.reset_robot_pose_rpy([-1, 3, 0.42], [0, 0.24, -1.57], name="amy")
self.reset_robot_pose_rpy([-1, -3, 0.42], [0, 0.24, 1.57], name="rory")
self.reset_robot_pose_rpy([-3, 3, 0.42], [0, 0.24, -1.57], name="jack")
self.reset_robot_pose_rpy([-3, -3, 0.42], [0, 0.24, 1.57], name="donna")
self.reset_robot_pose_rpy([0, 6, 0.42], [0, 0.24, -1.57], name="melody")
return EmptyResponse()
def robot_pose_callback(self, req=None):
self.reset_robot_pose([req.pose.position.x, req.pose.position.y, req.pose.position.z],
[req.pose.orientation.x, req.pose.orientation.y, req.pose.orientation.z,
req.pose.orientation.w], req.object_name)
return SetObjectPoseResponse()
def reset_ball(self, req=None):
self.ball.getField("translation").setSFVec3f([0, 0, 0.0772])
self.ball.getField("rotation").setSFRotation([0, 0, 1, 0])
self.ball.resetPhysics()
return EmptyResponse()
def ball_pos_callback(self, req=None):
self.set_ball_pose([req.position.x, req.position.y, req.position.z])
return SetObjectPositionResponse()
def set_ball_pose(self, pos):
self.ball.getField("translation").setSFVec3f(list(pos))
self.ball.resetPhysics()
def get_ball_pose(self):
return self.ball.getField("translation").getSFVec3f()
def get_ball_velocity(self):
if self.ball:
return self.ball.getVelocity()
def node(self):
s = self.supervisor.getSelected()
if s is not None:
print(f"id: {s.getId()}, type: {s.getType()}, def: {s.getDef()}")
def set_robot_axis_angle(self, axis, angle, name="amy"):
if name in self.rotation_fields:
self.rotation_fields[name].setSFRotation(list(np.append(axis, angle)))
def set_robot_rpy(self, rpy, name="amy"):
axis, angle = transforms3d.euler.euler2axangle(rpy[0], rpy[1], rpy[2], axes='sxyz')
self.set_robot_axis_angle(axis, angle, name)
def set_robot_quat(self, quat, name="amy"):
axis, angle = transforms3d.quaternions.quat2axangle([quat[3], quat[0], quat[1], quat[2]])
self.set_robot_axis_angle(axis, angle, name)
def set_robot_position(self, pos, name="amy"):
if name in self.translation_fields:
self.translation_fields[name].setSFVec3f(list(pos))
def set_robot_pose_rpy(self, pos, rpy, name="amy"):
self.set_robot_position(pos, name)
self.set_robot_rpy(rpy, name)
def set_robot_pose_quat(self, pos, quat, name="amy"):
self.set_robot_position(pos, name)
self.set_robot_quat(quat, name)
def get_robot_position(self, name="amy"):
if name in self.translation_fields:
return self.translation_fields[name].getSFVec3f()
def get_robot_orientation_axangles(self, name="amy"):
if name in self.rotation_fields:
return self.rotation_fields[name].getSFRotation()
def get_robot_orientation_rpy(self, name="amy"):
ax_angle = self.get_robot_orientation_axangles(name)
return list(transforms3d.euler.axangle2euler(ax_angle[:3], ax_angle[3], axes='sxyz'))
def get_robot_orientation_quat(self, name="amy"):
ax_angle = self.get_robot_orientation_axangles(name)
# transforms 3d uses scalar (i.e. the w part in the quaternion) first notation of quaternions, ros uses scalar last
quat_scalar_first = transforms3d.quaternions.axangle2quat(ax_angle[:3], ax_angle[3])
quat_scalar_last = | np.append(quat_scalar_first[1:], quat_scalar_first[0]) | numpy.append |
import gc
gc.collect()
import numpy as np
import pandas as pd
import scipy as sp
import sklearn as skl
from sklearn.model_selection import cross_val_score
from math import *
import random as rd
import cvxpy as cp
import multiprocessing as mp
import matplotlib.pyplot as plt
import gc
import statsmodels.api as sm
from sklearn.model_selection import KFold
from sklearn.model_selection import train_test_split
import time
def maternkernel(x,y,gamma):
x=np.array(x)
y=np.array(y)
return (1+sqrt(3)*sp.linalg.norm(x-y)/gamma)*exp(-sqrt(3)*sp.linalg.norm(x-y)/gamma)
def minmaxkernel(x,y,gamma):
aux=x
auy=y
x=np.array(x)
y=np.array(y)
if len(x.shape)==0:
x=[aux]
y=[auy]
d=len(x)
res=0
for i in range(d):
res=res+min(x[i],y[i])
return res
def pinball(z,t):
if t>1 or t<0:
print("tau must be in [0,1] \n")
t=float(input("try an other tau"))
return(0.5*cp.abs(z)+(t-0.5)*z)
#testing the pinball loss function output
out=[]
for i in np.arange(-5,5,0.1):
out.append(pinball(i,0.5))
#linear kernel
def linearkernel(x,y,gamma):
x=np.array(x)
y=np.array(y)
return x.T*y+gamma
#laplacian kernel
def LaplaceKernel(x,y,gamma):
x=np.array(x)
y= | np.array(y) | numpy.array |
import copy
import random
import gym
from gym.utils import seeding
from gym.spaces.discrete import Discrete
from gym.spaces import Box
from gym_sokoban import logger
from .room_utils import SokobanRoomGenerator
from .render_utils import room_to_rgb, room_to_tiny_world_rgb, room_to_one_hot, room_to_binary_map
import numpy as np
from matplotlib.pyplot import imread
import pkg_resources
import traceback
# modes meaning:
# binary_map - observations of shape (room_size[0], room_size[1], 4) with
# binary values. Channels represents if given part of room
# 0 - is interior (without wall)
# 1 - consist target
# 2 - consist box
# 3 - consist player
# e.g. pixel value [1, 1, 1, 0] indicates target tile with a box.
# Room state can be converted to binary_map and back using
# render_utils.{room_to_binary_map,binary_map_to_room}.
RENDERING_MODES = ['rgb_array', 'human', 'tiny_rgb_array', 'tiny_human', 'one_hot', 'one_hot_flatten', "binary_map"]
class SokobanEnv(gym.Env):
metadata = {
'render.modes': RENDERING_MODES
}
def __init__(self,
dim_room=(10, 10),
max_steps=np.inf, # 120
num_boxes=4,
num_gen_steps=None,
game_mode="NoAlice", # Alice, NoAlice, Magnetic
only_push_actions=True,
max_distinct_rooms=np.inf, # INFO: if finite, clone and restore do not reflect num_env_steps
mode='rgb_array',
penalty_pull_action=0., # used only in "Magnetic" mode
seed=None,
curriculum=300, # depth of DFS in reverse_play
reward_shaping='dense', # dense or sparse
verbose=True
):
assert game_mode in ["NoAlice", "Alice", "Magnetic"], "Incorrect game format!"
assert reward_shaping in ['dense', 'sparse'], 'Incorrect reward shaping mode!'
logger.info('Creating SokobanEnv')
logger.info('Game format: {}'.format(game_mode))
self.game_mode = game_mode
self.verbose = verbose
# General Configuration
self.dim_room = dim_room
if num_gen_steps is None:
self.num_gen_steps = int(1.7 * (dim_room[0] + dim_room[1]))
else:
self.num_gen_steps = num_gen_steps
self.num_boxes = num_boxes
self.boxes_on_target = 0
self.num_env_steps = 0
# Penalties and Rewards
self.penalty_for_step = -0.1
self.penalty_box_off_target = -1
self.penalty_pull_action = penalty_pull_action
self.reward_box_on_target = 1
self.reward_finished = 10
self.reward_shaping = reward_shaping
self.max_distinct_rooms = np.inf if max_distinct_rooms == -1 else max_distinct_rooms
assert self.max_distinct_rooms < 50000 or self.max_distinct_rooms == np.inf, \
"Setting high self.max_distinct_rooms creates potential memory leak. " \
"Uncomment if you know what your are doing"
self.generated_rooms = []
self.scale = 1
self._create_surface()
# Other Settings
self.viewer = None
self.max_steps = max_steps
num_actions = len(ACTION_LOOKUP) if self.game_mode == "Magnetic" else len(ACTION_LOOKUP) // 2
self.action_space = Discrete(num_actions)
self.observation_space = self.create_observation_space(mode=mode)
self.current_room_id = 0
self.mode = mode
self.curriculum = curriculum
self.seed(seed)
@property
def init_kwargs(self):
return {
attr: getattr(self, attr)
for attr in (
'dim_room', 'max_steps', 'num_boxes', 'num_gen_steps',
'game_mode', 'max_distinct_rooms', 'mode', 'penalty_pull_action',
'reward_shaping', 'verbose'
)
}
def create_observation_space(self, mode):
if mode in self.surfaces:
img = self.surfaces[mode][0]
img_shape = (1, 1, 3) if isinstance(img, list) else img.shape
screen_height, screen_width = (self.dim_room[0] * img_shape[0], self.dim_room[1] * img_shape[1])
return Box(low=0, high=255, shape=(screen_height, screen_width, 3), dtype=np.uint8)
elif mode == 'one_hot':
return Box(low=0, high=1, shape=(self.dim_room[0], self.dim_room[1], 7), dtype=np.uint8)
elif mode == 'one_hot_flatten':
return Box(low=0, high=1, shape=(self.dim_room[0] * self.dim_room[1] * 7,), dtype=np.uint8)
elif mode == 'binary_map':
return Box(low=0, high=1, shape=(self.dim_room[0], self.dim_room[1], 4), dtype=np.uint8)
else:
raise RuntimeError('unknown mode {}'.format(mode))
def seed(self, seed=None):
# We want the rooms generated to be the same, even if the actions taken in the env are different.
_, self._seed = seeding.np_random(seed)
self.other_rng = random.Random(self._seed)
self.room_generator = SokobanRoomGenerator(seed=self._seed,
game_mode=self.game_mode,
verbose=self.verbose)
self.current_seed = None
return [self._seed]
def step(self, action):
assert action in ACTION_LOOKUP, "Illegal action {}".format(action)
if not hasattr(self, 'room_generator'):
raise RuntimeError('Please call reset() first')
self.num_env_steps += 1
#if self.game_mode = "Alice":
# self.num_steps_bob
# self.num_steps_alice
self.new_box_position = None
self.old_box_position = None
moved_player = False
moved_box = False
# All push actions are in the range of [0, 3]
if action < 4:
moved_player, moved_box = self._push(action)
else:
if self.game_mode != "Magnetic":
raise RuntimeError("Cannot make 'pull' action if not in 'Magnetic' game mode.")
moved_player, moved_box = self._push(action, with_pull=True)
reward = self._calc_reward(action)
done = self._check_if_done()
# Convert the observation to RGB frame
observation = self.render(mode=self.mode)
info = {
'action.name': ACTION_LOOKUP[action],
'action.moved_player': moved_player,
'action.moved_box': moved_box,
'text': ['room_id={}'.format(self.current_room_id)],
'aux_rewards': {
'solved': self._check_if_all_boxes_on_target()
}
}
if done:
info["maxsteps_used"] = self._check_if_maxsteps()
#info["all_boxes_on_target"] = self._check_if_all_boxes_on_target()
info["solved"] = self._check_if_all_boxes_on_target()
return observation, reward, done, info
def _push(self, action, with_pull=False):
"""
INFO: if self.game_mode == "Alice", push is in fact pull.
Perform a push, if a box is adjacent in the right direction.
If no box, can be pushed, try to move.
:param action:
:param with_pull: if True, make pull along with push ("Magnetic" mode)
:return: Boolean, indicating a change of the room's state
"""
change = CHANGE_COORDINATES[action % 4]
if self.game_mode == "Alice": # Alice does reverse moves
new_position = self.player_position - change
else:
new_position = self.player_position + change
current_position = self.player_position.copy()
# No push, if the push would get the box out of the room's grid
# INFO: no need to check for negative, since it can be the least -1, which is legal in Python
if self.game_mode == "Alice":
new_box_position = self.player_position
else:
new_box_position = new_position + change
if new_box_position[0] >= self.room_state.shape[0] \
or new_box_position[1] >= self.room_state.shape[1]:
return False, False
if self.game_mode == "Alice":
# in this case push is a pull
old_box_position = self.player_position - change
can_push_box = self.room_state[old_box_position[0], old_box_position[1]] in [3, 4]
else:
can_push_box = self.room_state[new_position[0], new_position[1]] in [3, 4]
can_push_box &= self.room_state[new_box_position[0], new_box_position[1]] in [1, 2]
if can_push_box:
self.new_box_position = tuple(new_box_position)
if self.game_mode == "Alice":
self.old_box_position = tuple(old_box_position)
else:
self.old_box_position = tuple(new_position)
# Move Player
self.player_position = new_position
self.room_state[(new_position[0], new_position[1])] = 5
if self.game_mode == "Alice":
self.room_state[old_box_position[0], old_box_position[1]] = \
self.room_fixed[old_box_position[0], old_box_position[1]]
else:
self.room_state[current_position[0], current_position[1]] = \
self.room_fixed[current_position[0], current_position[1]]
# Move Box
box_type = 4
if self.room_fixed[new_box_position[0], new_box_position[1]] == 2:
box_type = 3
self.room_state[new_box_position[0], new_box_position[1]] = box_type
moved_player, moved_box = True, True
# Try to move if no box to push, available
else:
moved_player = self._move(action)
moved_box = False
# Pull box
if with_pull and moved_player:
if self.game_mode == "Alice":
raise RuntimeError("Using push with 'with_pull' flag in Alice mode is undefined.")
pull_content_position = current_position - change
is_box_next_to_player = self.room_state[pull_content_position[0], pull_content_position[1]] in [3, 4]
if is_box_next_to_player:
# Move Box
moved_box = True
box_type = 4
if self.room_fixed[current_position[0], current_position[1]] == 2:
box_type = 3
self.room_state[current_position[0], current_position[1]] = box_type
self.room_state[pull_content_position[0], pull_content_position[1]] = \
self.room_fixed[pull_content_position[0], pull_content_position[1]]
return moved_player, moved_box
def _move(self, action):
"""
Moves the player to the next field, if it is not occupied.
:param action:
:return: Boolean, indicating a change of the room's state
"""
change = CHANGE_COORDINATES[action % 4]
if self.game_mode == "Alice":
new_position = self.player_position - change
else:
new_position = self.player_position + change
current_position = self.player_position.copy()
# Move player if the field in the moving direction is either
# an empty field or an empty box target.
if self.room_state[new_position[0], new_position[1]] in [1, 2]:
self.player_position = new_position
self.room_state[(new_position[0], new_position[1])] = 5
self.room_state[current_position[0], current_position[1]] = \
self.room_fixed[current_position[0], current_position[1]]
return True
return False
def set_game_mode(self, game_mode=None):
self.game_mode = game_mode
def _calc_reward(self, action=None):
"""
Calculate Reward Based on
:return:
"""
# Every step a small penalty is given, This ensures
# that short solutions have a higher reward.
if self.game_mode == "Alice":
# reward is a tuple (reward_Bob, reward_Alice)
reward = (self.num_steps_bob, self.num_steps_alice)
elif self.reward_shaping == 'sparse':
game_won = self._check_if_all_boxes_on_target()
reward = 1 if game_won else 0
else: # dense reward
reward = self.penalty_for_step
# count boxes off or on the target
empty_targets = self.room_state == 2
player_on_target = (self.room_fixed == 2) & (self.room_state == 5)
total_targets = empty_targets | player_on_target
current_boxes_on_target = self.num_boxes - \
np.where(total_targets)[0].shape[0]
# Add the reward if a box is pushed on the target and give a
# penalty if a box is pushed off the target.
if current_boxes_on_target > self.boxes_on_target:
reward += self.reward_box_on_target
elif current_boxes_on_target < self.boxes_on_target:
reward += self.penalty_box_off_target
game_won = self._check_if_all_boxes_on_target()
if game_won:
reward += self.reward_finished
self.boxes_on_target = current_boxes_on_target
# Additional penalty for pull actions
if self.game_mode == "Magnetic" and action is not None and action > 3:
# Penalize pull actions
reward += self.penalty_pull_action
return reward
def _check_if_done(self):
# Check if the game is over either through reaching the maximum number
# of available steps or by pushing all boxes on the targets.
return self._check_if_all_boxes_on_target() or self._check_if_maxsteps()
def _check_if_all_boxes_on_target(self):
empty_targets = self.room_state == 2
player_hiding_target = (self.room_fixed == 2) & (self.room_state == 5)
are_all_boxes_on_targets = np.where(empty_targets | player_hiding_target)[0].shape[0] == 0
return are_all_boxes_on_targets
def _check_if_maxsteps(self):
return (self.num_env_steps >= self.max_steps)
def reset(self, second_player=False):
try:
if len(self.generated_rooms) < self.max_distinct_rooms:
# INFO: currently room_generator.generate_room does not return meaningful box_mapping
self.current_seed = self._seed
self.room_fixed, self.room_state, self.box_mapping, self._seed = self.room_generator.generate_room(
dim=self.dim_room,
num_steps=self.num_gen_steps,
num_boxes=self.num_boxes,
second_player=second_player,
curriculum=self.curriculum,
)
if self.max_distinct_rooms < np.inf:
room_to_save = copy.deepcopy((self.room_fixed, self.room_state, self.box_mapping))
self.generated_rooms.append(room_to_save)
else:
self.current_room_id = self.other_rng.randint(0, len(self.generated_rooms) - 1)
self.room_fixed, self.room_state, self.box_mapping \
= copy.deepcopy(self.generated_rooms[self.current_room_id])
except (RuntimeError, RuntimeWarning) as e:
if self.verbose:
print("[SOKOBAN] Runtime Error/Warning: {}".format(e))
print("[SOKOBAN] Retry . . .")
return self.reset()
self.player_position = np.argwhere(self.room_state == 5)[0]
self.num_env_steps = 0
self.boxes_on_target = 0
starting_observation = self.render(mode=self.mode)
return starting_observation
# kwargs could include 'mode' and 'scale'
def render(self, mode=None, close=None, **kwargs):
mode = mode if mode is not None else self.mode
assert mode in RENDERING_MODES, 'Unknown rendering mode {}'.format(mode)
obs = self.get_image(mode=mode, **kwargs)
if mode in ['one_hot', 'one_hot_flatten', 'binary_map', 'rgb_array']:
return obs
elif 'human' in mode:
from gym.envs.classic_control import rendering
if self.viewer is None:
self.viewer = rendering.SimpleImageViewer()
self.viewer.imshow(obs)
return self.viewer.isopen
else:
super(SokobanEnv, self).render(mode=mode) # just raise an exception
def get_image(self, mode, **kwargs):
if mode == 'one_hot':
return room_to_one_hot(self.room_state, self.room_fixed)
elif mode == 'one_hot_flatten':
return room_to_one_hot(self.room_state, self.room_fixed).flatten()
elif mode == 'binary_map':
return room_to_binary_map(self.room_state, self.room_fixed)
elif mode.startswith('tiny_'):
surfaces = self.surfaces[mode]
self.scale = kwargs.get('scale', 1)
img = room_to_tiny_world_rgb(self.room_state, self.room_fixed, surfaces=surfaces, scale=self.scale)
else:
surfaces = self.surfaces[mode]
img = room_to_rgb(self.room_state, self.room_fixed, surfaces=surfaces)
return img
# INFO: it does not clone self.num_env_steps
def clone_full_state(self):
state = np.vstack([self.room_fixed, self.room_state]) # copies
state = state.flatten()
state = np.append(state, self._seed)
return state # np.array can be np.save'd
# INFO: it does not restore self.num_env_steps
def restore_full_state(self, state):
seed = state[-1]
state = state[:-1].astype(np.uint8)
split = len(state) // 2
dim_room = self.dim_room
room_fixed = state[:split].reshape((dim_room[0], dim_room[1]))
room_state = state[split:].reshape((dim_room[0], dim_room[1]))
self.room_fixed = np.array(room_fixed) # copy
self.room_state = np.array(room_state) # copy
self._seed = seed
empty_targets = self.room_state == 2
player_on_target = (self.room_fixed == 2) & (self.room_state == 5)
total_targets = empty_targets | player_on_target
boxes_on_target = self.num_boxes - np.where(total_targets)[0].shape[0]
self.boxes_on_target = boxes_on_target
player_position = np.where(self.room_state == 5)
player_position = np.array([player_position[0][0], player_position[1][0]])
self.player_position = player_position
# INFO: self.num_env_steps is not restored
self.num_env_steps = 0
def close(self):
if self.viewer is not None:
self.viewer.close()
def set_maxsteps(self, num_steps):
self.max_steps = num_steps
def get_action_lookup(self):
return ACTION_LOOKUP
def get_action_meanings(self):
return ACTION_LOOKUP
@staticmethod
def load_surfaces():
surfaces = {}
# Load images, representing the corresponding situation
resource_package = __name__
box_filename = pkg_resources.resource_filename(resource_package, '/'.join(('surface', '8x8pixels', 'box.png')))
box = imread(box_filename)
box_on_target_filename = pkg_resources.resource_filename(resource_package,
'/'.join(('surface', '8x8pixels', 'box_on_target.png')))
box_on_target = imread(box_on_target_filename)
box_target_filename = pkg_resources.resource_filename(resource_package, '/'.join(('surface', '8x8pixels', 'box_target.png')))
box_target = imread(box_target_filename)
floor_filename = pkg_resources.resource_filename(resource_package, '/'.join(('surface', '8x8pixels', 'floor.png')))
floor = imread(floor_filename)
player_filename = pkg_resources.resource_filename(resource_package, '/'.join(('surface', '8x8pixels', 'player.png')))
player = imread(player_filename)
player_on_target_filename = pkg_resources.resource_filename(resource_package,
'/'.join(('surface', '8x8pixels', 'player_on_target.png')))
player_on_target = imread(player_on_target_filename)
wall_filename = pkg_resources.resource_filename(resource_package, '/'.join(('surface', '8x8pixels', 'wall.png')))
wall = imread(wall_filename)
surfaces["rgb_array"] = [wall, floor, box_target, box_on_target, box, player, player_on_target]
wall = [0, 0, 0]
floor = [243, 248, 238]
box_target = [254, 126, 125]
box_on_target = [254, 95, 56]
box = [142, 121, 56]
player = [160, 212, 56]
player_on_target = [219, 212, 56]
surfaces["tiny_rgb_array"] = [wall, floor, box_target, box_on_target, box, player, player_on_target]
return surfaces
def _create_surface(self):
self.surfaces = self.load_surfaces()
self._recover = {}
for mode in ['rgb_array', 'tiny_rgb_array']: # add 'one_hot', 'one_hot_flatten'
if mode not in self._recover:
self._recover[mode] = {}
#self._mode_shapes[mode] = np.array(self.surfaces[mode][0]).shape
for idx, img in enumerate(self.surfaces[mode]):
img = tuple(np.array(img).flatten())
self._recover[mode][img] = idx
self._mode_shapes = {}
self._mode_shapes['rgb_array'] = (self.dim_room[0] * self.surfaces['rgb_array'][0].shape[0],
self.dim_room[1] * self.surfaces['rgb_array'][1].shape[1],
3)
self._mode_shapes['tiny_rgb_array'] = (self.dim_room[0] * self.scale,
self.dim_room[1] * self.scale,
3)
def recover_state(self, obs):
mode = self.mode
assert mode in self._recover, "Mode {} not supported".format(mode)
assert obs.shape == self._mode_shapes[mode], \
"Dimension of obs {} and mode {} does not match".format(obs.shape, self._mode_shapes[mode])
sprite_shape = getattr(self.surfaces[mode][0], 'shape', (1, 1)) # when list need this to be (1,1)
room_state = | np.zeros_like(self.room_state) | numpy.zeros_like |
import numpy as np # Importing packages
import cv2 as cv
from matplotlib import pyplot as plt
IMAGE = cv.imread('D:\@Semester 06\Digital Image Processing\Lab\Manuals\Figures\lab15/_me.jpg', 0) # Reading image
def padding(image, paddingsize): # Adding padding
padded_img = | np.pad(image, (paddingsize, paddingsize), "constant") | numpy.pad |
from tvm.contrib.download import download_testdata
from PIL import Image
import numpy as np
img_url = "https://s3.amazonaws.com/model-server/inputs/kitten.jpg"
img_path = download_testdata(img_url, "imagenet_cat.png", module="data")
# Resize it to 224x224
resized_image = Image.open(img_path).resize((224, 224))
img_data = np.asarray(resized_image).astype("float32")
# ONNX expects NCHW input, so convert the array
img_data = np.transpose(img_data, (2, 0, 1))
# Normalize according to ImageNet
imagenet_mean = np.array([0.485, 0.456, 0.406])
imagenet_stddev = np.array([0.229, 0.224, 0.225])
norm_img_data = np.zeros(img_data.shape).astype("float32")
for i in range(img_data.shape[0]):
norm_img_data[i, :, :] = (img_data[i, :, :] / 255 - imagenet_mean[i]) / imagenet_stddev[i]
# Add batch dimension
img_data = np.expand_dims(norm_img_data, axis=0)
# Save to .npz (outputs imagenet_cat.npz)
| np.savez("imagenet_cat", data=img_data) | numpy.savez |
# -*- coding: utf-8 -*-
# Copyright 2018 <NAME>, <NAME>, <NAME>, <NAME>,
# <NAME>, <NAME>
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Functionality to evaluate results of networks.
Functions:
get_number_gt_per_class(...): calculates the number of ground truth boxes per class
prepare-predictions(...): prepares the predictions for further processing
match_predictions(...): matches predictions to ground truth boxes
get_precision_recall(...): computes the precision and recall values and returns them
get_f1_score(...): computes the F1 score for every class
get_mean_average_precisions(...): computes the mean average precision for each class and returns them
get_mean_average_precision(...): computes the mean average precision over all classes and returns it
"""
from typing import Sequence, Union, Tuple, List
import numpy as np
def get_number_gt_per_class(labels: Sequence[Sequence[Sequence[int]]],
nr_classes: int) -> np.ndarray:
"""
Calculates the number of ground truth boxes per class and returns result.
Args:
labels: list of labels per image
nr_classes: number of classes
Returns:
numpy array with respective counts
"""
number_gt_per_class = np.zeros(shape=(nr_classes + 1), dtype=np.int)
label_range = range(len(labels))
# iterate over images
for i in label_range:
boxes = np.asarray(labels[i])
# iterate over boxes in image
for j in range(boxes.shape[0]):
class_id = int(boxes[j, 0])
if class_id > nr_classes:
continue
number_gt_per_class[class_id] += 1
return number_gt_per_class
def prepare_predictions(predictions: Sequence[Sequence[Sequence[Union[int, float]]]],
nr_classes: int) -> \
List[List[Tuple[int, float, int, int, int, int]]]:
"""
Prepares the predictions for further processing.
Args:
predictions: list of predictions per image
nr_classes: number of classes
Returns:
list of predictions per class
"""
results = [list() for _ in range(nr_classes + 1)]
# index positions for bounding box coordinates
xmin = 2
ymin = 3
xmax = 4
ymax = 5
for i, batch_item in enumerate(predictions):
image_id = i
for box in batch_item:
if len(box) == 7:
# entropy is in box list
xmin += 1
ymin += 1
xmax += 1
ymax += 1
if len(box) > nr_classes:
class_id = np.argmax(box[:-5])
confidence = np.amax(box[:-5])
xmin = -5
ymin = -4
xmax = -3
ymax = -2
else:
class_id = int(box[0])
# Round the box coordinates to reduce the required memory.
confidence = box[1]
xmin_value = round(box[xmin])
ymin_value = round(box[ymin])
xmax_value = round(box[xmax])
ymax_value = round(box[ymax])
prediction = (image_id, confidence, xmin_value, ymin_value, xmax_value, ymax_value)
# Append the predicted box to the results list for its class.
results[class_id].append(prediction)
return results
def match_predictions(predictions: Sequence[Sequence[Tuple[int, float, int, int, int, int]]],
labels: Sequence[Sequence[Sequence[int]]],
iou_func: callable,
nr_classes: int,
iou_threshold: float,
border_pixels: str = "include",
sorting_algorithm: str = "quicksort") -> Tuple[List[np.ndarray], List[np.ndarray],
List[np.ndarray], List[np.ndarray],
np.ndarray, np.ndarray,
np.ndarray, np.ndarray]:
"""
Matches predictions to ground truth boxes.
Args:
predictions: list of predictions
labels: list of labels per image
iou_func: function to calculate the intersection over union
nr_classes: number of classes
iou_threshold: only matches higher than this value will be considered
border_pixels: How to treat the border pixels of the bounding boxes.
Can be 'include', 'exclude', or 'half'. If 'include', the border pixels belong
to the boxes. If 'exclude', the border pixels do not belong to the boxes.
If 'half', then one of each of the two horizontal and vertical borders belong
to the boxes, but not the other.
sorting_algorithm: Which sorting algorithm the matching algorithm should use. This
argument accepts any valid sorting algorithm for Numpy's `argsort()` function.
You will usually want to choose between 'quicksort' (fastest and most memory efficient,
but not stable) and 'mergesort' (slight slower and less memory efficient, but stable).
The official Matlab evaluation algorithm uses a stable sorting algorithm, so this algorithm
is only guaranteed to behave identically if you choose 'mergesort' as the sorting algorithm,
but it will almost always behave identically even if you choose 'quicksort' (but no guarantees).
Returns:
true positives, false positives, cumulative true positives, and cumulative false positives for
each class, open set error as defined by Miller et al, cumulative open set error,
cumulative true positives and cumulative false positives over all classes
"""
true_positives = [[]] # The false positives for each class, sorted by descending confidence.
false_positives = [[]] # The true positives for each class, sorted by descending confidence.
cumulative_true_positives = [[]]
cumulative_false_positives = [[]]
most_predictions = -1
for class_id in range(1, nr_classes + 1):
nr_predictions = len(predictions[class_id])
if nr_predictions > most_predictions:
most_predictions = nr_predictions
open_set_error = np.zeros(most_predictions, dtype=np.int)
true_positives_micro = np.zeros(most_predictions, dtype=np.int)
false_positives_micro = np.zeros(most_predictions, dtype=np.int)
for class_id in range(1, nr_classes + 1):
predictions_class = predictions[class_id]
# Store the matching results in these lists:
true_pos = np.zeros(len(predictions_class),
dtype=np.int) # 1 for every prediction that is a true positive, 0 otherwise
false_pos = np.zeros(len(predictions_class),
dtype=np.int) # 1 for every prediction that is a false positive, 0 otherwise
# In case there are no predictions at all for this class, we're done here.
if len(predictions_class) == 0:
true_positives.append(true_pos)
false_positives.append(false_pos)
cumulative_true_pos = np.cumsum(true_pos) # Cumulative sums of the true positives
cumulative_false_pos = np.cumsum(false_pos) # Cumulative sums of the false positives
cumulative_true_positives.append(cumulative_true_pos)
cumulative_false_positives.append(cumulative_false_pos)
continue
# Convert the predictions list for this class into a structured array so that we can sort it by confidence.
# Create the data type for the structured array.
preds_data_type = np.dtype([('image_id', np.int32),
('confidence', 'f4'),
('xmin', 'f4'),
('ymin', 'f4'),
('xmax', 'f4'),
('ymax', 'f4')])
# Create the structured array
predictions_class = np.array(predictions_class, dtype=preds_data_type)
# Sort the detections by decreasing confidence.
descending_indices = np.argsort(-predictions_class['confidence'], kind=sorting_algorithm)
predictions_sorted = predictions_class[descending_indices]
# Keep track of which ground truth boxes were already matched to a detection.
gt_matched = {}
for i in range(len(predictions_class)):
prediction = predictions_sorted[i]
image_id = prediction['image_id']
# Convert the structured array element to a regular array
pred_box = np.asarray(list(prediction[['xmin', 'ymin', 'xmax', 'ymax']]))
# Get the relevant ground truth boxes for this prediction,
# i.e. all ground truth boxes that match the prediction's
# image ID and class ID.
gt = labels[image_id]
gt = np.asarray(gt)
class_mask = gt[:, 0] == class_id
gt = gt[class_mask]
if gt.size == 0:
# If the image doesn't contain any objects of this class,
# the prediction becomes a false positive.
false_pos[i] = 1
false_positives_micro[i] += 1
open_set_error[i] += 1
continue
# Compute the IoU of this prediction with all ground truth boxes of the same class.
overlaps = iou_func(boxes1=gt[:, [1, 2, 3, 4]],
boxes2=pred_box,
coords='corners',
mode='element-wise',
border_pixels=border_pixels)
# For each detection, match the ground truth box with the highest overlap.
# It's possible that the same ground truth box will be matched to multiple
# detections.
gt_match_index = np.argmax(overlaps)
gt_match_overlap = overlaps[gt_match_index]
if gt_match_overlap < iou_threshold:
# False positive, IoU threshold violated:
# Those predictions whose matched overlap is below the threshold become
# false positives.
false_pos[i] = 1
false_positives_micro[i] += 1
else:
if image_id not in gt_matched:
# True positive:
# If the matched ground truth box for this prediction hasn't been matched to a
# different prediction already, we have a true positive.
true_pos[i] = 1
true_positives_micro[i] += 1
gt_matched[image_id] = np.zeros(shape=(gt.shape[0]), dtype=np.bool)
gt_matched[image_id][gt_match_index] = True
elif not gt_matched[image_id][gt_match_index]:
# True positive:
# If the matched ground truth box for this prediction hasn't been matched to a
# different prediction already, we have a true positive.
true_pos[i] = 1
true_positives_micro[i] += 1
gt_matched[image_id][gt_match_index] = True
else:
# False positive, duplicate detection:
# If the matched ground truth box for this prediction has already been matched
# to a different prediction previously, it is a duplicate detection for an
# already detected object, which counts as a false positive.
false_pos[i] = 1
false_positives_micro[i] += 1
true_positives.append(true_pos)
false_positives.append(false_pos)
cumulative_true_pos = np.cumsum(true_pos) # Cumulative sums of the true positives
cumulative_false_pos = np.cumsum(false_pos) # Cumulative sums of the false positives
cumulative_true_positives.append(cumulative_true_pos)
cumulative_false_positives.append(cumulative_false_pos)
cumulative_open_set_error = np.cumsum(open_set_error)
cumulative_false_positives_micro = np.cumsum(false_positives_micro)
cumulative_true_positives_micro = np.cumsum(true_positives_micro)
return (
true_positives, false_positives, cumulative_true_positives, cumulative_false_positives,
open_set_error, cumulative_open_set_error,
cumulative_true_positives_micro, cumulative_false_positives_micro
)
def get_precision_recall(number_gt_per_class: np.ndarray,
cumulative_true_positives: Sequence[np.ndarray],
cumulative_false_positives: Sequence[np.ndarray],
cumulative_true_positives_micro: np.ndarray,
cumulative_false_positives_micro: np.ndarray,
nr_classes: int) -> Tuple[List[np.ndarray], List[np.ndarray],
np.ndarray, np.ndarray,
np.ndarray, np.ndarray]:
"""
Computes the precision and recall values and returns them.
Args:
number_gt_per_class: number of ground truth bounding boxes per class
cumulative_true_positives: cumulative true positives per class
cumulative_false_positives: cumulative false positives per class
cumulative_true_positives_micro: cumulative true positives over all classes
cumulative_false_positives_micro: cumulative false positives over all classes
nr_classes: number of classes
Returns:
cumulative precisions and cumulative recalls per class,
micro averaged precision/recall, and
macro averaged precision/recall
"""
cumulative_precisions = [[]]
cumulative_recalls = [[]]
cumulative_precision_micro = np.zeros(cumulative_true_positives_micro.shape, dtype=np.float)
cumulative_recall_micro = np.zeros(cumulative_true_positives_micro.shape, dtype=np.float)
cumulative_precision_macro = np.zeros_like(cumulative_precision_micro)
cumulative_recall_macro = np.zeros_like(cumulative_recall_micro)
total_number_gt = 0
number_of_nonzero_classes = 0
# Iterate over all classes.
for class_id in range(1, nr_classes + 1):
if number_gt_per_class[class_id] == 0:
cumulative_precisions.append([])
cumulative_recalls.append([])
continue
tp = cumulative_true_positives[class_id]
fp = cumulative_false_positives[class_id]
cumulative_precision = np.where(tp + fp > 0, tp / (tp + fp), 0) # 1D array with shape `(num_predictions,)`
number_gt = number_gt_per_class[class_id]
total_number_gt += number_gt
cumulative_recall = tp / number_gt # 1D array with shape `(num_predictions,)`
cumulative_precisions.append(cumulative_precision)
cumulative_recalls.append(cumulative_recall)
diff_to_largest_class = cumulative_precision_micro.shape[0] - cumulative_precision.shape[0]
if diff_to_largest_class:
highest_precision = cumulative_precision[-1] if cumulative_precision.shape[0] else 0
highest_recall = cumulative_recall[-1] if cumulative_recall.shape[0] else 0
repeated_last_precision = np.tile(highest_precision, diff_to_largest_class)
repeated_last_recall = np.tile(highest_recall, diff_to_largest_class)
extended_precision = np.concatenate((cumulative_precision, repeated_last_precision))
extended_recall = np.concatenate((cumulative_recall, repeated_last_recall))
cumulative_precision_macro += extended_precision
cumulative_recall_macro += extended_recall
else:
cumulative_precision_macro += cumulative_precision
cumulative_recall_macro += cumulative_recall
number_of_nonzero_classes += 1
# calculate micro averaged precision and recall
tp = cumulative_true_positives_micro
fp = cumulative_false_positives_micro
cumulative_precision_micro = np.where(tp + fp > 0, tp / (tp + fp), 0)
cumulative_recall_micro = tp / total_number_gt
# calculate macro averaged precision and recall
cumulative_precision_macro /= number_of_nonzero_classes
cumulative_recall_macro /= number_of_nonzero_classes
return (cumulative_precisions, cumulative_recalls,
cumulative_precision_micro, cumulative_recall_micro,
cumulative_precision_macro, cumulative_recall_macro
)
def get_f1_score(cumulative_precisions: List[np.ndarray],
cumulative_recalls: List[np.ndarray],
cumulative_precision_micro: np.ndarray,
cumulative_recall_micro: np.ndarray,
cumulative_precision_macro: np.ndarray,
cumulative_recall_macro: np.ndarray,
nr_classes: int) -> Tuple[List[np.ndarray],
np.ndarray, np.ndarray]:
"""
Computes the F1 score for every class.
Args:
cumulative_precisions: cumulative precisions for each class
cumulative_recalls: cumulative recalls for each class
cumulative_precision_micro: cumulative precision micro averaged
cumulative_recall_micro: cumulative recall micro averaged
cumulative_precision_macro: cumulative precision macro averaged
cumulative_recall_macro: cumulative recall macro averaged
nr_classes: number of classes
Returns:
cumulative F1 score per class,
cumulative F1 score micro averaged, cumulative F1 score macro averaged
"""
cumulative_f1_scores = [[]]
# iterate over all classes
for class_id in range(1, nr_classes + 1):
cumulative_precision = cumulative_precisions[class_id]
cumulative_recall = cumulative_recalls[class_id]
if not np.count_nonzero(cumulative_precision + cumulative_recall):
cumulative_f1_scores.append([])
continue
f1_score = 2 * ((cumulative_precision * cumulative_recall) / (cumulative_precision + cumulative_recall + 0.001))
cumulative_f1_scores.append(f1_score)
f1_score_micro = 2 * ((cumulative_precision_micro * cumulative_recall_micro) /
(cumulative_precision_micro + cumulative_recall_micro + 0.001))
f1_score_macro = 2 * ((cumulative_precision_macro * cumulative_recall_macro) /
(cumulative_precision_macro + cumulative_recall_macro + 0.001))
return cumulative_f1_scores, f1_score_micro, f1_score_macro
def get_mean_average_precisions(cumulative_precisions: List[np.ndarray],
cumulative_recalls: List[np.ndarray],
nr_classes: int) -> List[float]:
"""
Computes the mean average precision for each class and returns them.
Args:
cumulative_precisions: cumulative precisions for each class
cumulative_recalls: cumulative recalls for each class
nr_classes: number of classes
Returns:
average precision per class
"""
average_precisions = [0.0]
# Iterate over all classes.
for class_id in range(1, nr_classes + 1):
cumulative_precision = cumulative_precisions[class_id]
cumulative_recall = cumulative_recalls[class_id]
# We will compute the precision at all unique recall values.
unique_recalls, unique_recall_indices, unique_recall_counts = np.unique(cumulative_recall,
return_index=True,
return_counts=True)
# Store the maximal precision for each recall value and the absolute difference
# between any two unique recall values in the lists below. The products of these
# two numbers constitute the rectangular areas whose sum will be our numerical
# integral.
maximal_precisions = np.zeros_like(unique_recalls)
recall_deltas = np.zeros_like(unique_recalls)
# Iterate over all unique recall values in reverse order. This saves a lot of computation:
# For each unique recall value `r`, we want to get the maximal precision value obtained
# for any recall value `r* >= r`. Once we know the maximal precision for the last `k` recall
# values after a given iteration, then in the next iteration, in order compute the maximal
# precisions for the last `l > k` recall values, we only need to compute the maximal precision
# for `l - k` recall values and then take the maximum between that and the previously computed
# maximum instead of computing the maximum over all `l` values.
# We skip the very last recall value, since the precision after the last recall value
# 1.0 is defined to be zero.
for i in range(len(unique_recalls) - 2, -1, -1):
begin = unique_recall_indices[i]
end = unique_recall_indices[i + 1]
# When computing the maximal precisions, use the maximum of the previous iteration to
# avoid unnecessary repeated computation over the same precision values.
# The maximal precisions are the heights of the rectangle areas of our integral under
# the precision-recall curve.
maximal_precisions[i] = np.maximum( | np.amax(cumulative_precision[begin:end]) | numpy.amax |
import torch
import numpy as np
from torch.autograd import Variable
from sklearn.preprocessing import MinMaxScaler
from sklearn.preprocessing import StandardScaler
import os
# restore hamiltonian from nonzeros
def restore_h(nonzero, nonzero_loc, dim):
data_count = nonzero.shape[0]
H = torch.zeros((data_count, dim, dim), device=nonzero.device).float()
triangle_shape = (data_count, int(dim * (dim + 1) / 2))
upper_triangle = torch.zeros(triangle_shape, device=nonzero.device)
upper_triangle[:, nonzero_loc] = nonzero
iu1 = np.triu_indices(dim)
il1 = np.tril_indices(dim)
H[:, iu1[0], iu1[1]] = upper_triangle
H_t = torch.transpose(H, dim0=1, dim1=2)
diag = torch.diagonal(H, offset=0, dim1=1, dim2=2)
diag_matrix = torch.diag_embed(diag, offset=0, dim1=1, dim2=2)
H += H_t - diag_matrix
return H
def getData(n_sites, path_to_data, train_test, dataset='new'):
if dataset == 'new':
try:
# load data from server
directory = path_to_data + "%d-qubits/100k-instances/single-phase/%s/" % (n_sites, train_test)
# read the files
with open(directory + "header.bin", 'rb') as file:
header = np.fromfile(file, dtype=np.int32)
with open(directory + "matloc.bin", 'rb') as file:
matloc = np.fromfile(file, dtype=np.int32)
with open(directory + "matval.bin", 'rb') as file:
matval = np.fromfile(file, dtype=np.float64)
with open(directory + "wavefx.bin", 'rb') as file:
wavefx = np.fromfile(file, dtype=np.float64)
with open(directory + "energy.bin", 'rb') as file:
energy = np.fromfile(file, dtype=np.float64)
with open(directory + "fields.bin", 'rb') as file:
fields = np.fromfile(file, dtype=np.float64)
with open(directory + "szdiag.bin", 'rb') as file:
szdiag = np.fromfile(file, dtype=np.float64)
# reshape/format data
data_count = header[0]
dim = header[2]
energy = torch.tensor(energy).float().view(data_count, 1)
Bx = torch.tensor(fields).float().view(data_count, 1)
szdiag = torch.diag(torch.tensor(szdiag)).float()
psi = torch.tensor(wavefx).float().view(data_count, dim)
nonzero_H_Ids = matloc.reshape((data_count, -1))
nonzero_H = torch.tensor(matval).float().view(data_count, -1)
except Exception as e:
print(e)
return Bx, nonzero_H, psi, energy, data_count, nonzero_H_Ids, szdiag
elif dataset == 'old':
"""
Compile all the data into arrays for use in NN training ans testing.
Parameters:
n_sites (int): The number of sites in your model
path_to_data (str): The path to the directory where the data is.
train_test (str): Options 'train' or 'test' depending on desired dataset.
Returns:
BxBz (np.ndarray): An array with the ordered Bx, Bz pairs in each row.
Ham (np.ndarray): An array with the flattened input Hamiltonian in each row.
targets (np.ndarray): An array with the ground state wavefunction in each row.
eigenvalues (np.ndarray): An array with the energy eigenvalues for the ground state in each row.
datapoints (int): The number of datapoints loaded.
"""
with open('%s%s-site-field-gs-%s.bin' % (path_to_data, n_sites, train_test), 'rb') as f:
params1 = np.fromfile(f, dtype=np.int32, count=3)
data1 = np.fromfile(f, dtype=np.float64)
BxBz = data1[0:params1[0] * params1[1]]
targets = data1[params1[0] * params1[1]::]
BxBz = BxBz.reshape((params1[0], params1[1]))
targets = targets.reshape((params1[0], params1[2]))
with open('%s%s-site-hamil-gs-%s.bin' % (path_to_data, n_sites, train_test), 'rb') as f:
params1 = np.fromfile(f, dtype=np.int32, count=3)
data1 = np.fromfile(f, dtype=np.float64)
Ham = data1[0:params1[0] * params1[1]]
Ham = Ham.reshape((params1[0], params1[1]))
with open('%s%s-site-gs-prior-%s.bin' % (path_to_data, n_sites, train_test), 'rb') as f:
params1 = np.fromfile(f, dtype=np.int32, count=3)
data1 = np.fromfile(f, dtype=np.float64)
eigenvals = data1[params1[0] * (params1[1]**2)::]
eigenvals = eigenvals.reshape((params1[0], params1[1] * params1[2]))
eigenvals = eigenvals[:,0]
eigenvals = eigenvals.reshape((params1[0], 1))
datapoints = params1[0]
return [BxBz, Ham, targets, eigenvals, datapoints]
# ------------> data loader start here <----------------
class DatasetLoader(object):
def __init__(
self,
data_path,
n_sites,
train_size,
val_size,
test_size,
dataset='new'
):
self.dataset = dataset
# store parameters
self.data_path = data_path
self.n_site = n_sites
if dataset == 'old':
# load training data
training_set = getData(
n_sites=n_sites,
path_to_data=data_path,
train_test='train',
dataset=dataset
)
# load test data
test_set = getData(
n_sites=n_sites,
path_to_data=data_path,
train_test='test',
dataset=dataset
)
else:
# load training data
training_set = getData(
n_sites=n_sites,
path_to_data=data_path,
train_test='training',
dataset=dataset
)
# load test data
test_set = getData(
n_sites=n_sites,
path_to_data=data_path,
train_test='testing',
dataset=dataset
)
val_set = getData(
n_sites=n_sites,
path_to_data=data_path,
train_test='validation',
dataset=dataset
)
# interpret training variables
BxBz_val = val_set[0]
Ham_val = val_set[1]
targets_val = val_set[2]
eigenvals_val = val_set[3]
# phased-locked validation dataset: always positive psi_0
self.val_X = Ham_val
self.val_y = np.concatenate((targets_val, eigenvals_val),axis=1)
self.val_y = torch.tensor(self.val_y).float()
self.available_val = Ham_val.shape[0]
self.sign_val = torch.sign(self.val_y[:, 0]).view(-1, 1)
self.val_y[:, :-1] *= self.sign_val
# szdiag
self.szdiag_train = training_set[6]
self.szdiag_val = val_set[6]
self.szdiag_test = test_set[6]
# original tensors
self.nonzero_loc = training_set[5][0]
# interpret training variables
BxBz_train = training_set[0]
Ham_train = training_set[1]
targets_train = training_set[2]
eigenvals_train = training_set[3]
# interpret test variables
BxBz_test = test_set[0]
Ham_test = test_set[1]
targets_test = test_set[2]
eigenvals_test = test_set[3]
# phased-locked training dataset: always positive psi_0
self.train_X = Ham_train
self.train_y = np.concatenate((targets_train, eigenvals_train),axis=1)
self.train_y = torch.tensor(self.train_y).float()
self.available_train = Ham_train.shape[0]
self.sign_train = torch.sign(self.train_y[:, 0]).view(-1, 1)
self.train_y[:, :-1] *= self.sign_train
# phased-locked test dataset: always positive psi_0
self.test_X = Ham_test
self.test_y = np.concatenate((targets_test, eigenvals_test),axis=1)
self.test_y = torch.tensor(self.test_y).float()
self.available_test = Ham_test.shape[0]
self.sign_test = torch.sign(self.test_y[:, 0]).view(-1, 1)
self.test_y[:, :-1] *= self.sign_test
# dimensions
self.x_dim = self.train_X.shape[1]
self.y_dim = self.train_y.shape[1]
self.h_height = n_sites * n_sites
self.h_width = n_sites * n_sites
# sample data
if dataset == 'new':
self.sample_data(train_size, val_size, test_size)
else:
self.sample_data_old(train_size, val_size, test_size)
# create original copy value to protect from normalization
self.X_train_origin = torch.tensor(self.X_train).float()
self.X_val_origin = torch.tensor(self.X_val).float()
self.X_test_origin = torch.tensor(self.X_test).float()
self.y_train_origin = torch.tensor(self.y_train).float()
self.y_val_origin = torch.tensor(self.y_val).float()
self.y_test_origin = torch.tensor(self.y_test).float()
# normalization
self.std_scaler_x = None
self.std_scaler_y = None
self.X_scale = None
self.X_mean = None
self.y_scale = None
self.y_mean = None
# claim tensors
self.X_train_tensor = None
self.y_train_tensor = None
self.X_val_tensor = None
self.y_val_tensor = None
self.X_test_tensor = None
self.y_test_tensor = None
self.X_scale_tensor = None
self.X_mean_tensor = None
self.y_scale_tensor = None
self.y_mean_tensor = None
def normalization(self, x=True, y=True):
# save parameters
self.x_norm = x
self.y_norm = y
# normalize on features
if x:
self.std_scaler_x = StandardScaler()
self.X_train = self.std_scaler_x.fit_transform(self.X_train)
self.X_val = self.std_scaler_x.transform(self.X_val)
self.X_test = self.std_scaler_x.transform(self.X_test)
self.X_scale = | np.array(self.std_scaler_x.scale_) | numpy.array |
import numpy as np
import tensorflow as tf
from tensorflow.python.keras import backend as K
from tensorflow.python.keras.layers import Layer, Lambda
from tensorflow.python.keras.layers import InputSpec
from tensorflow.python.ops import nn_ops
from tensorflow.python.keras import initializers, regularizers, constraints, activations
from tensorflow.python.keras.utils import conv_utils
def gaussian_init(shape, dtype=None, partition_info=None):
v = np.random.randn(*shape)
v = np.clip(v, -3, +3)
return K.constant(v, dtype=dtype)
def conv_init_linear(shape, dtype=None, partition_info=None):
v = np.random.randn(*shape)
v = np.clip(v, -3, +3)
fan_in = | np.prod(shape[:3]) | numpy.prod |
#####################################################################################################################
# more_nodes: This module implements several new nodes and helper functions. It is part of the Cuicuilco framework. #
# #
# These nodes include: BasicAdaptiveCutoffNode, SFA_GaussianClassifier, RandomizedMaskNode, GeneralExpansionNode, #
# PointwiseFunctionNode, RandomPermutationNode #
# #
# By <NAME>. <EMAIL> #
# Ruhr-University-Bochum, Institute for Neural Computation, Group of Prof. Dr. Wiskott #
#####################################################################################################################
from __future__ import absolute_import
from __future__ import print_function
from __future__ import division
import numpy
import scipy
import scipy.optimize
import scipy.stats
from scipy.stats import ortho_group
import copy
import sys
import inspect
import mdp
from mdp.utils import (mult, pinv, symeig, CovarianceMatrix, SymeigException)
from . import sfa_libs
from .sfa_libs import select_rows_from_matrix, distance_squared_Euclidean
# from . import inversion
from .histogram_equalization import *
def add_corrections(initial_corrections, added_corrections):
if initial_corrections is None:
return added_corrections
elif added_corrections is None:
return initial_corrections
else:
return initial_corrections * added_corrections
def combine_correction_factors(flow_or_node, average_over_layers = True, average_inside_layers=False):
"""This function takes into account all corrections performed by the BasicAdaptiveCutoffNodes of
a flow (possibly a hierarchical network) and combines them into a single vector. The function also
works on standard nodes.
average_over_layers: if True, the combined corrections are the average of the corrections of each
node in the flow, otherwise they are multiplied (omitting nodes without corrections)
average_inside_layers: if True, the combined corrections of Layers are computed as the average of
the corrections of each node in the layer, otherwise they are multiplied
The combined correction factor of each sample estimates the probability that it is not an anomaly. That is,
correction=1.0 implies "not anomaly", and smaller values increase the rareness of the sample.
"""
final_corrections = None
final_gauss_corrections = None
if isinstance(flow_or_node, mdp.Flow):
flow = flow_or_node
if average_over_layers:
corrections = []
gauss_corrections = []
for node in flow:
another_node_corrections, another_node_gauss_corrections = combine_correction_factors(node, average_over_layers)
if another_node_corrections is not None:
corrections.append(another_node_corrections)
if another_node_gauss_corrections is not None:
gauss_corrections.append(another_node_gauss_corrections)
if len(corrections) > 0:
corrections = numpy.stack(corrections, axis=1)
final_corrections = corrections.mean(axis=1)
gauss_corrections = numpy.stack(gauss_corrections, axis=1)
final_gauss_corrections = gauss_corrections.mean(axis=1)
else:
final_corrections = None
final_gauss_corrections = None
else:
for node in flow:
another_node_corrections, another_node_gauss_corrections = combine_correction_factors(node)
final_corrections = add_corrections(final_corrections, another_node_corrections)
final_gauss_corrections = add_corrections(final_gauss_corrections, another_node_gauss_corrections)
elif isinstance(flow_or_node, mdp.Node):
node = flow_or_node
if isinstance(node, mdp.hinet.CloneLayer):
err = "CloneLayers not yet supported when computing/storing correction factors"
print(err)
final_corrections = None
final_gauss_corrections = None
# raise Exception(err)
elif isinstance(node, mdp.hinet.Layer):
if average_inside_layers:
corrections = []
gauss_corrections = []
for another_node in node.nodes:
another_node_corrections, another_node_gauss_corrections = combine_correction_factors(another_node)
corrections.append(another_node_corrections)
gauss_corrections.append(another_node_gauss_corrections)
if len(corrections) > 0:
corrections = numpy.stack(corrections, axis=1)
final_corrections = corrections.mean(axis=1)
gauss_corrections = numpy.stack(gauss_corrections, axis=1)
final_gauss_corrections = gauss_corrections.mean(axis=1)
else:
final_corrections = None
final_gauss_corrections = None
else:
for another_node in node.nodes:
another_node_corrections, another_node_gauss_corrections = combine_correction_factors(another_node)
final_corrections = add_corrections(final_corrections, another_node_corrections)
final_gauss_corrections = add_corrections(final_gauss_corrections, another_node_gauss_corrections)
elif isinstance(node, BasicAdaptiveCutoffNode):
final_corrections = add_corrections(final_corrections, node.corrections)
final_gauss_corrections = add_corrections(final_gauss_corrections, node.gauss_corrections)
return final_corrections, final_gauss_corrections
class BasicAdaptiveCutoffNode(mdp.PreserveDimNode):
"""Node that allows to "cut off" values at bounds derived from the training data.
This node is similar to CutoffNode, but the bounds are computed based on the training data. And it is
also similar to AdaptiveCutoffNode, but no histograms are stored and the limits are hard.
This node does not have any have no effect on training data but it corrects atypical variances in test data
and may improve generalization.
"""
def __init__(self, input_dim=None, output_dim=None, num_rotations=1, measure_corrections=False,
only_measure=False, verbose=True, dtype=None):
"""Initialize node. """
super(BasicAdaptiveCutoffNode, self).__init__(input_dim=input_dim, output_dim=output_dim, dtype=dtype)
self.lower_bounds = None
self.upper_bounds = None
self.rotation_matrices = None
self.num_rotations = num_rotations
self.measure_corrections = measure_corrections
self.corrections = None
self.gauss_corrections = None
self.only_measure = only_measure
self.verbose = verbose
self._avg_x = None
self._avg_x_squared = None
self._num_samples = 0
self._std_x = None
if self.verbose:
print("num_rotations:", num_rotations, "measure_corrections:", measure_corrections,
"only_measure:", only_measure, "verbose:", verbose)
@staticmethod
def is_trainable():
return True
@staticmethod
def is_invertible():
return True
@staticmethod
def _get_supported_dtypes():
return (mdp.utils.get_dtypes('Float'))
def _train(self, x):
# initialize rotations and arrays that store the bounds
dim = x.shape[1]
if self.rotation_matrices is None:
self.rotation_matrices = [None] * self.num_rotations
self.lower_bounds = [None] * self.num_rotations
self.upper_bounds = [None] * self.num_rotations
if self.num_rotations >= 1:
self.rotation_matrices[0] = numpy.eye(dim)
for i in range(1, self.num_rotations):
self.rotation_matrices[i] = ortho_group.rvs(dim=dim)
# The training method updates the lower and upper bounds
for i in range(self.num_rotations):
rotated_data = numpy.dot(x, self.rotation_matrices[i])
if self.lower_bounds[i] is None:
self.lower_bounds[i] = rotated_data.min(axis=0)
else:
self.lower_bounds[i] = numpy.minimum(self.lower_bounds[i], rotated_data.min(axis=0))
if self.upper_bounds[i] is None:
self.upper_bounds[i] = rotated_data.max(axis=0)
else:
self.upper_bounds[i] = numpy.maximum(self.upper_bounds[i], rotated_data.max(axis=0))
if self._avg_x is None:
self._avg_x = x.sum(axis=0)
self._avg_x_squared = (x**2).sum(axis=0)
else:
self._avg_x += x.sum(axis=0)
self._avg_x_squared += (x ** 2).sum(axis=0)
self._num_samples += x.shape[0]
def _stop_training(self):
self._avg_x /= self._num_samples
self._avg_x_squared /= self._num_samples
self._std_x = (self._avg_x_squared - self._avg_x **2) ** 0.5
if self.verbose:
print("self._avg_x", self._avg_x)
print("self._avg_x_squared", self._avg_x_squared)
print("self._std_x", self._std_x)
def _execute(self, x):
"""Return the clipped data."""
num_samples = x.shape[0]
self.corrections = numpy.ones(num_samples)
self.gauss_corrections = numpy.ones(num_samples)
if self.only_measure:
x_copy = x.copy()
for i in range(self.num_rotations):
data_rotated = numpy.dot(x, self.rotation_matrices[i])
data_rotated_clipped = numpy.clip(data_rotated, self.lower_bounds[i], self.upper_bounds[i])
if self.measure_corrections:
interval = numpy.abs(self.upper_bounds[i] - self.lower_bounds[i])
delta = numpy.abs(data_rotated_clipped - data_rotated)
# factors = interval ** 2 / (delta + interval) ** 2
norm_delta = delta / interval
factors = 1.0 - (norm_delta / (norm_delta + 0.15)) ** 2
self.corrections *= factors.prod(axis=1) # consider using here and below the mean instead of the product
if self.verbose:
print("Factors of BasicAdaptiveCutoffNode:", factors)
# Computation of Gaussian probabilities
factors = scipy.stats.norm.pdf(x, loc=self._avg_x, scale=4*self._std_x)
if self.verbose:
print("Factors of BasicAdaptiveCutoffNode (gauss):", factors)
print("x.mean(axis=0):", x.mean(axis=0))
print("x.std(axis=0):", x.std(axis=0))
self.gauss_corrections *= factors.prod(axis=1)
x = numpy.dot(data_rotated_clipped, self.rotation_matrices[i].T) # Project back to original coordinates
if self.verbose:
print("Corrections of BasicAdaptiveCutoffNode:", self.corrections)
print("20 worst final corrections at indices:", numpy.argsort(self.corrections)[0:20])
print("20 worst final corrections:", self.corrections[numpy.argsort(self.corrections)[0:20]])
print("Gaussian corrections of BasicAdaptiveCutoffNode:", self.gauss_corrections)
print("20 worst final Gaussian corrections at indices:", numpy.argsort(self.gauss_corrections)[0:20])
print("20 worst final Gaussian corrections:",
self.corrections[numpy.argsort(self.gauss_corrections)[0:20]])
if self.only_measure:
return x_copy
else:
return x
def _inverse(self, x):
"""An approximate inverse applies the same clipping. """
return self.execute(x)
class SFA_GaussianClassifier(mdp.ClassifierNode):
""" This node is a simple extension of the GaussianClassifier node, where SFA is applied before the classifier.
The labels are important, since they are used to order the data samples before SFA.
"""
def __init__(self, reduced_dim=None, verbose=False, **argv):
super(SFA_GaussianClassifier, self).__init__(**argv)
self.gc_node = mdp.nodes.GaussianClassifier()
self.reduced_dim = reduced_dim
if self.reduced_dim > 0:
self.sfa_node = mdp.nodes.SFANode(output_dim=self.reduced_dim)
else:
self.sfa_node = mdp.nodes.IdentityNode()
self.verbose = verbose
def _train(self, x, labels=None):
if self.reduced_dim > 0:
ordering = numpy.argsort(labels)
x_ordered = x[ordering, :]
self.sfa_node.train(x_ordered)
self.sfa_node.stop_training()
if self.verbose:
print("SFA_GaussianClassifier: sfa_node.d = ", self.sfa_node.d)
else: # sfa_node is the identity node
pass
y = self.sfa_node.execute(x)
self.gc_node.train(y, labels=labels)
self.gc_node.stop_training()
def _label(self, x):
y = self.sfa_node.execute(x)
return self.gc_node.label(y)
def regression(self, x, avg_labels, estimate_std=False):
y = self.sfa_node.execute(x)
return self.gc_node.regression(y, avg_labels, estimate_std)
def regressionMAE(self, x, avg_labels):
y = self.sfa_node.execute(x)
return self.gc_node.regressionMAE(y, avg_labels)
def softCR(self, x, true_classes):
y = self.sfa_node.execute(x)
return self.gc_node.softCR(y, true_classes)
def class_probabilities(self, x):
y = self.sfa_node.execute(x)
return self.gc_node.class_probabilities(y)
@staticmethod
def is_trainable():
return True
# using the provided average and standard deviation
def gauss_noise(x, avg, std):
return numpy.random.normal(avg, std, x.shape)
# Zero centered
def additive_gauss_noise(x, std):
return x + numpy.random.normal(0, std, x.shape)
class RandomizedMaskNode(mdp.Node):
"""Selectively mask some components of a random variable by
hiding them with arbitrary noise or by removing them from the feature vector.
This code has been inspired by NoiseNode
"""
def __init__(self, remove_mask=None, noise_amount_mask=None, noise_func=gauss_noise, noise_args=(0, 1),
noise_mix_func=None, input_dim=None, dtype=None):
self.remove_mask = remove_mask
self.noise_amount_mask = noise_amount_mask
self.noise_func = noise_func
self.noise_args = noise_args
self.noise_mix_func = noise_mix_func
self.seen_samples = 0
self.x_avg = None
self.x_std = None
self.type = dtype
if remove_mask is not None and input_dim is None:
input_dim = remove_mask.size
elif remove_mask is None and input_dim is not None:
remove_mask = numpy.zeros(input_dim) > 0.5
elif remove_mask and input_dim is not None:
if remove_mask.size != input_dim:
err = "size of remove_mask and input_dim not compatible"
raise Exception(err)
else:
err = "At least one of input_dim or remove_mask should be specified"
raise Exception(err)
if noise_amount_mask is None:
print ("Signal will be only the computed noise")
self.noise_amount_mask = numpy.ones(input_dim)
else:
self.noise_amount_mask = noise_amount_mask
output_dim = remove_mask.size - remove_mask.sum()
print ("Output_dim should be:", output_dim)
super(RandomizedMaskNode, self).__init__(input_dim=input_dim, output_dim=output_dim, dtype=dtype)
@staticmethod
def is_trainable():
return True
def _train(self, x):
if self.x_avg is None:
self.x_avg = numpy.zeros(self.input_dim, dtype=self.type)
self.x_std = numpy.zeros(self.input_dim, dtype=self.type)
new_samples = x.shape[0]
self.x_avg = (self.x_avg * self.seen_samples + x.sum(axis=0)) / (self.seen_samples + new_samples)
self.x_std = (self.x_std * self.seen_samples + x.std(axis=0) * new_samples) / (self.seen_samples + new_samples)
self.seen_samples = self.seen_samples + new_samples
@staticmethod
def is_invertible():
return False
def _execute(self, x):
print ("computed X_avg=", self.x_avg)
print ("computed X_std=", self.x_std)
noise_mat = self.noise_func(x, self.x_avg, self.x_std)
# noise_mat = self._refcast(self.noise_func(*self.noise_args,
# **{'size': x.shape}))
print ("Noise_amount_mask:", self.noise_amount_mask)
print ("Noise_mat:", noise_mat)
noisy_signal = (1.0 - self.noise_amount_mask) * x + self.noise_amount_mask * noise_mat
preserve_mask = (self.remove_mask == False)
return noisy_signal[:, preserve_mask]
class GeneralExpansionNode(mdp.Node):
def __init__(self, funcs, input_dim=None, dtype=None, \
use_pseudoinverse=True, use_hint=False, output_dim=None, starting_point=None, use_special_features=False, max_steady_factor=1.5,
delta_factor=0.6, min_delta=0.00001, verbose=False):
self.funcs = funcs
self.exp_output_dim = output_dim
self.expanded_dims = None
self.starting_point = starting_point
self.use_special_features = use_special_features
if self.funcs == "RandomSigmoids" and self.exp_output_dim <= 0:
er = "output_dim in GeneralExpansion node with RandomSigmoids should be at least 1, but is" + \
str(self.exp_output_dim)
raise Exception(er)
self.use_pseudoinverse = use_pseudoinverse
self.use_hint = use_hint
self.max_steady_factor = max_steady_factor
self.delta_factor = delta_factor
self.min_delta = min_delta
self.verbose = verbose
if self.verbose:
print("GeneralExpansionNode with expansion functions:", funcs)
self.rs_coefficients = None
self.rs_offsets = None
self.rs_data_training_std = None
self.rs_data_training_mean = None
self.normalization_constant = None
super(GeneralExpansionNode, self).__init__(input_dim, dtype)
def expanded_dim(self, n):
exp_dim = 0
x = numpy.zeros((1, n))
for func in self.funcs:
outx = func(x)
# print "outx= ", outx
exp_dim += outx.shape[1]
return exp_dim
def output_sizes(self, n):
if self.funcs == "RandomSigmoids":
sizes = [self.exp_output_dim]
else:
sizes = numpy.zeros(len(self.funcs), dtype=int)
x = numpy.zeros((1, n))
for i, func in enumerate(self.funcs):
outx = func(x)
sizes[i] = outx.shape[1]
print ("S", end="")
return sizes
def is_trainable(self):
if self.funcs == "RandomSigmoids":
return True
else:
return False
def _train(self, x, verbose=None):
if verbose is None:
verbose = self.verbose
if self.input_dim is None:
self.set_input_dim(x.shape[1])
input_dim = self.input_dim
# Generate functions used for regression
self.rs_data_training_mean = x.mean(axis=0)
self.rs_data_training_std = x.std(axis=0)
if verbose:
print ("GeneralExpansionNode: output_dim=", self.output_dim, end="")
starting_point = self.starting_point
c1, l1 = generate_random_sigmoid_weights(self.input_dim, self.output_dim)
if starting_point == "Identity":
if verbose:
print ("starting_point: adding (encoded) identity coefficients to expansion")
c1[0:input_dim, 0:input_dim] = numpy.identity(input_dim)
l1[0:input_dim] = numpy.ones(input_dim) * 1.0 # Code identity
elif starting_point == "Sigmoids":
if verbose:
print ("starting_point: adding sigmoid of coefficients to expansion")
c1[0:input_dim, 0:input_dim] = 4.0 * numpy.identity(input_dim)
l1[0:input_dim] = numpy.ones(input_dim) * 0.0
elif starting_point == "08Exp":
if verbose:
print ("starting_point: adding (encoded) 08Exp coefficients to expansion")
c1[0:input_dim, 0:input_dim] = numpy.identity(input_dim)
c1[0:input_dim, input_dim:2 * input_dim] = numpy.identity(input_dim)
l1[0:input_dim] = numpy.ones(input_dim) * 1.0 # Code identity
l1[input_dim:2 * input_dim] = numpy.ones(input_dim) * 0.8 # Code abs(x)**0.8
elif starting_point == "Pseudo-Identity":
if verbose:
print ("starting_point: adding pseudo-identity coefficients to expansion")
c1[0:input_dim, 0:input_dim] = 0.1 * numpy.identity(input_dim)
l1[0:input_dim] = numpy.zeros(input_dim) # nothig is encoded
elif starting_point is None:
if verbose:
print ("starting_point: no starting point")
else:
er = "Unknown starting_point", starting_point
raise Exception(er)
self.rs_coefficients = c1
self.rs_offsets = l1
# 4.0 was working fine, 2.0 was apparently better. This also depends on how many features are computed!!!
self.normalization_constant = (2.0 / self.input_dim) ** 0.5
def is_invertible(self):
return self.use_pseudoinverse
def inverse(self, x, use_hint=None, max_steady_factor=None, delta_factor=None, min_delta=None):
if self.use_pseudoinverse is False:
ex = "Inversion not activated"
raise Exception(ex)
if use_hint is None:
use_hint = self.use_hint
if max_steady_factor is None:
max_steady_factor = self.max_steady_factor
if delta_factor is None:
delta_factor = self.delta_factor
if min_delta is None:
min_delta = self.min_delta
# print "Noisy pre = ", x, "****************************************************"
app_x_2, app_ex_x_2 = invert_exp_funcs2(x, self.input_dim, self.funcs, use_hint=use_hint,
max_steady_factor=max_steady_factor, delta_factor=delta_factor,
min_delta=min_delta)
# print "Noisy post = ", x, "****************************************************"
return app_x_2
def _set_input_dim(self, n):
self._input_dim = n
if self.funcs == "RandomSigmoids":
self._output_dim = self.exp_output_dim
else:
self._output_dim = self.expanded_dim(n)
self.expanded_dims = self.output_sizes(n)
def _execute(self, x):
if self.input_dim is None:
self.set_input_dim(x.shape[1])
if "expanded_dims" not in self.__dict__:
self.expanded_dims = self.output_sizes(self.input_dim)
if self.funcs != "RandomSigmoids":
num_samples = x.shape[0]
# output_dim = expanded_dim(self.input_dim)
# self.expanded_dims = self.output_sizes(self.input_dim)
out = numpy.zeros((num_samples, self.output_dim))
current_pos = 0
for i, func in enumerate(self.funcs):
out[:, current_pos:current_pos + self.expanded_dims[i]] = func(x)
current_pos += self.expanded_dims[i]
else:
data_norm = self.normalization_constant * (x - self.rs_data_training_mean) / self.rs_data_training_std
# A variation of He random weight initialization
out = extract_sigmoid_features(data_norm, self.rs_coefficients, self.rs_offsets, scale=1.0, offset=0.0,
use_special_features=self.use_special_features)
return out
class PointwiseFunctionNode(mdp.Node):
""""This node applies a function to the whole input.
It also supports a given 'inverse' function.
"""
def __init__(self, func, inv_func, input_dim=None, dtype=None):
self.func = func
self.inv_func = inv_func
super(PointwiseFunctionNode, self).__init__(input_dim, dtype)
@staticmethod
def is_trainable():
return False
def is_invertible(self):
if self.inv_func is None:
return True
else:
return False
def inverse(self, x):
if self.inv_func:
return self.inv_func(x)
else:
return x
def _set_input_dim(self, n):
self._input_dim = n
self._output_dim = n
def _execute(self, x):
if self.input_dim is None:
self.set_input_dim(x.shape[1])
if self.func:
return self.func(x)
else:
return x
class PairwiseAbsoluteExpansionNode(mdp.Node):
def expanded_dim(self, n):
return n + n * (n + 1) // 2
def is_trainable(self):
return False
def is_invertible(self):
return False
def _set_input_dim(self, n):
self._input_dim = n
self._output_dim = self.expanded_dim(n)
def _execute(self, x):
out = numpy.concatenate((x, pairwise_expansion(x, abs_sum)), axis=1)
return out
# TODO:ADD inverse type sum, suitable for when output_scaling is True
class PInvSwitchboard(mdp.hinet.Switchboard):
"""This node is a variation of the RectangularSwitchboard that facilitates (approximate) inverse operations. """
def __init__(self, input_dim, connections, slow_inv=False, type_inverse="average", output_scaling=True,
additive_noise_std=0.00004, verbose=False):
super(PInvSwitchboard, self).__init__(input_dim=input_dim, connections=connections)
self.pinv = None
self.mat2 = None
self.slow_inv = slow_inv
self.type_inverse = type_inverse
self.output_dim = len(connections)
self.output_scales = None
self.additive_noise_std = additive_noise_std
self.verbose = verbose
if verbose:
print ("self.inverse_connections=", self.inverse_connections, "self.slow_inv=", self.slow_inv)
# WARNING! IF/ELIF doesn't make any sense! what are the semantics of inverse_connections
if self.inverse_connections is None:
if verbose:
print ("type(connections)", type(connections))
all_outputs = numpy.arange(self.output_dim)
self.inverse_indices = [[]] * self.input_dim
for i in range(self.input_dim):
self.inverse_indices[i] = all_outputs[connections == i]
# print "inverse_indices[%d]="%i, self.inverse_indices[i]
# print "inverse_indices =", self.inverse_indices
elif self.inverse_connections is None and not self.slow_inv:
index_array = numpy.argsort(connections)
value_array = connections[index_array]
value_range = numpy.zeros((input_dim, 2))
self.inverse_indices = range(input_dim)
for i in range(input_dim):
value_range[i] = numpy.searchsorted(value_array, [i - 0.5, i + 0.5])
if value_range[i][1] == value_range[i][0]:
self.inverse_indices[i] = []
else:
self.inverse_indices[i] = index_array[value_range[i][0]: value_range[i][1]]
if verbose:
print ("inverse_indices computed in PINVSB")
elif self.inverse_connections is None and self.slow_inv:
if verbose:
print ("warning using slow inversion in PInvSwitchboard!!!")
# find input variables not used by connections:
used_inputs = numpy.unique(connections)
used_inputs_set = set(used_inputs)
all_inputs_set = set(range(input_dim))
unused_inputs_set = all_inputs_set - all_inputs_set.intersection(used_inputs_set)
unused_inputs = list(unused_inputs_set)
self.num_unused_inputs = len(unused_inputs)
# extend connections array
# ext_connections = numpy.concatenate((connections, unused_inputs))
# create connections matrix
mat_height = len(connections) + len(unused_inputs)
mat_width = input_dim
mat = numpy.zeros((mat_height, mat_width))
# fill connections matrix
for i in range(len(connections)):
mat[i, connections[i]] = 1
#
for i in range(len(unused_inputs)):
mat[i + len(connections), unused_inputs[i]] = 1
#
if verbose:
print ("extended matrix is:", mat)
# compute pseudoinverse
mat2 = numpy.matrix(mat)
self.mat2 = mat2
self.pinv = (mat2.T * mat2).I * mat2.T
else:
if verbose:
print ("Inverse connections already given, in PInvSwitchboard")
if output_scaling:
if self.inverse_connections is None and not self.slow_inv:
if verbose:
print ("**A", end="")
if self.type_inverse != "average":
err = "self.type_inverse not supported " + self.type_inverse
raise Exception(err)
self.output_scales = | numpy.zeros(self.output_dim) | numpy.zeros |
from __future__ import print_function, division
import matplotlib
#matplotlib.use('Agg')
import numpy as np
import scipy as sp
from operator import truediv
import math, time
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from itertools import groupby
import sisl as si
from numbers import Integral
# I don't know why, but the lines below were
# fucking up my routine "makeTB_FrameOutside", on the "contruct" command
#try:
# from itertools import izip as zip
#except:
# pass
def dagger(M):
return np.conjugate(np.transpose(M))
def displaySparse(m, filename, dpi=300):
if not isinstance(m, sp.sparse.coo_matrix):
m = sp.sparse.coo_matrix(m)
fig = plt.figure()
ax = fig.add_subplot(111, axisbg='black')
ax.plot(m.col, m.row, 's', color='white', ms=10)
ax.set_xlim(0, m.shape[1])
ax.set_ylim(0, m.shape[0])
ax.set_aspect('equal')
for spine in ax.spines.values():
spine.set_visible(False)
ax.invert_yaxis()
ax.set_aspect('equal')
ax.set_xticks([])
ax.set_yticks([])
plt.savefig(filename, facecolor='black', edgecolor='black', dpi=dpi)
return ax
def get_potential(TSHS, iio, atoms):
"""
iio: index (0-based) of orbital in basis set (i.e., pz in SZP: iio = 2)
"""
orbs = TSHS.a2o(atoms)+iio
on = TSHS.Hk(dtype=np.float64, format='array')[orbs, orbs]
return on
def check_Dirac(ts, mp, displacement=[0,0,0]):
mp = si.MonkhorstPack(ts, mp, displacement=displacement)
print('Check that Dirac is in here: ')
print(mp.k)
print('Check that this is in *.KP file : {}'.format(mp.tocartesian([0., 1./3, 0]) * si.unit.siesta.unit_convert('Bohr', 'Ang')))
i_dirac = (np.logical_and(mp.k[:,1] == 1./3, mp.k[:,0] == 0.)).nonzero()[0]
if len(i_dirac) != 1:
print('Dirac point is not in the grid')
exit(1)
else:
print('Dirac point is at kindex: {}'.format(i_dirac[0]))
def get_Dirac(hs, mp, displacement=[0,0,0]):
#check_Dirac(hs.geom, mp, displacement)
ens_dirac = hs.eigh(k=[0., 1./3, 0])
i_dirac = hs.na * 2 - 1
return np.average(ens_dirac[i_dirac:i_dirac+2])
def plot_PotDiff(TSHS, TSHS_0, ia, axis, iio, o_dev, o_inner): # include option for frame!
on, yy, atoms = get_potential(TSHS, ia, axis, iio)
on0 = get_potential(TSHS_0, ia, axis, iio)[0]
on0 = np.array([np.mean(on0)]*len(on))
# Check
print('y (Ang)\t\tPot (eV)\tPot0 (eV)\tPot-Pot0 (eV)')
a_dev = TSHS.o2a(o_dev, unique=True)
a_inner = TSHS.o2a(o_inner, unique=True)
for iia, y, o, o0 in zip(atoms, yy, on, on0):
if iia in a_inner:
print('{:7.4f}\t\t{:7.4f}\t\t{:7.4f}\t\t{:7.4f}\t\t(inner)'.format(y,o,o0,o-o0))
else:
print('{:7.4f}\t\t{:7.4f}\t\t{:7.4f}\t\t{:7.4f}'.format(y,o,o0,o-o0))
# Subtract pristine potential
PotDiff = on-on0
# Write to file
with open('PotDiff.dat', 'w') as pf:
for yc, pd in zip(yy, PotDiff):
pf.write('{}\t\t{}\n'.format(yc, pd))
# Plot
figure()
plot(yy, PotDiff, 'b')
md, Md = np.amin(TSHS.xyz[a_dev, axis]), np.amax(TSHS.xyz[a_dev, axis])
axvline(md, color='k', linestyle='dashed', linewidth=2)
axvline(Md, color='k', linestyle='dashed', linewidth=2)
tmp_dev = TSHS.geom.sub(a_dev); tmp_inner = tmp_dev.sub(a_inner)
mi, Mi = np.amin(tmp_inner.xyz[a_inner, axis]), np.amax(tmp_inner.xyz[a_inner, axis])
axvspan(mi, Mi, alpha=0.3, facecolor='blue', edgecolor='none')
ylabel(r'$H_{p_z}-H^0_{p_z}\, (e{\rm V})$', fontsize=20)
xlabel(r'$y\, (\AA)$', fontsize=20)
xlim(0, TSHS.cell[axis, axis])
#xlim(TSHS.center(what='cell')[1], TSHS.cell[1,1])
legend(loc=0); savefig('PotDiff.pdf', bbox_inches='tight')
def get_potential_profile(TSHS, ia, axis, iio):
"""
ia: atom crossed by the line
axis: direction of the line
iio: index (0-based) of orbital in basis set (i.e., pz in SZP: iio = 2)
"""
# Find atoms in line passing by center of
xyz0, xyz = TSHS.xyz[ia, axis%1], TSHS.xyz[:, axis%1]
atoms = np.where(np.logical_and(xyz0-1.43 < xyz, xyz < xyz0+1.43))[0]
v = TSHS.geom.copy(); v.atom[atoms] = si.Atom(8, R=[1.43]); v.write('checkPot.xyz')
orbs = TSHS.a2o(atoms)+iio
on = TSHS.Hk(dtype=np.float64, format='array')[orbs, orbs]
ylist = TSHS.xyz[atoms, axis]
idxs = np.argsort(ylist)
on, ylist = on[idxs], ylist[idxs]
return on, ylist, atoms
def xyz2polar(tbt, origin=0):
na = tbt.na
# radii from origin
if isinstance(origin, Integral):
origin = tbt.xyz[origin]
_, r = tbt.geom.close_sc(origin, R=np.inf, ret_rij=True)
# angles from origin
transl = tbt.geom.translate(-origin)
y = transl.xyz[:,1]
i_ypos = np.where(y >= 0)[0]
i_yneg = np.setdiff1d(np.arange(na), i_ypos)
t = np.zeros(na)
t[i_ypos] = transl.angle(i_ypos, dir=(1., 0, 0), rad=True)
t[i_yneg] = transl.angle(i_yneg, dir=(-1., 0, 0), rad=True) +np.pi
return r, t
def radial_T_from_bc(tbt, elec, E=None, kavg=True,
origin=0, thetamin=0., thetamax=2*np.pi, ntheta=360,
Rmin=5., Rmax=999999999, dr=40.,
input=None, save='radial_T_from_bc.txt', saveinput='rt.txt'):
if E:
Eidx = tbt.Eindex(E)
en = tbt.E[Eidx]
else:
en = tbt.E[0]
print('Using E = {} eV'.format(en))
na = tbt.na
if isinstance(origin, Integral):
origin = tbt.xyz[origin]
# (x, y) ----> (r, t)
if input:
r, t = np.loadtxt(input, delimiter='\t', usecols=(1, 2), unpack=True, skiprows=1)
else:
r, t = xyz2polar(tbt, origin=origin)
f = open(saveinput, 'w')
f.write('ia\tr (Angstrom)\tangle (radians; center {})\n'.format(origin))
for ia, rr, tt in zip(np.arange(na), r, t):
f.write('{}\t{}\t{}\n'.format(ia, rr, tt))
f.close()
print('(x,y) ---> (r,t): DONE')
# theta bins
thetas = | np.linspace(thetamin, thetamax, ntheta, endpoint=False) | numpy.linspace |
from .helpers import quat_inv_trans, quat_trans, check_filepath, import_value, quat_mult, quat_conj, quat_to_euler, euler_to_quat
from .airplane import Airplane
from .standard_atmosphere import StandardAtmosphere
from .exceptions import SolverNotConvergedError
import json
import time
import copy
import warnings
import numpy as np
import math as m
import scipy.interpolate as sinterp
import scipy.optimize as sopt
import matplotlib.pyplot as plt
from stl import mesh
from mpl_toolkits.mplot3d import Axes3D
from airfoil_db import DatabaseBoundsError
class Scene:
"""A class defining a scene containing one or more aircraft.
Parameters
----------
scene_input : string or dict, optional
Dictionary or path to the JSON object specifying the scene parameters (see
'Creating Input Files for MachUp'). If not specified, all default values are chosen.
Raises
------
IOError
If input filepath or filename is invalid
"""
def __init__(self, scene_input={}):
# Initialize basic storage objects
self._airplanes = {}
self._N = 0
self._num_aircraft = 0
# Track whether the scene in its current state has been solved
# Should be set to False any time any state variable is changed without immediately thereafter calling solve_forces()
self._solved = False
# Import information from the input
self._load_params(scene_input)
# Set the error handling state
self.set_err_state()
def _load_params(self, scene_input):
# Loads JSON object and stores input parameters and aircraft
# File
if isinstance(scene_input, str):
check_filepath(scene_input,".json")
with open(scene_input) as input_json_handle:
self._input_dict = json.load(input_json_handle)
# Dictionary
elif isinstance(scene_input, dict):
self._input_dict = copy.deepcopy(scene_input)
# Input format not recognized
else:
raise IOError("Input to Scene class initializer must be a file path or Python dictionary, not type {0}.".format(type(scene_input)))
# Store solver parameters
solver_params = self._input_dict.get("solver", {})
self._solver_type = solver_params.get("type", "nonlinear")
self._solver_convergence = solver_params.get("convergence", 1e-10)
self._solver_relaxation = solver_params.get("relaxation", 1.0)
self._max_solver_iterations = solver_params.get("max_iterations", 100)
self._use_swept_sections = solver_params.get("use_swept_sections", True)
self._use_total_velocity = solver_params.get("use_total_velocity", True)
self._use_in_plane = solver_params.get("use_in_plane", True)
self._match_machup_pro = solver_params.get("match_machup_pro", False)
self._impingement_threshold = solver_params.get("impingement_threshold", 1e-10)
# Store unit system
self._unit_sys = self._input_dict.get("units", "English")
# Setup atmospheric property getter functions
scene_dict = self._input_dict.get("scene", {})
atmos_dict = scene_dict.get("atmosphere", {})
self._std_atmos = StandardAtmosphere(unit_sys=self._unit_sys)
self._get_density = self._initialize_density_getter(**atmos_dict)
self._get_wind = self._initialize_wind_getter(**atmos_dict)
self._get_viscosity = self._initialize_viscosity_getter(**atmos_dict)
self._get_sos = self._initialize_sos_getter(**atmos_dict)
# Initialize aircraft geometries
aircraft_dict = scene_dict.get("aircraft", {})
for key in aircraft_dict:
# Get inputs
airplane_file = self._input_dict["scene"]["aircraft"][key]["file"]
state = self._input_dict["scene"]["aircraft"][key].get("state",{})
control_state = self._input_dict["scene"]["aircraft"][key].get("control_state",{})
# Instantiate
self.add_aircraft(key, airplane_file, state=state, control_state=control_state)
def _initialize_density_getter(self, **kwargs):
# Load value from dictionary
default_density = self._std_atmos.rho(0.0)
rho = import_value("rho", kwargs, self._unit_sys, default_density)
# Constant value
if isinstance(rho, float):
self._constant_rho = rho
def density_getter(position):
return self._constant_rho
# Atmospheric table name
elif isinstance(rho, str):
# Profile
if not rho in ["standard"]:
raise IOError("{0} is not an allowable profile name.".format(rho))
def density_getter(position):
pos = position.T
return self._std_atmos.rho(-pos[2])
# Array
elif isinstance(rho, np.ndarray):
self._density_data = rho
# Create getters
if self._density_data.shape[1] == 2: # Density profile
def density_getter(position):
pos = position.T
return np.interp(-pos[2], self._density_data[:,0], self._density_data[:,1])
elif self._density_data.shape[1] == 4: # Density field
self._density_field_interpolator = sinterp.LinearNDInterpolator(self._density_data[:,:3],self._density_data[:,3])
def density_getter(position):
return self._density_field_interpolator(position)
# Improper specification
else:
raise IOError("Density improperly specified as {0}.".format(rho))
return density_getter
def _initialize_wind_getter(self, **kwargs):
# Load value from dict
default_wind = [0.0, 0.0, 0.0]
V_wind = import_value("V_wind", kwargs, self._unit_sys, default_wind)
# Store wind
if isinstance(V_wind, np.ndarray):
if V_wind.shape == (3,): # Constant wind vector
self._constant_wind = V_wind
def wind_getter(position):
return self._constant_wind*np.ones(position.shape)
else: # Array
self._wind_data = V_wind
# Create getters
if self._wind_data.shape[1] == 6: # Wind field
self._wind_field_x_interpolator = sinterp.LinearNDInterpolator(self._wind_data[:,:3], self._wind_data[:,3], fill_value=0.0)
self._wind_field_y_interpolator = sinterp.LinearNDInterpolator(self._wind_data[:,:3], self._wind_data[:,4], fill_value=0.0)
self._wind_field_z_interpolator = sinterp.LinearNDInterpolator(self._wind_data[:,:3], self._wind_data[:,5], fill_value=0.0)
def wind_getter(position):
single = len(position.shape)==1
Vx = self._wind_field_x_interpolator(position)
Vy = self._wind_field_y_interpolator(position)
Vz = self._wind_field_z_interpolator(position)
if single:
return np.array([Vx.item(), Vy.item(), Vz.item()])
else:
return | np.array([Vx, Vy, Vz]) | numpy.array |
import numpy as np
from baselines.deepq.experiments.atari.knn_cuda import knn as knn_cuda
# each action -> a lru_knn buffer
class LRU_KNN_UCB_GPU(object):
def __init__(self, capacity, z_dim, env_name, action, mode="mean", num_actions=6,knn=4):
self.action = action
self.knn = knn
self.env_name = env_name
self.capacity = capacity
self.num_actions = num_actions
self.states = np.empty((capacity, z_dim), dtype=np.float32)
self.q_values_decay = np.zeros(capacity)
self.count = np.zeros(capacity)
self.lru = np.zeros(capacity)
self.best_action = np.zeros((capacity, num_actions), dtype=np.int)
self.curr_capacity = 0
self.tm = 0.0
self.addnum = 0
self.buildnum = 256
self.buildnum_max = 256
self.bufpath = './buffer/%s' % self.env_name
self.mode = mode
self.threshold = 1e-2
def peek(self, key, value_decay, action=-1, modify=False):
if self.curr_capacity ==0 :
return None, None, None
dist, ind = knn_cuda.knn(np.transpose(np.array([key])), np.transpose(self.states[:self.curr_capacity]), 1)
dist, ind = np.transpose(dist), np.transpose(ind - 1)
ind = ind[0][0]
# print(dist.shape,ind.shape)
if dist[0][0] < self.threshold:
# print("peek success")
self.lru[ind] = self.tm
self.tm += 0.01
if modify:
if self.mode == "max":
if value_decay > self.q_values_decay[ind]:
self.q_values_decay[ind] = value_decay
if action >= 0:
self.best_action[ind, action] = 1
elif self.mode == "mean":
self.q_values_decay[ind] = (value_decay + self.q_values_decay[ind] * self.count[ind]) / (
self.count[ind] + 1)
self.count[ind] += 1
return self.q_values_decay[ind], self.best_action[ind], self.count[ind]
# print self.states[ind], key
# if prints:
# print("peek", dist[0][0])
return None, None, None
def knn_value(self, key, knn, ):
# knn = min(self.curr_capacity, knn)
if self.curr_capacity < knn:
return 0.0, None, 1.0
dist, ind = knn_cuda.knn(np.transpose(key), np.transpose(self.states[:self.curr_capacity]), knn)
dist, ind = np.transpose(dist), np.transpose(ind - 1)
coeff = np.exp(dist[0])
coeff = coeff / np.sum(coeff)
value = 0.0
action = np.zeros((self.num_actions,))
value_decay = 0.0
count = 0
# print("nearest dist", dist[0][0])
for j, index in enumerate(ind[0]):
value_decay += self.q_values_decay[index] * coeff[j]
count += self.count[index] * coeff[j]
action += self.best_action[index] * coeff[j]
self.lru[index] = self.tm
self.tm += 0.01
q_decay = value_decay
return q_decay, action, count
def act_value(self, key, knn):
# knn = min(self.curr_capacity, knn)
values = []
actions = np.zeros((len(key), self.num_actions))
counts = []
exact_refer = []
if self.curr_capacity < knn:
for i in range(len(key)):
actions[i, self.action] = 1
values.append(0)
counts.append(1)
exact_refer.append(False)
return values, actions, counts, np.array(exact_refer)
dist, ind = knn_cuda.knn(np.transpose(key), np.transpose(self.states[:self.curr_capacity]), knn)
dist, ind = | np.transpose(dist) | numpy.transpose |
"""
A module defining routines for creating antenna array configurations. Input arguments for each function are
arbitrary, but the return value is always a dictionary with keys representing antenna numbers, and values
giving the 3D position of each antenna.
"""
from __future__ import division
from __future__ import unicode_literals
from __future__ import print_function
from __future__ import absolute_import
from future import standard_library
standard_library.install_aliases()
# from builtins import *
import numpy as np
from builtins import range
def linear_array(nants, sep=14.6):
"""
Build a linear (east-west) array configuration.
Args:
nants (int): the number of antennas in the configuration.
sep (float): the separation between linearly spaced antennas (meters).
Returns:
dict: A dictionary of antenna numbers and positions. Positions are x,y,z
in topocentric coordinates, in meters.
"""
antpos = {i: | np.array([sep * i, 0, 0]) | numpy.array |
# -*- coding: utf-8 -*-
"""
editeur de Spyder
Ceci est un script temporaire.
"""
import numpy as np
import pandas as pd
import json
from pprint import pprint
File = {"Profiles" : { "Academie" : [60000, 30000, 40000], "Departement" : [5, 6, 7], "Dernier" : [80, 90, 100] },
"Content" : {"Academie" : [2000, 3000, 4000], "Departement" : [5, 6, 7], "Dernier" : [8, 9, 10] },
"Param" : {"maximiser" : ["1", "1", "0"], "norm" : ["1000", "1", "20"], "nbProfiles" : ["0"], "N" : ["3"], "mu_ij" : [.1, .3, .4], "mu_i" : [5, 6, 7], "poids" : [8, 9, 10] },
"Method" : "1"
}
def read_params(File) :
utilite = 0 #fonction par defaut (a definir)
poids = None
mu_i = None
mu_ij = None
columns = None
N = 0 #Ce parametre doit etre renseigne avant mu_ij
Lambda = 0
norm = None
nbProfiles = None
maximiser = None
params = File['Param']
for param_c, value_param in params.items() :
#param_c = p.split(';')
#Nombre de criteres
if (param_c == 'N') :
N = int(value_param[0])
#Nombre de criteres
if (param_c == 'nbProfiles') :
nbProfiles = int(value_param[0])
#lambda
if (param_c == 'lambda') :
Lambda = float(value_param[0])
#Poids
if ((param_c == 'poids') or (param_c == 'poids_2') or (param_c == 'w') or (param_c == 'v')) :
poids = []
for x in value_param :
if(x != ''):
poids = poids + [float(x)]
#colonne
if ((param_c == 'colonne') or (param_c == 'cols') or (param_c == 'columns')) :
columns = []
for x in value_param :
columns = columns + [float(x)]
#Utilite
if ((param_c == 'utilite') or (param_c == 'u')) :
utilite = int(value_param[0])
#norm
if (param_c == 'norm') :
norm = []
for x in value_param :
if(x != ''):
norm = norm + [float(x)]
#mu_i
if (param_c == 'mu_i') :
mu_i = []
for x in value_param :
if(x != ''):
mu_i = mu_i + [float(x)]
#maximiser
if (param_c == 'maximiser') :
maximiser = []
for x in value_param :
if(x != ''):
maximiser = maximiser + [int(x)]
if (param_c == 'mu_ij') :
N = int(params["N"][0])
mu_ij = np.zeros((N, N))
idx = 0
for i in range(0, N - 1) :
for j in range(i + 1, N) :
mu_ij[i, j] = float(value_param[idx])
mu_ij[j, i] = mu_ij[i, j]
idx = idx + 1
#print(mu_ij)
return (utilite, poids, mu_i, mu_ij, columns, N, Lambda, norm, nbProfiles, maximiser)
#read_params(File)
def I_ij(i, j, mu_i, mu_ij, N) :
#print(mu_ij[i, j] , mu_i[i], mu_i[j])
return 0 if (i == j) else mu_ij[i, j] - mu_i[i] - mu_i[j]
def V_i(i, mu_i, mu_ij, N) :
tmp_I = [I_ij(i, j, mu_i, mu_ij, N) for j in range(0, N) if (j != i)]
tmp_I = np.array(tmp_I).sum()
return mu_i[i] - .5 * tmp_I
def v(mu_i, mu_ij, N) :
"""Calcule le tableau V[i]"""
return [V_i(i, mu_i, mu_ij, N) for i in range (0, N)]
def i(mu_i, mu_ij, N) :
"""Calcule le tableau I[i, j]"""
return [[I_ij(i, j, mu_i, mu_ij, N) for j in range(0, N)] for i in range(0, N)]
def valide_N(N) :
""" Valide si N >= 2"""
return N > 2
def valide_I(I) :
"""Valide si I[i, j] >= 0"""
return np.all(np.all((I >= 0) & (I <= 1), axis=1))
def valide_V(V) :
"""Valide si V appartient a [0, 1] et somme(V[i]) = 1"""
return np.all((V >= 0) & (V <= 1)) and (V.sum() == 1)
def valide_Lambda(Lambda) :
""" Valide si Lambda est entre .5 et 1"""
return (Lambda >= .5) and (Lambda < 1)
def valide_poids(poids) :
poids = np.array(poids)
return | np.all((poids >= 1) & (poids <= 10)) | numpy.all |
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# pylint: disable=method-hidden,C0103,E265,E303,R0914,W0621,W503
"""Module describing the weighted non-linear optimization scheme used to
determine the wavelength sensitivity of the spectrometer using a polynomial
as a model function"""
import os
import sys
import math
import logging
from datetime import datetime
import numpy as np
import scipy.optimize as opt
import matplotlib.pyplot as plt
import compute_series_para
import boltzmann_popln as bp
# ------------------------------------------------------
# ------------------------------------------------------
# RUN PARAMETERS (CHANGE THESE BEFORE RUNNING
# OPTIMIZATION
# ------------------------------------------------------
# LOAD EXPERIMENTAL BAND AREA DATA
# | band area | error |
# | value | value |
# | value | value |
# | value | value |
# without header in the following files
# Change following paths to load expt data
#xaxis = np.loadtxt("Ramanshift_axis")
# Q(J) band intensities --------------------------------
dataD2Q = np.loadtxt("BA_D2_q1.txt")
dataHDQ = np.loadtxt("BA_HD_q1.txt")
dataH2Q = np.loadtxt("BA_H2_q1.txt")
dataD2_Q2 = np.loadtxt("D2_Q2_testdata")
dataD2Q4 = np.loadtxt("BA_D2_q1_J4.txt")
dataD2OS = np.loadtxt("D2_model_O2S0")
# ------------------------------------------------------
# PARALLEL POLARIZATION
# set indices for OJ,QJ and SJ for H2, HD and D2 in the residual functions below
# ------------------------------------------------------
# ----------------------------------------
# norm type
# Do not change the variable name on the LHS
# available norm types : Frobenius, Frobenius_sq, absolute
# lower case : frobenius, frobenius_sq, absolute
# or abbreviations: F , FS , A
norm = 'Frobenius'
# if norm is not set then the default is sum of absolute values
# See readme for more details
# ----------------------------------------
print('Dimension of input data of Q bands')
print('\t', dataH2Q.shape)
print('\t', dataHDQ.shape)
print('\t', dataD2Q.shape)
print('\t', dataD2_Q2.shape)
print('\t', dataD2Q4.shape)
print('\t', dataD2OS.shape)
# ------------------------------------------------------
# SET INIT COEFS
temp_init = np.zeros((1))
temp_init[0] = 296
# initial run will be with above parameters
# ------------------------------------------------
# ------------------------------------------------------
print('\t**********************************************************')
print('\t ')
print('\t This module is for determining the temperature from ')
print('\t observed vibration-rotation Raman intensities of H2, HD and D2. ')
print('\t This module is useful for testing the accuracy of the intensity ')
print('\t calibration procedure. ')
print('\n\t >> Ratios of all observed Raman intensities are treated here as a matrix. << ')
print('\n\t >> This function deals with parallel polarized intensities. << ')
print('\n\t >> Temperature is the only fit parameter here << ')
print('\n\t This modeule requires edit on line 32 to 74 to ')
print('\n\t load and set parameters for the analysis.')
print('\t ')
print('\t**********************************************************')
print('\n\t\t Checking imported data and set params')
data_error=0
if isinstance(dataH2Q, np.ndarray):
print("\t\t ", "dataH2Q found, OK")
else:
print("\t\t ", "dataH2Q not found.")
data_error=1
if isinstance(dataHDQ, np.ndarray):
print("\t\t ", "dataHDQ found, OK")
else:
print("\t\t ", "dataHDQ not found.")
data_error=1
if isinstance(dataD2Q, np.ndarray):
print("\t\t ", "dataD2Q found, OK")
else:
print("\t\t ", "dataD2Q not found.")
data_error=1
print('\n\t\t Analysis parameters:')
print("\t\t Norm (defn of residual): ", norm)
print('\t**********************************************************')
print('\n\t REQUIRED DATA')
print('\t\t\t Ramanshift = vector, the x-axis in relative wavenumbers')
print('\t\t\t band area and error = 2D (2 columns), for H2, HD and D2')
print('\n\t\t\t J_max = scalar, for H2, HD and D2 (to compute reference')
print('\t\t\t\t spectra), See residual functions')
print('\t**********************************************************')
print('\n\t\t\t Example:')
print('\t\t\t run_fit_D2_O2S0 (298 )')
print('\t**********************************************************')
# ------------------------------------------------------
# ------------------------------------------------------
# *******************************************************************
# Set logging ------------------------------------------
fileh = logging.FileHandler('./log_temperature_determination', 'w+')
formatter = logging.Formatter('%(message)s')
fileh.setFormatter(formatter)
log = logging.getLogger() # root logger
for hdlr in log.handlers[:]: # remove all old handlers
log.removeHandler(hdlr)
log.addHandler(fileh) # set the new handler
# ------------------------------------------------------
# Logging starts here
logger = logging.getLogger(os.path.basename(__file__))
log.info(logger)
logging.getLogger().setLevel(logging.INFO)
log.warning(datetime.now().strftime('%Y-%m-%d %H:%M:%S'))
log.warning('\n',)
log.error("------------ Run log ------------\n")
log.error("---Temperature determination from Raman intensities---\n")
log.error("---Parallel polarization---\n")
# ------------------------------------------------------
# ------------------------------------------------
# COMMON FUNCTIONS
# ------------------------------------------------
# *******************************************************************
def gen_intensity_mat(arr, index):
"""To obtain the intensity matrix for the numerator or denominator\
in the Intensity ratio matrix
array = 2D array of data where index column contains the intensity
data
index = corresponding to the column which has intensity data
returns => square matrix of intensity ratio : { I(v1)/I(v2) } """
spec1D = arr[:, index]
spec_mat = np.zeros((spec1D.shape[0], spec1D.shape[0]))
for i in range(spec1D.shape[0]):
spec_mat[:, i] = spec1D / spec1D[i]
return spec_mat
# ------------------------------------------------
def clean_mat(square_array):
"""Set the upper triangular portion of square matrix to zero
including the diagonal
input = any square array """
np.fill_diagonal(square_array, 0)
return | np.tril(square_array, k=0) | numpy.tril |
from abc import ABC
from collections import defaultdict
from dataclasses import dataclass
from functools import cached_property
from typing import (
Any,
Callable,
ClassVar,
DefaultDict,
Dict,
List,
Optional,
Tuple,
Type,
TypeVar,
)
import numpy as np
from lisdf.utils.transformations import (
euler_from_quaternion,
quaternion_from_euler,
quaternion_multiply,
)
from lisdf.utils.transformations_more import lookat_rpy
from lisdf.utils.typing import Vector3f, Vector4f, Vector6f
T = TypeVar("T")
NAME_SCOPE_SEP: Optional[str] = "::"
def set_name_scope_sep(sep: Optional[str]) -> None:
"""Set the name scope seperator to None to disable name scoping."""
global NAME_SCOPE_SEP
NAME_SCOPE_SEP = sep
class StringifyContext(object):
def __init__(self, **kwargs) -> None:
self.stacks: DefaultDict[str, List[Any]] = defaultdict(list)
self.warnings: List[Tuple[StringConfigurable, str]] = list()
self.options = kwargs
def warning(self, obj: "StringConfigurable", message: str) -> None:
self.warnings.append((obj, message))
def st_push(self, name: str, value: Any) -> None:
self.stacks[name].append(value)
def st_pop(self, name: str, default: Any = None) -> Any:
return self.stacks[name].pop() if len(self.stacks[name]) > 0 else default
def st_top(self, name: str, default: Any = None) -> Any:
return self.stacks[name][-1] if len(self.stacks[name]) > 0 else default
def get_scoped_name(self, name: str) -> str:
"""
Prepend the current scope to the name.
Args:
name: the input name.
Returns:
When the use_scoped_name option is True, the name is prepended with
the current scope. For example, when we are stringifying a model,
the to_sdf method will do seomthing like this:
```
ctx.push_scoped_name(self.model_name)
for link in self.links:
link.to_sdf()
ctx.pop_scoped_name()
```
Then, inside the link.to_sdf method, users can call the function
get_scoped_name to get the name of the link. It will return:
`model_name + "::" + link.name`.
"""
if not self.options["use_scoped_name"]:
return name
parent_name = self.st_top("model_name", None)
if parent_name is None:
return name
if NAME_SCOPE_SEP is None:
return name
return f"{parent_name}{NAME_SCOPE_SEP}{name}"
def push_scoped_name(self, name: str) -> None:
self.st_push("model_name", self.get_scoped_name(name))
def pop_scoped_name(self) -> None:
self.st_pop("model_name")
def get_scoped_pose(self, pose: "Pose") -> "Pose":
"""
In SDF files we constantly allow nested definition of poses.
For example, we can specify the pose of a model then all links under
this model will be transformed. This helper function maintains a stack
of poses from the root node. The usage is similar to the `get_scoped_name`.
"""
parent_pose = self.st_top("pose", None)
if parent_pose is None:
return pose
return parent_pose * pose
def push_scoped_pose(self, pose: "Pose") -> None:
self.st_push("pose", self.get_scoped_pose(pose))
def pop_scoped_pose(self) -> None:
self.st_pop("pose")
class StringConfigurable(ABC):
# TODO(<NAME> @ 03/24): implement these methods for the child classes.
DEFAULT_LISDF_STRINGIFY_OPTIONS: ClassVar[Dict[str, Any]] = {}
DEFAULT_SDF_STRINGIFY_OPTIONS: ClassVar[Dict[str, Any]] = {}
DEFAULT_URDF_STRINGIFY_OPTIONS: ClassVar[Dict[str, Any]] = {
# The URDF standard supports defining the material for a visual element
# inside the visual element itself. However, this is not supported by
# some URDF parsers. Set this option to False to enforce all material
# definitions to be defined at the root level.
"allow_embedded_material": False,
# When export the URDF model, whether to use the scoped name (i.e. names
# that is composed of the parent name and the child name).
"use_scoped_name": False,
}
def to_lisdf(self, ctx: Optional[StringifyContext] = None, **kwargs) -> str:
if ctx is None:
for k, v in type(self).DEFAULT_LISDF_STRINGIFY_OPTIONS.items():
kwargs.setdefault(k, v)
ctx = StringifyContext(**kwargs)
return self._to_lisdf(ctx)
def to_sdf(self, ctx: Optional[StringifyContext] = None, **kwargs) -> str:
if ctx is None:
for k, v in type(self).DEFAULT_SDF_STRINGIFY_OPTIONS.items():
kwargs.setdefault(k, v)
ctx = StringifyContext(**kwargs)
return self._to_sdf(ctx)
def to_urdf(self, ctx: Optional[StringifyContext] = None, **kwargs) -> str:
if ctx is None:
for k, v in type(self).DEFAULT_URDF_STRINGIFY_OPTIONS.items():
kwargs.setdefault(k, v)
ctx = StringifyContext(**kwargs)
return self._to_urdf(ctx)
def _to_lisdf(self, ctx: StringifyContext) -> str:
return self._to_sdf(ctx)
def _to_sdf(self, ctx: StringifyContext) -> str:
raise NotImplementedError()
def _to_urdf(self, ctx: StringifyContext) -> str:
raise NotImplementedError()
def unsupported_stringify(
*, disable_sdf: bool = False, disable_urdf: bool = False
) -> Callable[[Type[T]], Type[T]]:
# TODO (<NAME> @ 04/03): find a more checker/IDE-friendly way to inject.
def decorator(cls: Type[T]) -> Type[T]:
if not disable_sdf:
def _to_sdf(self: StringConfigurable, ctx: StringifyContext) -> str:
ctx.warning(
self, "Unsupported SDF stringification for {}".format(cls.__name__)
)
return ""
setattr(cls, "to_sdf", _to_sdf)
if not disable_urdf:
def _to_urdf(self: StringConfigurable, ctx: StringifyContext) -> str:
ctx.warning(
self,
"Unsupported URDF stringification for {}.".format(cls.__name__),
)
return ""
setattr(cls, "to_urdf", _to_urdf)
return cls
return decorator
@dataclass
class Pose(StringConfigurable):
pos: Vector3f
quat_wxyz: Vector4f
@classmethod
def from_rpy_6d(cls, a: Vector6f) -> "Pose":
"""Construct a Pose object from a 6-dimensional vector: x, y, z, r, p, y."""
return cls.from_rpy(a[:3], a[3:])
@classmethod
def from_rpy(cls, pos: Vector3f, rpy: Vector3f) -> "Pose":
"""Construct a Pose object two 3-dimensional vector."""
return cls.from_quat_xyzw(pos, quaternion_from_euler(*rpy)) # type: ignore
@classmethod
def from_quat_xyzw(cls, pos: Vector3f, xyzw: Vector4f) -> "Pose":
"""Construct a Pose object from a 3d position vector and a
4d quaternion vector, expressed in xyzw."""
return cls(pos, np.array([xyzw[3], xyzw[0], xyzw[1], xyzw[2]]))
@classmethod
def from_lookat(cls, xyz: Vector3f, point_to: Vector3f) -> "Pose":
"""Construct the roll, pitch, yaw angles of a camera looking at a target.
This function assumes that the camera is pointing to the z-axis ([0, 0, 1]),
in the camera frame.
Args:
camera_pos: the position of the camera.
target_pos: the target position.
Returns:
a Pose object.
"""
return cls.from_rpy(xyz, lookat_rpy(xyz, point_to))
@classmethod
def identity(cls) -> "Pose":
"""Construct the identity pose (x=y=z=r=p=y=0)."""
return cls(
pos=np.zeros(3, dtype="float32"),
quat_wxyz= | np.array([1, 0, 0, 0], dtype="float32") | numpy.array |
#!/usr/bin/env python2
from moke import *
from itertools import izip, chain
from multiprocessing import Pool
import pickle
import numpy as np
import scipy.stats as ss
from sklearn import decomposition, cross_validation, grid_search, linear_model, metrics
from sklearn.decomposition.nmf import nnls
from pysam import Samfile
MINBAMS = 3
def load_epi(epi):
"""(internal) load epi file
"""
chk_exit(*inp_file(path(epi)))
with open(epi) as fh:
marks = fh.readline().strip().split("\t")
h = np.loadtxt(fh, delimiter="\t")
return (marks, h)
def load_arr(arr):
"""(internal) load arr file
"""
chk_exit(*inp_file(path(arr)))
with open(arr) as fh:
marks = fh.readline().strip().split("\t")
x = np.loadtxt(fh, delimiter="\t")
return (marks, x)
def load_arrs(arrs):
"""(internal) load multiple arr files, assumes same marks (columns)
"""
xs = []
for arr in arrs:
marks, x = load_arr(arr)
xs.append(x)
return (marks, xs)
## statistical functions
def sparsevec(x):
"""(internal) Calculates the sparsity of a vector.
"""
eps = np.finfo(x.dtype).eps if 'int' not in str(x.dtype) else 1e-9
n = x.shape[0]
x1 = np.sqrt(n) - (np.abs(x).sum() + eps) / (np.sqrt(np.multiply(x, x).sum()) + eps)
x2 = np.sqrt(n) - 1
return x1 / x2
def sparsemat(X):
"""(internal) Calculates the average sparsity of a matrx.
"""
return np.mean([sparsevec(x) for x in X])
def dsig(a, lq, loc, uq):
"""(internal) Double sigmoid function to normalize features (columns).
see:
<NAME>., <NAME>. and <NAME>. Score normalization in multimodal biometric systems.
Pattern Recognition 38, 2270-2285 (2005).
"""
a = | np.asanyarray(a, dtype="f") | numpy.asanyarray |
"""module for doing innerloop procedures"""
import asyncio
import functools
import heapq
import logging
import numpy as np
from gameanalysis import collect
from gameanalysis import nash
from gameanalysis import regret
from gameanalysis import restrict
# TODO There's something to be said about individual rationality constraints
# relative to best deviation, i.e. if all are positive gains, but negative
# payoff, that might mean we should warn, or at least explore something else.
# TODO Restrict size should maybe be a num strats per role and set such that
# and restriction that has less than the number of profiles is valid. For
# backwards compatibility, it'd be nice to have a good way to interpret a
# single number for games with multiple roles, potentially the division that
# produces the maximum number of profiles?
# TODO Schedule restriction should only schedule if equilibria < num or haven't
# started queuing backups
# TODO It'd be cool to have an option to explore better responses proportional
# to gain instead of best response. This would require a deterministic random
# seed in order to get consistent output.
# TODO in failure conditions, some tasks are left hanging, instead we should be
# cancelling, and awaiting them so they're not left running
async def inner_loop( # pylint: disable=too-many-locals
agame,
*,
initial_restrictions=None,
regret_thresh=1e-3,
dist_thresh=0.1,
support_thresh=1e-4,
restricted_game_size=3,
num_equilibria=1,
num_backups=1,
devs_by_role=False,
style="best",
executor=None
):
"""Inner loop a game using a scheduler
Parameters
----------
game : RsGame
The game to find equilibria in. This function is most useful when game
is a SchedulerGame, but any complete RsGame will work.
initial_restriction : [[bool]], optional
Initial restrictions to start inner loop from. If unspecified, every
pure restriction is used.
regret_thresh : float > 0, optional
The maximum regret to consider an equilibrium an equilibrium.
dist_thresh : float > 0, optional
The minimum norm between two mixed profiles for them to be considered
distinct.
support_thresh : float > 0, optional
Candidate equilibria strategies with probability lower than this will
be truncated. This is useful because often Nash finding returns
strategies with very low support, which now mean extra deviating
strategies need to be sampled. Trimming saves these samples, but may
increase regret above the threshold.
restricted_game_size : int > 0, optional
The maximum restricted game support size with which beneficial
deviations must be explored. Restricted games with support larger than
this are queued and only explored in the event that no equilibrium can
be found in beneficial deviations smaller than this.
num_equilibria : int > 0, optional
The number of equilibria to attempt to find. Only one is guaranteed,
but this might be beneifical if the game has a known degenerate
equilibria, but one which is still helpful as a deviating strategy.
num_backups : int > 0, optional
In the event that no equilibrium can be found in beneficial deviations
to small restricted games, other restrictions will be explored. This
parameter indicates how many restricted games for each role should be
explored.
devs_by_role : boolean, optional
If specified, deviations will only be explored for each role in order,
proceeding to the next role only when no beneficial deviations are
found. This can reduce the number of profiles sampled, but may also
fail to find certain equilibria due to the different path through
restricted games.
style : string, optional
A string describing the thoroughness of equilibrium finding. Seed
`nash.mixed_equilibria` for options and a description.
executor : Executor, optional
The executor to be used for Nash finding. The default setting will
allow async networking calls to continue to happen during long nash
finding, but buy using a process pool this can take advantage of
parallel computation.
"""
init_role_dev = 0 if devs_by_role else None
exp_restrictions = collect.bitset(agame.num_strats)
backups = [[] for _ in range(agame.num_roles)]
equilibria = collect.mcces(dist_thresh)
loop = asyncio.get_event_loop()
async def add_restriction(rest):
"""Adds a restriction to be evaluated"""
if not exp_restrictions.add(rest):
return # already explored
if agame.is_pure_restriction(rest):
# Short circuit for pure restriction
return await add_deviations(rest, rest.astype(float), init_role_dev)
data = await agame.get_restricted_game(rest)
reqa = await loop.run_in_executor(
executor,
functools.partial(
nash.mixed_equilibria,
data,
regret_thresh=regret_thresh,
dist_thresh=dist_thresh,
style=style,
processes=1,
),
)
if reqa.size:
eqa = restrict.translate(
data.trim_mixture_support(reqa, thresh=support_thresh), rest
)
await asyncio.gather(
*[add_deviations(rest, eqm, init_role_dev) for eqm in eqa]
)
else:
logging.warning(
"couldn't find equilibria in %s with restriction %s. This is "
"likely due to high variance in payoffs which means "
"quiesce should be re-run with more samples per profile. "
"This could also be fixed by performing a more expensive "
"equilibria search to always return one.",
agame,
agame.restriction_to_repr(rest),
)
async def add_deviations(rest, mix, role_index):
"""Add deviations to be evaluated"""
# We need the restriction here, since trimming support may increase
# regret of strategies in the initial restriction
data = await agame.get_deviation_game(mix > 0, role_index)
devs = data.deviation_payoffs(mix)
exp = np.add.reduceat(devs * mix, agame.role_starts)
gains = devs - exp.repeat(agame.num_role_strats)
if role_index is None:
if np.all((gains <= regret_thresh) | rest):
# Found equilibrium
reg = gains.max()
if equilibria.add(mix, reg):
logging.warning(
"found equilibrium %s in game %s with regret %f",
agame.mixture_to_repr(mix),
agame,
reg,
)
else:
await asyncio.gather(
*[
queue_restrictions(rgains, ri, rest)
for ri, rgains in enumerate(
np.split(gains, agame.role_starts[1:])
)
]
)
else: # Set role index
rgains = np.split(gains, agame.role_starts[1:])[role_index]
rrest = np.split(rest, agame.role_starts[1:])[role_index]
if np.all((rgains <= regret_thresh) | rrest): # No deviations
role_index += 1
if role_index < agame.num_roles: # Explore next deviation
await add_deviations(rest, mix, role_index)
else: # found equilibrium
# This should not require scheduling as to get here all
# deviations have to be scheduled
data = await agame.get_deviation_game(mix > 0)
reg = regret.mixture_regret(data, mix)
if equilibria.add(mix, reg):
logging.warning(
"found equilibrium %s in game %s with regret %f",
agame.mixture_to_repr(mix),
agame,
reg,
)
else:
await queue_restrictions(rgains, role_index, rest)
async def queue_restrictions(role_gains, role_index, rest):
"""Queue new restrictions appropriately"""
role_rest = np.split(rest, agame.role_starts[1:])[role_index]
if role_rest.all():
return # Can't deviate
rest_size = rest.sum()
role_start = agame.role_starts[role_index]
best_resp = np.nanargmax(np.where(role_rest, np.nan, role_gains))
if role_gains[best_resp] > regret_thresh and rest_size < restricted_game_size:
br_sub = rest.copy()
br_sub[role_start + best_resp] = True
await add_restriction(br_sub)
else:
best_resp = None # Add best response to backup
back = backups[role_index]
for strat_ind, (gain, role) in enumerate(zip(role_gains, role_rest)):
if strat_ind == best_resp or role or gain <= 0:
continue
sub = rest.copy()
sub[role_start + strat_ind] = True
heapq.heappush(back, (-gain, id(sub), sub)) # id for tie-breaking
restrictions = (
agame.pure_restrictions()
if initial_restrictions is None
else np.asarray(initial_restrictions, bool)
)
iteration = 0
while len(equilibria) < num_equilibria and (
any(q for q in backups) or not next(iter(exp_restrictions)).all()
):
if iteration == 1:
logging.warning(
"scheduling backup restrictions in game %s. This only happens "
"when quiesce criteria could not be met with current "
"maximum restriction size (%d). This probably means that "
"the maximum restriction size should be increased. If "
"this is happening frequently, increasing the number of "
"backups taken at a time might be desired (currently %s).",
agame,
restricted_game_size,
num_backups,
)
elif iteration > 1:
logging.info("scheduling backup restrictions in game %s", agame)
await asyncio.gather(*[add_restriction(r) for r in restrictions])
restrictions = collect.bitset(agame.num_strats, exp_restrictions)
for role, back in enumerate(backups):
unscheduled = num_backups
while unscheduled > 0 and back:
rest = heapq.heappop(back)[-1]
unscheduled -= restrictions.add(rest)
for _ in range(unscheduled):
added = False
for mask in restrictions:
rmask = np.split(mask, agame.role_starts[1:])[role]
if rmask.all():
continue
rest = mask.copy()
# TODO We could randomize instead of taking the first
# strategy, but this would remove reproducability unless it
# was somehow predicated on all of the explored
# restrictions or something...
strat = np.split(rest, agame.role_starts[1:])[role].argmin()
rest[agame.role_starts[role] + strat] = True
restrictions.add(rest)
added = True
break
if not added:
break
iteration += 1
# Return equilibria
if equilibria: # pylint: disable=no-else-return
return | np.stack([eqm for eqm, _ in equilibria]) | numpy.stack |
# Copyright 2022 DeepMind Technologies Limited
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""tests for rollout function."""
from absl.testing import absltest
from absl.testing import parameterized
import mujoco
import numpy as np
import concurrent.futures
import threading
from mujoco import rollout
#--------------------------- models used for testing ---------------------------
TEST_XML = r"""
<mujoco>
<worldbody>
<light pos="0 0 2"/>
<geom type="plane" size="5 5 .1"/>
<body pos="0 0 .1">
<joint name="yaw" axis="0 0 1"/>
<joint name="pitch" axis="0 1 0"/>
<geom type="capsule" size=".02" fromto="0 0 0 1 0 0"/>
<geom type="box" pos="1 0 0" size=".1 .1 .1"/>
<site name="site" pos="1 0 0"/>
</body>
</worldbody>
<actuator>
<general joint="pitch" gainprm="100"/>
<general joint="yaw" dyntype="filter" dynprm="1" gainprm="100"/>
</actuator>
<sensor>
<accelerometer site="site"/>
</sensor>
</mujoco>
"""
TEST_XML_NO_SENSORS = r"""
<mujoco>
<worldbody>
<light pos="0 0 2"/>
<geom type="plane" size="5 5 .1"/>
<body pos="0 0 .1">
<joint name="yaw" axis="0 0 1"/>
<joint name="pitch" axis="0 1 0"/>
<geom type="capsule" size=".02" fromto="0 0 0 1 0 0"/>
<geom type="box" pos="1 0 0" size=".1 .1 .1"/>
<site name="site" pos="1 0 0"/>
</body>
</worldbody>
<actuator>
<general joint="pitch" gainprm="100"/>
<general joint="yaw" dyntype="filter" dynprm="1" gainprm="100"/>
</actuator>
</mujoco>
"""
TEST_XML_NO_ACTUATORS = r"""
<mujoco>
<worldbody>
<light pos="0 0 2"/>
<geom type="plane" size="5 5 .1"/>
<body pos="0 0 .1">
<joint name="yaw" axis="0 0 1"/>
<joint name="pitch" axis="0 1 0"/>
<geom type="capsule" size=".02" fromto="0 0 0 1 0 0"/>
<geom type="box" pos="1 0 0" size=".1 .1 .1"/>
<site name="site" pos="1 0 0"/>
</body>
</worldbody>
<sensor>
<accelerometer site="site"/>
</sensor>
</mujoco>
"""
TEST_XML_MOCAP = r"""
<mujoco>
<worldbody>
<body name="1" mocap="true">
</body>
<body name="2" mocap="true">
</body>
</worldbody>
<sensor>
<framepos objtype="xbody" objname="1"/>
<framequat objtype="xbody" objname="2"/>
</sensor>
</mujoco>
"""
TEST_XML_EMPTY = r"""
<mujoco>
</mujoco>
"""
ALL_MODELS = {'TEST_XML': TEST_XML,
'TEST_XML_NO_SENSORS': TEST_XML_NO_SENSORS,
'TEST_XML_NO_ACTUATORS': TEST_XML_NO_ACTUATORS,
'TEST_XML_EMPTY': TEST_XML_EMPTY}
#------------------------------- tests -----------------------------------------
class MuJoCoRolloutTest(parameterized.TestCase):
def setUp(self):
super().setUp()
np.random.seed(42)
#----------------------------- test basic operation
@parameterized.parameters(ALL_MODELS.keys())
def test_single_step(self, model_name):
model = mujoco.MjModel.from_xml_string(ALL_MODELS[model_name])
data = mujoco.MjData(model)
initial_state = np.random.randn(model.nq + model.nv + model.na)
ctrl = np.random.randn(model.nu)
state, sensordata = rollout.rollout(model, data, initial_state, ctrl)
mujoco.mj_resetData(model, data)
py_state, py_sensordata = step(model, data, initial_state, ctrl=ctrl)
np.testing.assert_array_equal(state, py_state)
np.testing.assert_array_equal(sensordata, py_sensordata)
@parameterized.parameters(ALL_MODELS.keys())
def test_single_rollout(self, model_name):
nstep = 3 # number of timesteps
model = mujoco.MjModel.from_xml_string(ALL_MODELS[model_name])
data = mujoco.MjData(model)
initial_state = np.random.randn(model.nq + model.nv + model.na)
ctrl = np.random.randn(nstep, model.nu)
state, sensordata = rollout.rollout(model, data, initial_state, ctrl)
py_state, py_sensordata = single_rollout(model, data, initial_state,
ctrl=ctrl)
np.testing.assert_array_equal(state, np.asarray(py_state))
np.testing.assert_array_equal(sensordata, np.asarray(py_sensordata))
@parameterized.parameters(ALL_MODELS.keys())
def test_multi_step(self, model_name):
model = mujoco.MjModel.from_xml_string(ALL_MODELS[model_name])
data = mujoco.MjData(model)
nstate = 5 # number of initial states
initial_state = np.random.randn(nstate, model.nq + model.nv + model.na)
ctrl = np.random.randn(nstate, 1, model.nu)
state, sensordata = rollout.rollout(model, data, initial_state, ctrl)
mujoco.mj_resetData(model, data)
py_state, py_sensordata = multi_rollout(model, data, initial_state,
ctrl=ctrl)
np.testing.assert_array_equal(state, py_state)
np.testing.assert_array_equal(sensordata, py_sensordata)
@parameterized.parameters(ALL_MODELS.keys())
def test_single_rollout_fixed_ctrl(self, model_name):
nstep = 3
model = mujoco.MjModel.from_xml_string(ALL_MODELS[model_name])
data = mujoco.MjData(model)
initial_state = np.random.randn(model.nq + model.nv + model.na)
ctrl = np.random.randn(model.nu)
state = np.empty((nstep, model.nq + model.nv + model.na))
sensordata = np.empty((nstep, model.nsensordata))
rollout.rollout(model, data, initial_state, ctrl,
state=state, sensordata=sensordata)
ctrl = np.tile(ctrl, (nstep, 1)) # repeat??
py_state, py_sensordata = single_rollout(model, data, initial_state,
ctrl=ctrl)
np.testing.assert_array_equal(state, py_state)
np.testing.assert_array_equal(sensordata, py_sensordata)
@parameterized.parameters(ALL_MODELS.keys())
def test_multi_rollout(self, model_name):
model = mujoco.MjModel.from_xml_string(ALL_MODELS[model_name])
data = mujoco.MjData(model)
nstate = 2 # number of initial states
nstep = 3 # number of timesteps
initial_state = np.random.randn(nstate, model.nq + model.nv + model.na)
ctrl = np.random.randn(nstate, nstep, model.nu)
state, sensordata = rollout.rollout(model, data, initial_state, ctrl)
py_state, py_sensordata = multi_rollout(model, data, initial_state,
ctrl=ctrl)
np.testing.assert_array_equal(py_state, py_state)
np.testing.assert_array_equal(py_sensordata, py_sensordata)
@parameterized.parameters(ALL_MODELS.keys())
def test_multi_rollout_fixed_ctrl_infer_from_output(self, model_name):
model = mujoco.MjModel.from_xml_string(ALL_MODELS[model_name])
data = mujoco.MjData(model)
nstate = 2 # number of initial states
nstep = 3 # number of timesteps
initial_state = np.random.randn(nstate, model.nq + model.nv + model.na)
ctrl = np.random.randn(nstate, 1, model.nu) # 1 control in the time dimension
state = np.empty((nstate, nstep, model.nq + model.nv + model.na))
state, sensordata = rollout.rollout(model, data, initial_state, ctrl,
state=state)
ctrl = np.repeat(ctrl, nstep, axis=1)
py_state, py_sensordata = multi_rollout(model, data, initial_state,
ctrl=ctrl)
np.testing.assert_array_equal(state, py_state)
np.testing.assert_array_equal(sensordata, py_sensordata)
@parameterized.product(arg_nstep=[[3, 1, 1], [3, 3, 1], [3, 1, 3]],
model_name=list(ALL_MODELS.keys()))
def test_multi_rollout_multiple_inputs(self, arg_nstep, model_name):
model = mujoco.MjModel.from_xml_string(ALL_MODELS[model_name])
data = mujoco.MjData(model)
nstate = 4 # number of initial states
initial_state = np.random.randn(nstate, model.nq + model.nv + model.na)
# arg_nstep is the horizon for {ctrl, qfrc_applied, xfrc_applied}, respectively
ctrl = np.random.randn(nstate, arg_nstep[0], model.nu)
qfrc_applied = np.random.randn(nstate, arg_nstep[1], model.nv)
xfrc_applied = np.random.randn(nstate, arg_nstep[2], model.nbody*6)
state, sensordata = rollout.rollout(model, data, initial_state, ctrl,
qfrc_applied=qfrc_applied,
xfrc_applied=xfrc_applied)
# tile singleton arguments
nstep = max(arg_nstep)
if arg_nstep[0] == 1:
ctrl = np.repeat(ctrl, nstep, axis=1)
if arg_nstep[1] == 1:
qfrc_applied = np.repeat(qfrc_applied, nstep, axis=1)
if arg_nstep[2] == 1:
xfrc_applied = np.repeat(xfrc_applied, nstep, axis=1)
py_state, py_sensordata = multi_rollout(model, data, initial_state,
ctrl=ctrl,
qfrc_applied=qfrc_applied,
xfrc_applied=xfrc_applied)
np.testing.assert_array_equal(state, py_state)
np.testing.assert_array_equal(sensordata, py_sensordata)
#----------------------------- test threaded operation
def test_threading(self):
model = mujoco.MjModel.from_xml_string(TEST_XML)
num_workers = 32
nstate = 10000
nstep = 5
initial_state = np.random.randn(nstate, model.nq+model.nv+model.na)
state = np.zeros((nstate, nstep, model.nq+model.nv+model.na))
sensordata = np.zeros((nstate, nstep, model.nsensordata))
ctrl = np.random.randn(nstate, nstep, model.nu)
thread_local = threading.local()
def thread_initializer():
thread_local.data = mujoco.MjData(model)
def call_rollout(initial_state, ctrl, state):
rollout.rollout(model, thread_local.data, skip_checks=True,
nstate=initial_state.shape[0], nstep=nstep,
initial_state=initial_state, ctrl=ctrl, state=state)
n = initial_state.shape[0] // num_workers # integer division
chunks = [] # a list of tuples, one per worker
for i in range(num_workers-1):
chunks.append(
(initial_state[i*n:(i+1)*n], ctrl[i*n:(i+1)*n], state[i*n:(i+1)*n]))
# last chunk, absorbing the remainder:
chunks.append(
(initial_state[(num_workers-1)*n:], ctrl[(num_workers-1)*n:],
state[(num_workers-1)*n:]))
with concurrent.futures.ThreadPoolExecutor(
max_workers=num_workers, initializer=thread_initializer) as executor:
futures = []
for chunk in chunks:
futures.append(executor.submit(call_rollout, *chunk))
for future in concurrent.futures.as_completed(futures):
future.result()
data = mujoco.MjData(model)
py_state, py_sensordata = multi_rollout(model, data, initial_state,
ctrl=ctrl)
np.testing.assert_array_equal(state, py_state)
#----------------------------- test advanced operation
def test_time(self):
model = mujoco.MjModel.from_xml_string(TEST_XML)
data = mujoco.MjData(model)
nstate = 1
nstep = 3
initial_time = np.array([[2.]])
initial_state = np.random.randn(nstate, model.nq + model.nv + model.na)
ctrl = np.random.randn(nstate, nstep, model.nu)
state, sensordata = rollout.rollout(model, data, initial_state, ctrl,
initial_time=initial_time)
self.assertAlmostEqual(data.time, 2 + nstep*model.opt.timestep)
def test_warmstart(self):
model = mujoco.MjModel.from_xml_string(TEST_XML)
data = mujoco.MjData(model)
state0 = np.zeros(model.nq + model.nv + model.na)
ctrl = np.zeros(model.nu)
state1, _ = step(model, data, state0, ctrl=ctrl)
initial_warmstart = data.qacc_warmstart.copy()
state2, _ = step(model, data, state1, ctrl=ctrl)
state, _ = rollout.rollout(model, data, state1, ctrl)
assert np.linalg.norm(state-state2) > 0
state, _ = rollout.rollout(model, data, state1, ctrl,
initial_warmstart=initial_warmstart)
np.testing.assert_array_equal(state, state2)
def test_mocap(self):
model = mujoco.MjModel.from_xml_string(TEST_XML_MOCAP)
data = mujoco.MjData(model)
initial_state = np.zeros(model.nq + model.nv + model.na)
pos1 = np.array((1., 2., 3.))
quat1 = np.array((1., 2., 3., 4.))
quat1 /= np.linalg.norm(quat1)
pos2 = np.array((2., 3., 4.))
quat2 = np.array((2., 3., 4., 5.))
quat2 /= np.linalg.norm(quat2)
mocap = np.hstack((pos1, quat1, pos2, quat2))
state, sensordata = rollout.rollout(model, data, initial_state, mocap=mocap)
np.testing.assert_array_almost_equal(sensordata[:3], pos1)
np.testing.assert_array_almost_equal(sensordata[3:], quat2)
#----------------------------- test correctness
def test_intercept_mj_errors(self):
model = mujoco.MjModel.from_xml_string(TEST_XML)
data = mujoco.MjData(model)
initial_state = np.zeros(model.nq + model.nv + model.na)
ctrl = np.zeros((3, model.nu))
model.opt.solver = 10 # invalid solver type
with self.assertRaisesWithLiteralMatch(mujoco.FatalError,
'Unknown solver type 10'):
state, sensordata = rollout.rollout(model, data, initial_state, ctrl)
def test_invalid(self):
model = mujoco.MjModel.from_xml_string(TEST_XML)
data = mujoco.MjData(model)
initial_state = np.zeros(model.nq + model.nv + model.na)
ctrl = 'string'
with self.assertRaisesWithLiteralMatch(
ValueError, 'ctrl must be a numpy array or float'):
state, sensordata = rollout.rollout(model, data, initial_state, ctrl)
qfrc_applied = np.zeros((2, 3, 4, 5))
with self.assertRaisesWithLiteralMatch(
ValueError, 'qfrc_applied can have at most 3 dimensions'):
state, sensordata = rollout.rollout(model, data, initial_state,
qfrc_applied=qfrc_applied)
def test_bad_sizes(self):
model = mujoco.MjModel.from_xml_string(TEST_XML)
data = mujoco.MjData(model)
initial_state = np.random.randn(model.nq + model.nv + model.na+1)
with self.assertRaisesWithLiteralMatch(
ValueError, 'trailing dimension of initial_state must be 5, got 6'):
state, sensordata = rollout.rollout(model, data, initial_state)
initial_state = np.random.randn(model.nq + model.nv + model.na)
ctrl = np.random.randn(model.nu+1)
with self.assertRaisesWithLiteralMatch(
ValueError, 'trailing dimension of ctrl must be 2, got 3'):
state, sensordata = rollout.rollout(model, data, initial_state, ctrl)
ctrl = np.random.randn(2, model.nu)
qfrc_applied = np.random.randn(3, model.nv) # incompatible horizon
with self.assertRaisesWithLiteralMatch(
ValueError, 'dimension 1 inferred as 2 but qfrc_applied has 3'):
state, sensordata = rollout.rollout(model, data, initial_state, ctrl,
qfrc_applied=qfrc_applied)
def test_stateless(self):
model = mujoco.MjModel.from_xml_string(TEST_XML)
model.opt.disableflags |= mujoco.mjtDisableBit.mjDSBL_WARMSTART.value
data = mujoco.MjData(model)
# call step with a clean mjData
initial_state = np.random.randn(model.nq + model.nv + model.na)
ctrl = np.random.randn(model.nu)
state, sensordata = rollout.rollout(model, data, initial_state, ctrl)
# fill mjData with some debug value, see that we still get the same outputs
mujoco.mj_resetDataDebug(model, data, 255)
debug_state, debug_sensordata = rollout.rollout(model, data, initial_state,
ctrl)
np.testing.assert_array_equal(state, debug_state)
np.testing.assert_array_equal(sensordata, debug_sensordata)
#--------------- Python implementation of rollout functionality ----------------
def get_state(data):
return np.hstack((data.qpos, data.qvel, data.act))
def set_state(model, data, state):
data.qpos = state[:model.nq]
data.qvel = state[model.nq:model.nq+model.nv]
data.act = state[model.nq+model.nv:model.nq+model.nv+model.na]
def step(model, data, state, **kwargs):
if state is not None:
set_state(model, data, state)
for key, value in kwargs.items():
if value is not None:
setattr(data, key, np.reshape(value, getattr(data, key).shape))
mujoco.mj_step(model, data)
return (get_state(data), data.sensordata)
def single_rollout(model, data, initial_state, **kwargs):
arg_nstep = set([a.shape[0] for a in kwargs.values()])
assert len(arg_nstep) == 1 # nstep dimensions must match
nstep = arg_nstep.pop()
state = np.empty((nstep, model.nq + model.nv + model.na))
sensordata = | np.empty((nstep, model.nsensordata)) | numpy.empty |
import numpy as np
from keras_explain.deep_viz_keras.integrated_gradients import IntegratedGradients
class IntegratedGrad:
name = "Integrated gradients"
authors = "<NAME>."
def __init__(self, model):
self.model = model
def explain(self, image, target_class):
print(self.model)
try:
ig = IntegratedGradients(self.model)
mask = ig.get_mask(image)
except AttributeError:
print("Your model has no optimizer defined. Please use the complie"
"function on your model to define the optimizer.")
raise
# TODO: check if positive really means positive impact and
# TODO: negative value negative impact
# that idea found at
# https://github.com/hiranumn/IntegratedGradients/blob/master/examples/example.ipynb
# i cant get so nice representations
mask = np.sum(mask, axis=2)
mask /= np.abs(mask).max()
# print(mask.min(), mask.max())
#
# positive_impacts = np.copy(mask)
# positive_impacts[positive_impacts < 0] = 0
#
# negative_impacts = np.copy(mask) * -1
# negative_impacts[negative_impacts < 0] = 0
mask = | np.abs(mask) | numpy.abs |
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
A kernel-density-based, embarrassingly parallel ensemble sampler.
"""
from __future__ import (division, print_function, absolute_import, unicode_literals)
from .interruptible_pool import Pool
from .serialpool import SerialPool
import numpy as np
import numpy.ma as ma
from scipy.stats import chisquare
from .clustered_kde import optimized_kde, TransdimensionalKDE
class _GetLnProbWrapper(object):
"""Convenience class for evaluating multiple probability densities at a single point."""
def __init__(self, lnpost, kde, *args):
self.lnpost = lnpost
self.kde = kde
self.args = args
def lnprobs(self, p):
"""
Evaluate the log probability density of the stored target distribution fuction
and KDE at `p`.
:param p: Location to evaluate probability densties at.
:returns: ``lnpost(p)``, ``kde(p)``
"""
result = self.lnpost(p, *self.args)
kde = self.kde(p)
# allow posterior function to optionally
# return additional metadata
try:
lnpost = result[0]
blob = result[1]
return lnpost, kde, blob
except (IndexError, TypeError):
lnpost = result
return lnpost, kde
__call__ = lnprobs
class Sampler(object):
"""
An Ensemble sampler.
The :attr:`chain` member of this object has the shape: `(nsteps, nwalkers, ndim)` where
`nsteps` is the stored number of steps taken thus far.
:param nwalkers:
The number of individual MCMC chains to include in the ensemble.
:param ndim:
Number of dimensions in the parameter space. If `transd` is ``True`` this is the number of
unique dimensions across the parameter spaces.
:param lnpostfn:
A function that takes a vector in the parameter space as input and returns the natural
logarithm of the posterior probability for that position.
:param transd:
If ``True``, the sampler will operate across parameter spaces using a
:class:`.clustered_kde.TransdimensionalKDE` proposal distribution. In this mode a masked
array with samples in each of the possible sets of dimensions must be given for the initial
ensemble distribution.
:param processes: (optional)
The number of processes to use with :mod:`multiprocessing`. If ``None``, all available
cores are used.
:param pool: (optional)
A pre-constructed pool with a map method. If ``None`` a pool will be created using
:mod:`multiprocessing`.
"""
def __init__(self, nwalkers, ndim, lnpostfn, transd=False,
processes=None, pool=None, args=[]):
self.nwalkers = nwalkers
self.dim = ndim
self._kde = None
self._kde_size = self.nwalkers
self._updates = []
self._burnin_length = None
self._get_lnpost = lnpostfn
self._lnpost_args = args
self.iterations = 0
self.stored_iterations = 0
self.processes = processes
self._managing_pool = False
if pool is not None:
self.pool = pool
elif self.processes == 1:
self.pool = SerialPool()
else:
self._managing_pool = True
# create a multiprocessing pool
self.pool = Pool(self.processes)
if not hasattr(self.pool, 'map'):
raise AttributeError("Pool object must have a map() method.")
self._transd = transd
if self._transd:
self._chain = ma.masked_all((0, self.nwalkers, self.dim))
else:
self._chain = np.zeros((0, self.nwalkers, self.dim))
self._lnpost = np.empty((0, self.nwalkers))
self._lnprop = np.empty((0, self.nwalkers))
self._acceptance = np.zeros((0, self.nwalkers))
self._blobs = []
self._last_run_mcmc_result = None
self._burnin_spaces = None
self._failed_p = None
def burnin(self, p0=None, lnpost0=None, lnprop0=None, blob0=None,
test_steps=16, critical_pval=0.05, max_steps=None,
verbose=False, callback=None, **kwargs):
"""
Evolve an ensemble until the acceptance rate becomes roughly constant. This is done by
splitting acceptances in half and checking for statistical consistency. This isn't
guaranteed to return a fully burned-in ensemble, but usually does.
:param p0: (optional)
A list of the initial walker positions. It should have the shape `(nwalkers, ndim)`.
If ``None`` and the sampler has been run previously, it'll pick up where it left off.
:param lnpost0: (optional)
The list of log posterior probabilities for the walkers at positions `p0`. If ``lnpost0
is None``, the initial values are calculated. It should have the shape `(nwalkers,
ndim)`.
:param lnprop0: (optional)
List of log proposal densities for walkers at positions `p0`. If ``lnprop0 is None``,
the initial values are calculated. It should have the shape `(nwalkers, ndim)`.
:param blob0: (optional)
The list of blob data for walkers at positions `p0`.
:param test_steps: (optional)
The (rough) number of accepted steps over which to check for acceptance rate
consistency. If you find burnin repeatedly ending prematurely try increasing this.
:param critical_pval: (optional)
The critial p-value for considering the acceptance distribution
consistent. If the calculated p-value is over this, then the acceptance rate
is considered to be stationary. Lower this if you want burnin criteria to be
less strict.
:param max_steps: (optional)
An absolute maximum number of steps to take, in case burnin is too painful.
:param verbose: (optional)
Print status messages each time a milestone is reached in the burnin.
:param kwargs: (optional)
The rest is passed to :meth:`run_mcmc`.
After burnin...
:returns:
* ``p`` - A list of the current walker positions with shape `(nwalkers, ndim)`.
* ``lnpost`` - Array of log posterior probabilities for walkers at positions `p`; has
shape `(nwalkers, ndim)`.
* ``lnprop`` - Array of log proposal densities for walkers at positions `p`; has shape
`(nwalkers, ndim)`.
* ``blob`` - (if `lnprobfn` returns blobs) The list of blob data for the walkers at
positions `p`.
"""
if p0 is not None:
p0 = np.atleast_2d(p0)
# Determine the maximum iteration to look for
start = self.iterations
# Confine walkers to their space during burnin
freeze_transd = False
if self._transd:
freeze_transd = True
self._burnin_spaces = ~p0.mask
max_iter = np.inf
if max_steps is not None:
max_iter = start + max_steps
step_size = 2
while step_size <= test_steps:
# Update the proposal
if p0 is not None:
self.update_proposal(p0, max_samples=self.nwalkers)
lnprop0 = self._kde(p0)
if verbose:
print('Updated proposal')
# Take one step to estimate acceptance rate
test_interval = 1
results = self.run_mcmc(test_interval, p0, lnpost0, lnprop0, blob0,
freeze_transd=freeze_transd, spaces=self._burnin_spaces,
**kwargs)
try:
p, lnpost, lnprop, blob = results
except ValueError:
p, lnpost, lnprop = results
blob = None
# Use the fraction of acceptances in the last step to estimate acceptance rate
# Bottom out at 1% if acceptances are really bad
last_acc_rate = max(np.mean(self.acceptance[-1]), 0.01)
# Estimate ACT based on acceptance
act = int(np.ceil(2.0/last_acc_rate - 1.0))
if verbose:
print('Single-step acceptance rate is ', last_acc_rate)
print('Producing ACT of ', act)
# Use the ACT to set the new test interval, but avoid
# overstepping a specified max. We throw away the first
# 2*act worth of steps as an initial burnin when comparing
# acceptance rates
test_interval = min((step_size+2)*act, max_iter - self.iterations)
# Make sure we're taking at least one step
test_interval = max(test_interval, 1)
results = self.run_mcmc(test_interval, p, lnpost, lnprop, blob,
freeze_transd=freeze_transd, spaces=self._burnin_spaces,
**kwargs)
try:
p, lnpost, lnprop, blob = results
except ValueError:
p, lnpost, lnprop = results
blob = None
if callback is not None:
callback(self)
# Quit if we hit the max
if self.iterations >= max_iter:
print("Burnin hit {} iterations before completing.".format(max_iter))
break
# Only check for consistency past the burn-in stage of 2*act
if self.consistent_acceptance_rate(window_size=step_size*act, critical_pval=critical_pval):
if verbose:
print('Acceptance rate constant over ', step_size, ' ACTs')
step_size *= 2
else:
if verbose:
print('Acceptance rate varies, trying again')
if verbose:
print('') # Newline
p0, lnpost0, lnprop0, blob0 = p, lnpost, lnprop, blob
self._burnin_length = self.updates[-1]
if blob is None:
return p, lnpost, lnprop
else:
return p, lnpost, lnprop, blob
def sample(self, p0=None, lnpost0=None, lnprop0=None, blob0=None,
iterations=1, kde=None, update_interval=None, kde_size=None,
freeze_transd=False, spaces=None, storechain=True, **kwargs):
"""
Advance the ensemble `iterations` steps as a generator.
:param p0: (optional)
A list of the initial walker positions. It should have the shape `(nwalkers, ndim)`.
If ``None`` and a proposal distribution exists, walker positions will be drawn from the
proposal.
:param lnpost0: (optional)
The list of log posterior probabilities for the walkers at positions `p0`. If ``lnpost0
is None``, the initial values are calculated. It should have the shape `(nwalkers,
ndim)`.
:param lnprop0: (optional)
List of log proposal densities for walkers at positions `p0`. If ``lnprop0 is None``,
the initial values are calculated. It should have the shape `(nwalkers, ndim)`.
:param blob0: (optional)
The list of blob data for walkers at positions `p0`.
:param iterations: (optional)
The number of steps to run.
:param kde: (optional)
An already-constucted, evaluatable KDE with a ``draw`` method.
:param update_interval: (optional)
Number of steps between proposal updates.
:param kde_size: (optional)
Maximum sample size for KDE construction. When the KDE is updated, existing samples are
thinned by factors of two until there's enough room for `nwalkers` new samples. The
default is `nwalkers`, and must be greater than :math:`\geq``nwalkers` if specified.
:param freeze_transd: (optional)
If ``True`` when transdimensional sampling, walkers are confined to their parameter
space. This is helpful during burnin, and allows fox fixed-D burnin before
transdimensional sampling.
:param spaces: (optional)
Confine walkers to the requested parameter spaces. Expects an inverted mask with shape
`(nwalkers, ndim)`.
:param storechain: (optional)
Flag for disabling chain and probability density storage in :attr:`chain`,
:attr:`lnpost`, and :attr:`lnprop`.
:param kwargs: (optional)
The rest is passed to :meth:`update_proposal`.
After each iteration...
:yields:
* ``p`` - An array of current walker positions with shape `(nwalkers, ndim)`.
* ``lnpost`` - The list of log posterior probabilities for the walkers at positions
``p``, with shape `(nwalkers, ndim)`.
* ``lnprop`` - The list of log proposal densities for the walkers at positions `p`, with
shape `(nwalkers, ndim)`.
* ``blob`` - (if `lnprobfn` returns blobs) The list of blob data for the walkers at
positions `p`.
"""
if p0 is None:
p = self.draw(self.nwalkers)
else:
try:
# Try copying to preserve array type (i.e.masked or not)
p = p0.copy()
except AttributeError:
# If not already an array, make it a non-masked array by default.
# Operations with masked arrays can be slow.
p = np.array(p0, copy=True)
m = self.pool.map
if kde_size:
self._kde_size = kde_size
# Build a proposal if one doesn't already exist
if kde is not None:
self._kde = kde
elif self._kde is None:
self.update_proposal(p, max_samples=self._kde_size, **kwargs)
lnprop0 = self._kde(p)
lnpost = lnpost0
lnprop = lnprop0
blob = blob0
if lnpost is None or lnprop is None:
results = list(m(_GetLnProbWrapper(self._get_lnpost, self._kde, *self._lnpost_args), p))
lnpost = | np.array([r[0] for r in results]) | numpy.array |
#-*-coding:utf-8-*-
# date:2020-04-25
# Author: X.L.Eric
#function : train for mask
import os
os.environ["CUDA_VISIBLE_DEVICES"] = "1"
from network.AEI_Net import *
from network.MultiscaleDiscriminator import *
from utils.Dataset import FaceEmbed, With_Identity
from torch.utils.data import DataLoader
import torch.optim as optim
from face_modules.model import Backbone, Arcface, MobileFaceNet, Am_softmax, l2_norm
import torch.nn.functional as F
import torch
import time
import torchvision
import cv2
from apex import amp
import visdom
import numpy as np
#
from model import BiSeNet
from PIL import Image
import torchvision.transforms as transforms
import cv2
def hinge_loss(X, positive=True):
if positive:
return torch.relu(1-X).mean()
else:
return torch.relu(X+1).mean()
def get_grid_image(X):
X = X[:8]
X = torchvision.utils.make_grid(X.detach().cpu(), nrow=X.shape[0]) * 0.5 + 0.5
return X
def make_image(Xs, Xt, Y):
Xs = get_grid_image(Xs)
Xt = get_grid_image(Xt)
Y = get_grid_image(Y)
return torch.cat((Xs, Xt, Y), dim=1).numpy()
def create_faceparse_model(path_model):
n_classes = 19
net = BiSeNet(n_classes=n_classes)
net.cuda()
print('model : {}'.format(path_model))
net.load_state_dict(torch.load(path_model))
net.eval()
return net
# Compute gaussian kernel
def CenterGaussianHeatMap(img_height, img_width, c_x, c_y, variance):
gaussian_map = np.zeros((img_height, img_width))
for x_p in range(img_width):
for y_p in range(img_height):
dist_sq = (x_p - c_x) * (x_p - c_x) + \
(y_p - c_y) * (y_p - c_y)
exponent = dist_sq / 2.0 / variance / variance
gaussian_map[y_p, x_p] = np.exp(-exponent)
return gaussian_map
def create_mask(X_,str_w,vis = False):
width = 512
height = 512
cy, cx = height/2.0, width/2.0
heatmap1 = CenterGaussianHeatMap(width, height, cx, cy, 150)
heatmap2 = CenterGaussianHeatMap(width, height, cx, cy, 200)
face_hair_mask_list = []
face_mask_list = []
hair_list = []
face_edge_list = []
background_list = []
with torch.no_grad():
Xt_0 = F.interpolate(X_, [512, 512], mode='bilinear', align_corners=True)
Xt_0 = Xt_0.cpu().numpy()
# print(Xt_0.shape)
for k in range(Xt_0.shape[0]):
d = to_tensor(Xt_0[k].transpose((1, 2, 0)))
d = torch.unsqueeze(d, 0)
d = d.cuda()
out_ = model_faceparse(d)[0]
parsing = out_.squeeze(0).cpu().numpy().argmax(0)
parsing_s = (parsing*10).astype(np.uint8)
if vis:
print('parsing shape :',parsing.shape)
cv2.namedWindow('parsing_'+str_w,0)
cv2.imshow('parsing_'+str_w,parsing_s)
cv2.namedWindow('img_'+str_w,0)
cv2.imshow('img_'+str_w,Xt_0[k].transpose((1, 2, 0))* 0.5 + 0.5)
#------------------------
face_hair_mask = np.zeros((parsing.shape[0], parsing.shape[1],3))
face_mask = np.zeros((parsing.shape[0], parsing.shape[1],3))
hair = np.zeros((parsing.shape[0], parsing.shape[1],3))
num_of_class = np.max(parsing)
for pi in range(1, num_of_class + 1):
index = np.where(parsing == pi)# 获得对应分类的的像素坐标
# vis_parsing_anno_color[index[0], index[1], :] = part_colors[pi]# 给对应的类别的掩码赋值
if pi in [1,2,3,4,5,6,7,8,9,10,11,12,13,14]:
face_hair_mask[index[0], index[1]] = 1.
face_mask[index[0], index[1]] = 1.
elif pi in [17,18,6]:
hair[index[0], index[1]] = 1.
face_hair_mask = hair + face_hair_mask
#----------- 背景掩码
background = np.array(np.logical_not(face_hair_mask)).astype(np.float32)
background = cv2.resize(background, (256,256))
background = cv2.erode(background, np.ones((11, 11), np.uint8)) # 执行腐蚀操作
background = cv2.blur(background,(3,3))
#------------
# kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (3, 3))
# face_hair_mask = cv2.dilate(face_hair_mask, kernel)
# face_hair_mask = face_hair_mask * np.expand_dims(heatmap1,axis =2)
# kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (3, 3))
# face_mask = cv2.dilate(face_mask, kernel)
# face_mask = face_mask * np.expand_dims(heatmap2,axis =2)
face_hair_mask = np.minimum(1.,face_hair_mask[:,:,:])
face_mask = np.minimum(1.,face_mask[:,:,:])
# hair = cv2.dilate(hair, kernel)
hair = np.minimum(1.,hair[:,:,:])
kernel = np.ones((5, 5), np.uint8)
face_hair_mask = cv2.resize(face_hair_mask, (256,256))
# face_hair_mask = cv2.erode(face_hair_mask, kernel) # 执行腐蚀操作
# for k in range(2):
# face_hair_mask = cv2.blur(face_hair_mask,(7,7))
face_mask = cv2.resize(face_mask, (256,256))
# ------------ face edge
kernel_edge = cv2.getStructuringElement(cv2.MORPH_RECT, (5, 5))
face_mask = cv2.erode(face_mask, kernel) # 执行腐蚀操作
for k in range(3):
face_mask_dilate = cv2.dilate(face_mask, kernel_edge)
kernel_edge = cv2.getStructuringElement(cv2.MORPH_RECT, (15, 15))
face_edge_dilate = np.array(np.logical_xor(face_mask_dilate,cv2.erode(face_mask, kernel_edge))).astype(np.float32)
kernel_edge = cv2.getStructuringElement(cv2.MORPH_RECT, (5, 5))
face_edge_dilate = cv2.dilate(face_edge_dilate, kernel_edge)
face_edge_dilate = cv2.blur(face_edge_dilate,(3,3))
# ------------
# face_mask = cv2.erode(face_mask, kernel) # 执行腐蚀操作
# for k in range(2):
# face_mask = cv2.blur(face_mask,(7,7))
hair = cv2.resize(hair, (256,256))
# hair = cv2.erode(hair, kernel) # 执行腐蚀操作
# for k in range(2):
# hair = cv2.blur(hair,(7,7))
face_hair_mask_list.append(face_hair_mask.transpose(2, 0, 1))
face_mask_list.append(face_mask.transpose(2, 0, 1))
hair_list.append(hair.transpose(2, 0, 1))
face_edge_list.append(face_edge_dilate.transpose(2, 0, 1))
background_list.append(background.transpose(2, 0, 1))
if vis:
cv2.namedWindow('face_hair_mask'+str_w,0)
cv2.imshow('face_hair_mask'+str_w,face_hair_mask)
cv2.namedWindow('face_mask'+str_w,0)
cv2.imshow('face_mask'+str_w,face_mask)
cv2.namedWindow('hair'+str_w,0)
cv2.imshow('hair'+str_w,hair)
cv2.waitKey(1)
#----------------------------
face_hair_mask_list = np.array(face_hair_mask_list)
face_hair_mask_list = face_hair_mask_list.astype(np.float32)
face_mask_list = np.array(face_mask_list)
face_mask_list = face_mask_list.astype(np.float32)
hair_list = | np.array(hair_list) | numpy.array |
"""
====================
Jumeg MFT Plotting.
====================
"""
import numpy as np
import matplotlib.pyplot as plt
import warnings
from mne import SourceEstimate, VolSourceEstimate
from mne.transforms import invert_transform, apply_trans
def plot_global_cdv_dist(stcdata, fwdmag=None):
"""
Plot global cdv-distribution at time of max |cdv|
Parameters
----------
stcdata: stc with ||cdv|| (point sequence as in fwdmag['source_rr'])
fwdmag: (opt) forward solution (to colorize srcs)
"""
print("##### Plot global cdv-distribution at time of max |cdv|:")
time_idx = np.argmax(np.max(stcdata, axis=0))
fig = plt.figure()
plt.xlim((0, stcdata.shape[0] + 100))
plt.ylim((-0.1 * np.max(stcdata[:, time_idx]),
1.1 * | np.max(stcdata[:, time_idx]) | numpy.max |
import random as rn
import multiprocessing
import platform
import sys
import os
from pathlib import Path
import numpy as np
import pytest
if platform.system() != 'Windows':
if sys.version_info[1] >= 8:
try:
#multiprocessing.get_start_method() != 'fork'
multiprocessing.set_start_method("fork")
except: #pylint:disable=bare-except # noqa: E722
pass
path = str(Path(os.getcwd()))
sys.path.insert(0, path)
from quanguru.QuantumToolbox import states#pylint: disable=import-error,wrong-import-position
from quanguru.QuantumToolbox import operators as ops #pylint: disable=import-error,wrong-import-position
class Helpers:
# used for the helper function fixture, put any helper function for testing as a static method in here and use
# helpers fixture (below) in the testing
@staticmethod
def generateRndDimAndExc(minval, dim=None):
# generates a random integer btw 2 to 20 to be used as dimension, and another integer btw 0 to dim-1 to be used
# either as the excitation or number of components in a super-position state
if dim is None:
dim = rn.randint(2, 20)
return dim, rn.randint(minval, dim-1)
@staticmethod
def generateRndStateParams(dim=None):
# using a randomly generated dimension and number of components, create a dictionary of random excitation
# positions and correponding (random populations) as a key:value combination. it is already normalised
dim, ncom = Helpers.generateRndDimAndExc(0, dim)
comps = list(dict.fromkeys([rn.randint(0, dim-1) for k in range(ncom+1)]))
pops = np.random.dirichlet(np.ones(len(comps)), size=1)[0]
excs = dict(zip(comps, pops))
return dim, excs
@staticmethod
def generateRndPureState(po=1, dim=None):
# generate a random ket state.
dim, excs = Helpers.generateRndStateParams(dim)
state = sum([(np.sqrt(v)**po)*states.basis(dim, k) for k, v in excs.items()])
return state, dim, excs
@pytest.fixture
def helpers():
# helpers fixture to access above helper functions in the testing
return Helpers
@pytest.fixture
def referenceValues():
# a fixture returning dictionary storing some reference values, such as some special operators, constants, etc
return {
'sigmaMinusReference': np.array([[0, 0], [1, 0]]), 'sigmaPlusReference': np.array([[0, 1], [0, 0]]),
'sigmaXReference': np.array([[0, 1], [1, 0]]), 'sigmaYReference': np.array([[0, -1j], [1j, 0]]),
'sigmaZReference': np.array([[1, 0], [0, -1]])
}
qubitStates = {
'0': np.array([[0], [1]]), '1': np.array([[1], [0]]),
'x+': (1/np.sqrt(2))*np.array([[1], [1]]), 'x-': (1/ | np.sqrt(2) | numpy.sqrt |
import sys, string
import numpy as np
from scipy.sparse.linalg import LinearOperator, cg, cgs, bicgstab
from math import *
#from mpi4py import MPI
import matplotlib.path as mplPath
import time
def display_init():
# Initial display
print("########################################################")
print("CoFFEE: Corrections For Formation Energies and ")
print(" Eigenvalues for charged defect simulations")
print("########################################################")
def IFFTnew(F_G, lmax, mmax, nmax):
#
# Compute 3D inverse Fourier transform of F_G.
# Dimension of the IFFT: (2*lmax+1,2*mmax+1,2*nmax+1)
#
F_r_tr = np.fft.ifftn(np.fft.ifftshift(F_G*(2*lmax+1)*(2*mmax+1)*(2*nmax+1)))
return F_r_tr
def ComputeEnergy(V_r,rho_r,lmax,mmax,nmax,cell_s):
#
# Calculate and print the electrostatic energy using the potential generated
# Integral of 0.5*V_r*dV
# Function takes inputs: real-space potential, V_r, charge density, rho_r
# Dimension of the arrays: (2*lmax+1,2*mmax+1,2*nmax+1)
# cell_s: object of the class cell
#
Vol = np.dot(cell_s.A2[0], np.cross(cell_s.A2[1],cell_s.A2[2]))
print("Volume: %4.3f"%( Vol))
dV = (1./float(2*lmax+1)/float(2*mmax+1)/float(2*nmax+1))*Vol
Sum = 0.0
for l in range(2*lmax+1):
for m in range(2*mmax+1):
for n in range(2*nmax+1):
Sum+= 0.5*V_r[l][m][n]*rho_r[l][m][n]*dV
print("! Total Energy (eV): %.4f"%( np.real(Sum)*13.60569253*2.))
def matvec2D(V,kmax,eps,c,i,j):
#
# Python routine to perform the matvec for the Poisson equation
# solved in the case of a 2D system. This routine is not used by
# default to compute the matvec. The Cython routine is used by default.
# Inputs:
# V: potential array; the x of Ax=b
# kmax: dimension of V is 2*kmax+1
# eps: object of the class epsilon, initialised at the beginning
# c: object of the class cell, initialised at the beginning
# i,j: indices of the G1, G2 vectors we are solving the linear equation for.
#
a_n = []
K1 = list(range(-kmax, kmax+1))
K2 = list(range(-kmax, kmax+1))
# Remove the G=0 element. We set V(G=0) = 0.
if i == 0. and j == 0.:
del K1[kmax]
del K2[kmax]
for k1 in K1:
Gz1 = k1*2.*np.pi/c.celldm3
Sum = 0.
j1 = 0
for k2 in K2:
Gz2 = k2*2.*np.pi/c.celldm3
Gx = i*c.B[0][0] + j*c.B[1][0]
Gy = i*c.B[0][1] + j*c.B[1][1]
# Eqn 10 in the paper.
Sum+= (eps.epsGz_a3[2*kmax+(k1-k2)]*Gz2*Gz1 + eps.epsGz_a1[2*kmax+(k1-k2)]*( Gx**2) + \
eps.epsGz_a2[2*kmax+(k1-k2)]*(Gy**2 ))*V[j1]
j1 = j1+1
b_n.append(Sum)
return np.array(b_n, dtype = complex)
def matvec1D_py(V,lmax,mmax,eps,c,k):
#
# Python routine to perform the matvec for the Poisson equation
# solved in the case of a 1D system. This routine is not used by
# default to compute the matvec. The Cython routine is used by default.
# Inputs:
# V: potential array; the x of Ax=b
# lmax,mmax: dimension of V is (2*lmax+1,2*mmax+1)
# eps: object of the class epsilon, initialised at the beginning
# c: object of the class cell, initialised at the beginning
# k: index of the G3 vector we are solving the linear equation for.
#
#
matvec = []
L1 = list(range(-lmax, lmax+1))
L2 = list(range(-lmax, lmax+1))
M1 = list(range(-mmax, mmax+1))
M2 = list(range(-mmax, mmax+1))
for l1 in L1:
Gx1 = l1*2.*np.pi/c.celldm1
for m1 in M1:
Gy1 = m1*2.*np.pi/c.celldm2
Sum = 0.0
j1 = 0
for l2 in L2:
Gx2 = l2*2.*np.pi/c.celldm1
for m2 in M2:
Gy2 = m2*2.*np.pi/c.celldm2
Gz = k*2.*np.pi/c.celldm3
# Eqn 11 in the paper.
Sum+= ( (Gx2*Gx1)*eps.eps_GxGy_a1[2*lmax+(l1-l2)][2*mmax+(m1-m2)]
(Gy2*Gy1)*eps.eps_GxGy_a2[2*lmax+(l1-l2)][2*mmax+(m1-m2)]
+ Gz**2*eps.eps_GxGy_a3[2*lmax+(l1-l2)][2*mmax+(m1-m2)]
)*V[j1]
j1 = j1+1
matvec.append(Sum)
matvec = np.array(matvec, dtype = complex)
return matvec
class cell:
#
# The cell class defines the cell parameters for the
# model calculation. It also sets up the reciprocal
# space grid based on the plane wave energy cut off.
#
def __init__(self):
#
# A stores the lattice vectors
# B stores the reciprocal lattice vectors
# celldm(1 to 3) are the cell dimension
# ecut is the plane wave energy cut-off
#
self.A = np.zeros((3,3))
self.B = np.zeros((3,3))
self.A2 = np.zeros((3,3))
self.celldm1 = 0.0
self.celldm2 = 0.0
self.celldm3 = 0.0
self.ecut = 18.0
def init_calc(self):
#
# Initialises the calculation. Sets up the
# grid in reciprocal space.
#
a_1 = self.A2[0]
a_2 = self.A2[1]
a_3 = self.A2[2]
self.B = 2*np.pi*np.linalg.inv(np.transpose(self.A2))
b_1 = 2*np.pi*np.cross(a_2,a_3)/np.dot(a_1, np.cross(a_2,a_3))
b_2 = 2*np.pi*np.cross(a_3,a_1)/np.dot(a_1, np.cross(a_2,a_3))
b_3 = 2*np.pi*np.cross(a_1,a_2)/np.dot(a_1, np.cross(a_2,a_3))
Gmax = np.sqrt(2*self.ecut)
imax = int( Gmax/np.sqrt(np.dot(b_1, b_1)) )+1
jmax = int( Gmax/np.sqrt(np.dot(b_2, b_2)) )+1
kmax = int( Gmax/np.sqrt(np.dot(b_3, b_3)) )+1
return imax,jmax,kmax
def disp_params(self):
#
# Display the simulation cell parameter read from the
# input file.
#
print("CELL PARAMETERS:")
print("Cell dimensions (bohr): %4.3f, %4.3f,%4.3f "%( \
self.celldm1, self.celldm2, self.celldm3))
print("Lattice vectors (normalized):")
print("a1: %4.3f, %4.3f, %4.3f"%( self.A[0][0],self.A[0][1],self.A[0][2]))
print("a2: %4.3f, %4.3f, %4.3f"%( self.A[1][0],self.A[1][1],self.A[1][2]))
print("a3: %4.3f, %4.3f, %4.3f"%( self.A[2][0],self.A[2][1],self.A[2][2]))
print("Plane-wave energy cut-off (Ry): %4.3f \n"%( self.ecut*2))
def read_params(self,file_name):
#
# Read "&CELL_PARAMETERS" section of the input file.
#
fp = open(file_name,'r')
lines = fp.readlines()
for il in range(len(lines)):
if "&CELL_PARAMETERS" in lines[il]:
for jl in range(il+1,len(lines)):
if "/" in lines[jl]:
break
if "Lattice_Vectors" in lines[jl]:
for ilv in range(3):
w = lines[ilv+jl+1].split()
w = list(filter(bool,w))
self.A[ilv] = [eval(w[0]),eval(w[1]),eval(w[2])]
self.A = np.array(self.A)
elif "Cell_dimensions" in lines[jl]:
w = lines[jl].split()
w = list(filter(bool,w))
if len(w) > 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
elif len(w)==2:
if w[1] == "bohr":
bohr_flag = True
elif w[1] == "angstrom":
bohr_flag = False
else:
print("ERROR while parsing input file; wrong units:%s, line: %d"%(file_name,jl+1))
sys.exit()
else:
bohr_flag = True
w = lines[jl+1].split()
w = list(filter(bool,w))
if len(w) > 3:
print("ERROR while parsing input file; too much data:%s, line: %d"%(file_name,jl+1+1))
sys.exit()
else:
if bohr_flag:
self.celldm1 = eval(w[0])
self.celldm2 = eval(w[1])
self.celldm3 = eval(w[2])
else:
self.celldm1 = eval(w[0])/0.529177249
self.celldm2 = eval(w[1])/0.529177249
self.celldm3 = eval(w[2])/0.529177249
elif "Ecut" in lines[jl]:
w = lines[jl].split("=")
if len(w) < 2 or len(w) > 3:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) == 2:
if w1[1] == "Hartree":
self.ecut = eval(w1[0])
elif w1[1] == "Rydberg":
self.ecut = eval(w1[0])*0.5
else:
self.ecut = eval(w1[0])
self.A2 = np.array([self.A[0]*self.celldm1,self.A[1]*self.celldm2,self.A[2]*self.celldm3])
class diel_profile:
def __init__(self):
#
# Initialise attributes of the class.
#
# Profile for 2D systems, along a1, a2 and a3 directions.
self.epsZ_a1 = []
self.epsZ_a2 = []
self.epsZ_a3 = []
# FT of the above arrays
self.epsGz_a1 = []
self.epsGz_a2 = []
self.epsGz_a3 = []
# Sets the profile type: "Slab/Gaussian/Wire/Ribbon"
self.Profile = "Slab"
# eps1_* is the value of epsilon inside the material
# eps2_* is the value of epsilon outside.
self.eps1_a1 = 1.0
self.eps2_a1 = 1.0
self.eps1_a2 = 1.0
self.eps2_a2 = 1.0
self.eps1_a3 = 1.0
self.eps2_a3 = 1.0
# Profile for 1D systems, along a1, a2 and a3 directions.
self.eps_xy_a1 = []
self.eps_xy_a2 = []
self.eps_xy_a3 = []
# Fourier transform of the above arrays
self.eps_GxGy_a1 = []
self.eps_GxGy_a2 = []
self.eps_GxGy_a3 = []
# Flag to write epsilon profile to file
self.plot_eps = True
# Slab/Gaussian profile properties
self.width = 1.0
self.center = 1.0
self.gauss_amp_a1 = 0.0
self.gauss_amp_a2 = 0.0
self.gauss_amp_a3 = 0.0
self.gauss_sigma = 1.0
self.smp = 1.0
# Wire profile properties
self.vertices_file = ""
self.circle = False
self.radius = 0.0
self.center_a1 = 0.5
self.center_a2 = 0.0
self.vertices = []
# Ribbon profile properties
self.center_x = 0.0
self.center_y = 0.0
self.width_y = 1.0
self.width_x = 1.0
self.gauss_along_x = True
self.gauss_along_y = False
def disp_params(self):
#
# Displays the parameters read from input file under the
# &DIELECTRIC PARAMETERS section
#
print("DIELECTRIC PARAMETERS")
if self.Profile == "Bulk":
print("Profile: Bulk")
print("epsilon tensor:")
e_tensor = np.array([[self.eps1_a1,0.0, 0.0],[0.0,self.eps1_a2,0.0], \
[0.0,0.0,self.eps1_a3]])
print(e_tensor)
elif self.Profile == "Slab":
print("Profile:", self.Profile)
print("Epsilon tensor inside the material:")
e_tensor = np.array([[self.eps1_a1,0.0, 0.0],[0.0,self.eps1_a2,0.0], \
[0.0,0.0,self.eps1_a3]])
print(e_tensor)
print("Epsilon tensor outside the material:")
e_tensor = np.array([[self.eps2_a1,0.0, 0.0],[0.0,self.eps2_a2,0.0], \
[0.0,0.0,self.eps2_a3]])
print(e_tensor)
print("Slab width (bohr):", self.width)
print("Slab center (bohr):", self.center)
print("Smoothness parameter (bohr):", self.smp)
elif self.Profile == "Ribbon":
print("Profile:", self.Profile)
print("Epsilon tensor inside the material:")
e_tensor = np.array([[self.gauss_amp_a1,0.0, 0.0],[0.0,self.gauss_amp_a2,0.0], \
[0.0,0.0,self.gauss_amp_a3]])
print(e_tensor)
if self.gauss_along_x:
print("Gaussian profile is along x")
print("Center of the gaussian (bohr):", self.center_x)
print("Width of the gaussian (bohr):", self.width_x)
elif self.gauss_along_y:
print("Gaussian profile is along y")
print("Center of the gaussian (bohr):", self.center_y)
print("Width of the gaussian (bohr):", self.width_y)
if not self.gauss_along_x:
print("Slab profile along x")
print("Center of the slab along x (bohr):", self.center_y)
print("Width of the slab along x (bohr):", self.width_y)
if not self.gauss_along_y:
print("Slab profile along y")
print("Center of the slab along y (bohr):", self.center_y)
print("Width of the slab along y (bohr):", self.width_y)
print("\n")
def construct_ribbon(self,gauss_amp,gauss_along_x,gauss_along_y,sigma,
c_x,c_y,w_x,w_y,smp,lmax,mmax,cell_s):
#
# Constructs the ribbon dielectric profile
# Constructs a slab-like profile along x and y directions
# unless gauss_along_x or gauss_along_y are specified
#
# Inputs:
# gauss_amp: Amplitude/max height of the Gaussian
# gauss_along_x: Flag to construct Gaussian along x
# gauss_along_y: Flag to construct Gaussian along y
# sigma:
# c_x, c_y: Center of the Gaussian
# w_x, w_y: Width of the slab-like profile
# smp: smoothening parameter at the edges of the slab profile
# lmax, mmax: Dimensions of the profile: (2*lmax+1,2*mmax+1)
# Set during initialisation of the calculation
# depending on the energy cut-off.
# cell_s: Object of the class cell, initialised at the beginning
#
# Returns:
# eps_xy: The ribbon profile
#
eps_xy = np.zeros((2*lmax+1,2*mmax+1))
a1_list = np.arange(0,1,1./(2*lmax+1))
a2_list = np.arange(0,1,1./(2*mmax+1))
c_crys_x = c_x/cell_s.celldm1
c_crys_y = c_y/cell_s.celldm2
c_crys_x_n = np.searchsorted(a1_list,c_crys_x)/float(2*lmax+1)
c_crys_y_n = np.searchsorted(a2_list,c_crys_y)/float(2*mmax+1)
c_x = c_crys_x_n*cell_s.celldm1
c_y = c_crys_y_n*cell_s.celldm2
a1_list = a1_list*cell_s.celldm1
a2_list = a2_list*cell_s.celldm2
# Facilitate periodic boundary conditions.
# Checking left and right of the box along a1
# overflow flags: of_* are set after checks.
of_a1_l = False
of_a1_r = False
of_a2_l = False
of_a2_r = False
if gauss_along_x:
if c_x - 4*sigma < 0.:
of_a1_l = True
if c_x + 4*sigma > cell_s.celldm1:
of_a1_r = True
if c_y - (w_y/2 + 2*smp) < 0.:
of_a2_l = True
if c_y + (w_y/2 + 2*smp) > cell_s.celldm2:
of_a2_r = True
else:
if c_y - 4*sigma < 0.:
of_a2_l = True
if c_y + 4*sigma > cell_s.celldm2:
of_a2_r = True
if c_x - (w_x/2 + 2*smp) < 0.:
of_a1_l = True
if c_x + (w_x/2 + 2*smp) > cell_s.celldm1:
of_a1_r = True
# Initially construct Gaussian with gauss_amp - 1; Add 1 at the end
amp_sqrt = (gauss_amp-1)**0.5
l=0
#
# Construct the ribbon profile in accordance with the input flags,
# respecting the periodic boundary consitions.
#
for x_e in a1_list:
if gauss_along_x:
if of_a1_l and cell_s.celldm1 - x_e < 4*sigma:
x = 0 - (cell_s.celldm1 - x_e)
elif of_a1_r and x_e < 4*sigma:
x = cell_s.celldm1 + x_e
else:
x = x_e
else:
if of_a1_l and cell_s.celldm1 - x_e < (w_x/2 + 2*smp):
x = 0 - (cell_s.celldm1 - x_e)
elif of_a1_r and x_e < (w_x/2 + 2*smp):
x = cell_s.celldm1 + x_e
else:
x = x_e
m=0
for y_e in a2_list:
if gauss_along_y:
if of_a2_l and cell_s.celldm2 - y_e < 4*sigma:
y = 0 - (cell_s.celldm2 - y_e)
elif of_a2_r and y_e < 4*sigma:
y = cell_s.celldm2 + y_e
else:
y = y_e
else:
if of_a2_l and cell_s.celldm2 - y_e < (w_y/2 + 2*smp):
y = 0 - (cell_s.celldm2 - y_e)
elif of_a2_r and y_e < (w_y/2 + 2*smp):
y = cell_s.celldm2 + y_e
else:
y = y_e
if gauss_along_x:
eps_x = amp_sqrt*np.exp(-1.*(x-c_x)**2/(2*sigma**2))
eps_y = ((0.5*(-1*amp_sqrt)*erf( (y-(c_y+w_y/2.))/smp))
- (0.5*(-1*amp_sqrt)*erf( (y-(c_y-w_y/2.))/smp)))
eps_xy[l][m] = eps_x*eps_y
else:
eps_y = amp_sqrt*np.exp(-1.*(y-c_y)**2/(2*sigma**2))
eps_x = ((0.5*(-1*amp_sqrt)*erf( (x-(c_x+w_x/2.))/smp))
- (0.5*(-1*amp_sqrt)*erf( (x-(c_x-w_x/2.))/smp)) )
eps_xy[l][m] = eps_x*eps_y
m = m + 1
l = l + 1
# This ensures the epsilon outside the material (in vacuum) is 1
eps_xy = eps_xy + 1
return eps_xy
def construct_epsxy(self,cell_s,lmax,mmax):
#
# Constructs Wire or Ribbon profile and updates the
# relevant attributes of the epsilon class object calling it.
#
if self.Profile == "Wire":
self.eps_xy_a3 = self.construct_wire(self.eps1_a3,self.eps2_a3,cell_s,lmax,mmax,self.circle,self.vertices_file)
self.eps_xy_a2 = self.construct_wire(self.eps1_a2,self.eps2_a2,cell_s,lmax,mmax,self.circle,self.vertices_file)
self.eps_xy_a1 = self.construct_wire(self.eps1_a1,self.eps2_a1,cell_s,lmax,mmax,self.circle,self.vertices_file)
if self.Profile == "Ribbon":
self.eps_xy_a3 = self.construct_ribbon(self.gauss_amp_a3,self.gauss_along_x,
self.gauss_along_y,self.gauss_sigma,self.center_x,self.center_y,self.width_x,
self.width_y,self.smp,lmax,mmax,cell_s)
self.eps_xy_a2 = self.construct_ribbon(self.gauss_amp_a2,self.gauss_along_x,
self.gauss_along_y,self.gauss_sigma,self.center_x,self.center_y,self.width_x,
self.width_y,self.smp,lmax,mmax,cell_s)
self.eps_xy_a1 = self.construct_ribbon(self.gauss_amp_a1,self.gauss_along_x,
self.gauss_along_y,self.gauss_sigma,self.center_x,self.center_y,self.width_x,
self.width_y,self.smp,lmax,mmax,cell_s)
def construct_wire(self,eps1,eps2,cell_s,lmax,mmax,circle=False,vertices_file=""):
#
# Construct the wire profile.
# Inputs:
# eps1, eps2: eps1 is the epsilon inside the material. eps2 outside.
# cell_s: An object of the class cell, initialised at the beginning
# lmax,mmax: (2*lmax+1,2*mmax+1) dimension of the wire profile
# circle: Flag for a circular cross-section of the wire profile
# vertices_file: File to read in the vertices of the polygon forming the
# cross-section of the wire
#
if circle==False and vertices_file=="":
print("Supply information on wire cross-section; circular or provide vertices file.")
exit()
if circle==False:
fp = open(vertices_file,"r")
lines = fp.readlines()
fp.close()
V = []
for i in range(len(lines)):
if "vertices_pos" in lines[i]:
w = lines[i+1].split()
w = list(filter(bool,w))
n_v = eval(w[0])
for j in range(n_v):
w = lines[i+j+2].split()
w = list(filter(bool,w))
V.append([eval(w[0]),eval(w[1])])
break
V = np.array(V)
xmin = min(V[:,0])
ymin = min(V[:,1])
xmax = max(V[:,0])
ymax = max(V[:,1])
bbPath = mplPath.Path(V)
X = np.arange(0.,cell_s.celldm1,cell_s.celldm1/(2*lmax+1))
Y = np.arange(0.,cell_s.celldm2,cell_s.celldm2/(2*mmax+1))
eps_xy = np.zeros((2*lmax+1,2*mmax+1))
for i in range(2*lmax+1):
for j in range(2*mmax+1):
if bbPath.contains_point((X[i],Y[j])):
eps_xy[i][j] = eps1
else:
eps_xy[i][j] = eps2
if ymin < 0:
y = 0 - cell_s.celldm1/(2*mmax+1)
cnt = 1
while(y>=ymin):
for i in range(len(X)):
if not bbPath.contains_point((X[i],y)):
eps_xy[i][2*mmax+1-cnt] = eps1
else:
eps_xy[i][2*mmax+1-cnt] = eps2
cnt = cnt + 1
y = y - cell_s.celldm1/(2*mmax+1)
else:
s0 = self.radius
c_x = self.center_a1*cell_s.A2[0][0] + self.center_a2*cell_s.A2[1][0]
c_y = self.center_a1*cell_s.A2[0][1] + self.center_a2*cell_s.A2[1][1]
eps_xy = np.zeros((2*lmax+1,2*mmax+1))
for l in range(2*lmax+1):
x = l*cell_s.celldm1/(2*lmax+1)
for m in range(2*mmax+1):
y = m*cell_s.celldm1/(2*mmax+1)
s = np.sqrt((x-c_x)**2 + (y-c_y)**2)
eps_xy[l][m] = (0.5*(eps2-eps1)*erf( (s-s0)/self.smp )) - (0.5*(eps2-eps1)*erf( (s+s0)/self.smp) ) + eps2
return eps_xy
def construct_epsZ(self,cell_s,nmax):
if self.Profile == "Slab":
self.epsZ_a1 = self.construct_slab(self.eps1_a1,self.eps2_a1,cell_s,nmax)
self.epsZ_a2 = self.construct_slab(self.eps1_a2,self.eps2_a2,cell_s,nmax)
self.epsZ_a3 = self.construct_slab(self.eps1_a3,self.eps2_a3,cell_s,nmax)
elif self.Profile == "Gaussian":
self.epsZ_a1 = self.construct_gauss(self.gauss_amp_a1,self.gauss_sigma,cell_s,nmax)
self.epsZ_a2 = self.construct_gauss(self.gauss_amp_a2,self.gauss_sigma,cell_s,nmax)
self.epsZ_a3 = self.construct_gauss(self.gauss_amp_a3,self.gauss_sigma,cell_s,nmax)
def construct_slab(self,eps1,eps2,cell_s,nmax):
epsZ_tmp = []
a3_list = np.arange(0,1,1./(2*nmax+1))
c_crys = self.center/cell_s.celldm3
c_crys_n = np.searchsorted(a3_list,c_crys)/float(2*nmax+1)
# Crys -> Cartesian
c_z = c_crys_n*cell_s.celldm3
a3_list = a3_list*cell_s.celldm3
# Facilitate periodic boundary conditions.
# Checking left and right of the box along a3
of_a3_l = False
if c_z - self.width/2 - 2*self.smp < 0.:
of_a3_l = True
of_a3_r = False
if c_z + self.width/2 + 2*self.smp > cell_s.celldm3:
of_a3_r = True
for a3_e in a3_list:
if of_a3_l and cell_s.celldm3 - a3_e < self.width/2 + 2*self.smp:
z = 0 - (cell_s.celldm3 - a3_e)
elif of_a3_r and a3_e < self.width/2 + 2*self.smp:
z = cell_s.celldm3 + a3_e
else:
z = a3_e
epsZ_tmp.append( (0.5*(eps2-eps1)*erf( (z-(c_z+self.width/2.))/self.smp)) - (0.5*(eps2-eps1)*erf( (z-(c_z-self.width/2.))/self.smp) ) + eps2 )
return epsZ_tmp
def construct_gauss(self,amp,sig,cell_s,nmax):
epsZ_tmp = []
# Facilitate periodic boundary conditions.
# Checking left and right of the box along a3
of_a3_l = False
if self.center - 4*sig < 0:
of_a3_l = True
of_a3_r = False
if self.center + 4*sig > cell_s.celldm3:
of_a3_r = True
for n in range(0, 2*nmax+1):
z = n*cell_s.celldm3/(2*nmax)
if of_a3_l and cell_s.celldm3 - z < 4*sig:
z = 0 - (cell_s.celldm3 - z)
elif of_a3_r and z < 4*sig:
z = cell_s.celldm3 + z
epsZ_tmp.append(1.0 + amp*np.exp(-1.*(z-self.center)**2/(2*sig**2)))
return epsZ_tmp
def FFT(self,lmax,mmax,nmax):
if self.Profile == "Slab" or self.Profile == "Gaussian":
self.epsGz_a1 = self.FFT_1D(self.epsZ_a1,nmax)
self.epsGz_a2 = self.FFT_1D(self.epsZ_a2,nmax)
self.epsGz_a3 = self.FFT_1D(self.epsZ_a3,nmax)
elif self.Profile == "Wire" or self.Profile == "Ribbon":
self.eps_GxGy_a1 = self.FFT_2D(self.eps_xy_a1,lmax,mmax)
self.eps_GxGy_a2 = self.FFT_2D(self.eps_xy_a2,lmax,mmax)
self.eps_GxGy_a3 = self.FFT_2D(self.eps_xy_a3,lmax,mmax)
def FFT_2D(self,F_xy, lmax, mmax): #2D Fourier transform
F_GxGy = np.fft.fft2(F_xy)
F_GxGy_shift = np.fft.fftshift(F_GxGy)
F_GxGy_req = F_GxGy_shift/np.double(2*lmax+1)/np.double(2*mmax+1)
return F_GxGy_req
def IFFT_2D(self,F_GxGy, lmax, mmax): #2D Inverse fourier transform
F_xy = np.fft.ifft2(np.fft.ifftshift(F_GxGy*np.double(2*lmax+1)*np.double(2*mmax+1)))
return F_xy
# 1D fourier transform
def FFT_1D(self,F_z,nmax):
F_Gz = np.fft.fft(F_z)
F_Gz_shift = np.fft.fftshift(F_Gz)
F_Gz_req = F_Gz_shift/float(2*nmax+1)
return F_Gz_req
# Parameters to be read from the &DIELECTRIC_PARAMETERS section
def read_params(self,file_name):
fp = open(file_name,'r')
lines = fp.readlines()
for il in range(len(lines)):
if "&DIELECTRIC_PARAMETERS" in lines[il]:
w = lines[il].split()
w = list(filter(bool,w))
if len(w) == 1:
print("ERROR, please specify type of profile in input: %s, line: %d"%(file_name,il+1))
else:
self.Profile = w[1]
for jl in range(il+1,len(lines)):
if "/" in lines[jl]:
break
if "Epsilon1_a1" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
self.eps1_a1 = eval(w[1])
elif "Epsilon2_a1" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
self.eps2_a1 = eval(w[1])
elif "Epsilon1_a2" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
self.eps1_a2 = eval(w[1])
elif "Epsilon2_a2" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
self.eps2_a2 = eval(w[1])
elif "Epsilon1_a3" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
self.eps1_a3 = eval(w[1])
elif "Epsilon2_a3" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
self.eps2_a3 = eval(w[1])
elif "Width" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.width = eval(w1[0])
elif w1[1] == "angstrom":
self.width = eval(w1[0])/0.529177249
else:
self.width = eval(w1[0])
elif "W_x" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.width_x = eval(w1[0])
elif w1[1] == "angstrom":
self.width_x = eval(w1[0])/0.529177249
else:
self.width_x = eval(w1[0])
elif "W_y" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.width_y = eval(w1[0])
elif w1[1] == "angstrom":
self.width_y = eval(w1[0])/0.529177249
else:
self.width_y = eval(w1[0])
elif "Centre" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.center = eval(w1[0])
elif w1[1] == "angstrom":
self.center = eval(w1[0])/0.529177249
else:
self.center = eval(w1[0])
elif "C_x" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.center_x = eval(w1[0])
elif w1[1] == "angstrom":
self.center_x = eval(w1[0])/0.529177249
else:
self.center_x = eval(w1[0])
elif "C_y" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.center_y = eval(w1[0])
elif w1[1] == "angstrom":
self.center_y = eval(w1[0])/0.529177249
else:
self.center_y = eval(w1[0])
elif "Gauss_amp_a1" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.gauss_amp = eval(w1[0])
elif w1[1] == "angstrom":
self.gauss_amp_a1 = eval(w1[0])/0.529177249
else:
self.gauss_amp_a1 = eval(w1[0])
elif "Gauss_amp_a2" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.gauss_amp_a2 = eval(w1[0])
elif w1[1] == "angstrom":
self.gauss_amp_a2 = eval(w1[0])/0.529177249
else:
self.gauss_amp_a2 = eval(w1[0])
elif "Gauss_amp_a3" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.gauss_amp_a3 = eval(w1[0])
elif w1[1] == "angstrom":
self.gauss_amp_a3 = eval(w1[0])/0.529177249
else:
self.gauss_amp_a3 = eval(w1[0])
elif "Sigma" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.gauss_sigma = eval(w1[0])
elif w1[1] == "angstrom":
self.gauss_sigma = eval(w1[0])/0.529177249
else:
self.gauss_sigma = eval(w1[0])
elif "Smoothness" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.smp = eval(w1[0])
elif w1[1] == "angstrom":
self.smp = eval(w1[0])/0.529177249
else:
self.smp = eval(w1[0])
elif "Radius" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.radius = eval(w1[0])
elif w1[1] == "angstrom":
self.radius = eval(w1[0])/0.529177249
else:
self.radius = eval(w1[0])
elif "c_a1" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.center_a1 = eval(w1[0])
elif w1[1] == "angstrom":
self.center_a1 = eval(w1[0])/0.529177249
else:
self.center_a1 = eval(w1[0])
elif "c_a2" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1]
w1 = w1.split()
w1 = list(filter(bool,w1))
if len(w1) > 1:
if w1[1] == "bohr":
self.center_a2 = eval(w1[0])
elif w1[1] == "angstrom":
self.center_a2 = eval(w1[0])/0.529177249
else:
self.center_a2 = eval(w1[0])
elif "Vertices_file" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
w1 = w[1].split()
w1 = list(filter(bool,w1))
self.vertices_file = w1[0]
elif "Circle" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
self.circle = eval(w[1])
elif "Plot_eps" in lines[jl]:
w = lines[jl].split("=")
if len(w) != 2:
print("ERROR while parsing input file: %s, line: %d"%(file_name,jl+1))
sys.exit()
self.plot_eps = eval(w[1])
class gaussian:
def __init__(self):
self.sigma = 0.5
self.tot_charge = 0
self.c_a1 = 0.5
self.c_a2 = 0.5
self.c_a3 = 0.5
self.rho_r = []
self.rho_G = []
def FFT(self,lmax,mmax,nmax):
F_G = np.fft.fftn(self.rho_r)
F_G_shift = np.fft.fftshift(F_G)
self.rho_G = F_G_shift/(2.*lmax+1)/(2.*mmax+1)/(2.*nmax+1)
def disp_params(self):
print("GAUSSIAN_PARAMETERS:")
print("Total charge:", self.tot_charge)
print("Center of the gaussian (in crystal units):")
print(self.c_a1, self.c_a2, self.c_a3)
print("Gaussian width (bohr):")
print(self.sigma)
print("\n")
def construct_rho(self,cell_s,lmax,mmax,nmax):
a1_list = np.zeros(2*lmax+1)
a2_list = np.zeros(2*mmax+1)
a3_list = np.zeros(2*nmax+1)
for l in range(2*lmax+1):
a1_list[l] = l*1./(2*lmax+1)
for m in range(2*mmax+1):
a2_list[m] = m*1./(2*mmax+1)
for n in range(2*nmax+1):
a3_list[n] = n*1./(2*nmax+1)
# Original center of the Gaussian, in crystal units
c_crys = np.array([self.c_a1,self.c_a2,self.c_a3])
c_a1_g = np.searchsorted(a1_list,self.c_a1)/float(2*lmax+1)
c_a2_g = np.searchsorted(a2_list,self.c_a2)/float(2*mmax+1)
c_a3_g = np.searchsorted(a3_list,self.c_a3)/float(2*nmax+1)
# New, slightly shifted center.
c_crys_n = np.array([c_a1_g,c_a2_g,c_a3_g])
# In Cartesian
c_x = np.dot(c_crys_n,cell_s.A2[:,0])
c_y = | np.dot(c_crys_n,cell_s.A2[:,1]) | numpy.dot |
# Create by Packetsss
# Personal use is allowed
# Commercial use is prohibited
import numpy as np
a = np.array([1, 2, 3])
# numpy list
b = np.array([[9.0, 8.0, 7.0], [6.0, 5.0, 4.0]])
'''print(b)'''
# 2d array
'''print(b.ndim)'''
# get dimension
'''print(a.shape)'''
# get # of elements in 1st, 2nd... dimension
'''print(a.dtype)'''
# int32 by default
# a = np.array([1, 2, 3], dtype="int16") to change type
'''print(a.itemsize)'''
# int 32 have size of 4
'''print(a.size * a.itemsize)
or
print(a.nbytes)'''
# total size
c = np.array([[1, 2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14]])
'''print(c[0, 2] == 3)'''
# get specific element
'''print(c[0, :])'''
# get whole 1st row
'''print(c[0, 1:-1:2])'''
# step the array
c[1, 5] = 20
'''print(c)'''
# change element
c[:, 2] = [1, 2]
# change all 2nd cln to 5
d = np.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
'''print(d)'''
# 3d array
'''print(d[0, 1, 1])'''
# index for 4
d[:, 1, :] = [[9, 9], [8, 8]]
# replace value
e = np.zeros((5, 3, 4))
'''print(e)'''
# get multidimensional zeros matrix
f = np.ones(3)
'''print(f)'''
# get all ones
'''print(np.full((2, 2), 99))'''
# get all 99's
'''print(np.full_like(c, 4))'''
# get all 4's using c's dimension
'''print(np.random.rand(4, 2))
print(np.random.random_sample(c.shape))'''
# random from 0 to 1 using given size
'''print(np.random.randint(1, 5, size=(3, 3)))'''
# get a randi matrix from 2 to 4
'''print(np.identity(5))'''
# identity matrix
arr = np.array([[1, 2, 3]])
r1 = np.repeat(arr, 3, axis=0)
'''print(r1)'''
# repeat arr 3 times
quiz = np.zeros((9, 9))
quiz[0, :] = 1
quiz[:, 0] = 1
quiz[-1, :] = 1
quiz[:, -1] = 1
dim = int(np.floor(quiz.shape[0] / 2))
quiz[dim, dim] = 9
'''print(quiz)'''
g = np.array([1, 2, 3, 4])
'''print(g+2)'''
# add every element by 2
g * 2
g - 2
g ** 3
np.sin(g)
# all calculation
h = np.array([1, 0, 1, 0])
'''print(g + h)'''
# array add array
a1 = np.ones((2, 3))
b1 = np.full((3, 2), 2)
'''print(np.matmul(a1, b1))'''
# matrix multiplication
c1 = | np.identity(3) | numpy.identity |
import glob
import os
import pickle
import matplotlib.pyplot as plt
import numpy as np
import scipy.stats as spst
from scipy.integrate import odeint
from hmc import summarize
from hmc.applications.fitzhugh_nagumo import fn_dynamics
from load_data import load_data
def euclidean_samples():
num_samples = [1000, 10000, 100000]
euclid = {}
for ns in num_samples:
d = {}
fns = sorted(glob.glob(os.path.join('samples', '*num-samples-{}-*euclidean*'.format(ns))))
for f in fns:
ss = f.split('-step-size-')[1].split('-')[0]
ss = float(ss)
with open(f, 'rb') as g:
d[ss] = pickle.load(g)
euclid[ns] = d
return euclid
def iid_samples():
iid = []
with open(os.path.join('data', 'samples.pkl'), 'rb') as f:
iid.append(pickle.load(f))
with open(os.path.join('data', 'samples-{}.pkl'.format(1)), 'rb') as f:
iid.append(pickle.load(f))
return iid
def riemannian_samples(newton_momentum=False, newton_position=False):
num_samples = [1000, 10000, 100000]
rmn = {}
for ns in num_samples:
d = {}
fns = sorted(glob.glob(os.path.join('samples', '*num-steps-6*-num-samples-{}-*riemannian*partial-momentum-0.0*-correct-True*newton-momentum-{}*newton-position-{}*'.format(ns, newton_momentum, newton_position))))
for f in fns:
t = f.split('-thresh-')[1].split('-m')[0]
t = float(t)
with open(f, 'rb') as g:
d[t] = pickle.load(g)
rmn[ns] = d
return rmn
def fitzhugh_nagumo():
euclid = euclidean_samples()[100000]
rmn = riemannian_samples()[100000]
y, time, sigma, state = load_data()
rkeys = sorted(rmn.keys(), reverse=False)
ekeys = sorted(euclid.keys(), reverse=False)
m = len(rkeys) + len(ekeys)
fig = plt.figure(figsize=(30, 5))
for i, t in enumerate(ekeys):
s = euclid[t]['samples']
yh = []
for j in range(0, len(s), 100):
params = tuple(s[j])
yh.append(odeint(fn_dynamics, state, time, params))
yh = np.array(yh)
ax = fig.add_subplot(1, m, i+1)
ax.plot(time, yh[..., 0].T, '-', color='tab:blue', alpha=0.1)
ax.plot(time, yh[..., 1].T, '-', color='tab:orange', alpha=0.1)
ax.plot(time, y[..., 0], '.', color='tab:blue', markersize=2)
ax.plot(time, y[..., 1], '.', color='tab:orange', markersize=2)
ax.set_ylim((-3, 3))
ax.set_title('Euclid. {:.0e}'.format(t), fontsize=35)
ax.axes.get_xaxis().set_visible(False)
ax.axes.get_yaxis().set_visible(False)
for i, t in enumerate(rkeys):
s = rmn[t]['samples']
yh = []
for j in range(0, len(s), 100):
params = tuple(s[j])
yh.append(odeint(fn_dynamics, state, time, params))
yh = np.array(yh)
ax = fig.add_subplot(1, m, i+len(ekeys)+1)
ax.plot(time, yh[..., 0].T, '-', color='tab:blue', alpha=0.1)
ax.plot(time, yh[..., 1].T, '-', color='tab:orange', alpha=0.1)
ax.plot(time, y[..., 0], '.', color='tab:blue', markersize=2)
ax.plot(time, y[..., 1], '.', color='tab:orange', markersize=2)
ax.set_ylim((-3, 3))
ax.set_title('Thresh. {:.0e}'.format(t), fontsize=35)
ax.axes.get_xaxis().set_visible(False)
ax.axes.get_yaxis().set_visible(False)
fig.tight_layout()
fig.savefig(os.path.join('images', 'fitzhugh-nagumo.png'))
def effective_sample_size():
euclid = euclidean_samples()[100000]
rmn = riemannian_samples()[100000]
ekeys = sorted(euclid.keys(), reverse=False)
rkeys = sorted(rmn.keys(), reverse=False)
labels = ['Euclidean {}'.format(t) for t in ekeys] + ['Threshold {:.0e}'.format(t) for t in rkeys]
fig = plt.figure(figsize=(10, 4))
ax = fig.add_subplot(111)
num_breaks = 20
ess = {}
for t in ekeys:
breaks = np.split(euclid[t]['samples'], num_breaks, axis=0)
k = 'euclid-{}'.format(t)
ess[k] = []
for i, b in enumerate(breaks):
metrics = summarize(b)
m = metrics['ess'].min()
ess[k].append(m)
ax.violinplot([ess[k] for k in ess.keys()], showmeans=True, showmedians=True, showextrema=False)
ess = {}
for t in rkeys:
breaks = np.split(rmn[t]['samples'], num_breaks, axis=0)
k = 'rmn-{}'.format(t)
ess[k] = []
for i, b in enumerate(breaks):
metrics = summarize(b)
m = metrics['ess'].min()
ess[k].append(m)
vpb = ax.violinplot([ess[k] for k in ess.keys()], positions=np.arange(len(rkeys)) + 2, showmeans=True, showmedians=True, showextrema=False)
ax.set_xticks(np.arange(1, len(labels) + 1))
ax.set_xticklabels(['' for l in labels])
ax.set_xticklabels(labels)
ax.set_xlim(0.25, len(labels) + 0.75)
for tick in ax.get_xticklabels():
tick.set_rotation(90)
ax.axvline(len(ekeys) + 0.5, color='black', linestyle='--')
ax.set_xlabel('')
ax.set_ylabel('Min. ESS', fontsize=16)
ax.tick_params(axis='y', labelsize=16)
ax.tick_params(axis='x', labelsize=16)
ax.grid(linestyle=':')
fig.tight_layout()
fig.savefig(os.path.join('images', 'minimum-ess.pdf'))
def effective_sample_size_per_second():
euclid = euclidean_samples()[100000]
rmn = riemannian_samples()[100000]
nm_rmn = riemannian_samples(True)[100000]
nb_rmn = riemannian_samples(True, True)[100000]
ekeys = sorted(euclid.keys(), reverse=False)
rkeys = sorted(rmn.keys(), reverse=False)
labels = ['Euclid. {}'.format(t) for t in ekeys] + ['Thresh. {:.0e}'.format(t) for t in rkeys]
for vidx in range(1, 4):
labels = ['Euclid. {}'.format(t) for t in ekeys] + ['Thresh. {:.0e}'.format(t) for t in rkeys]
fig = plt.figure()
ax = fig.add_subplot(111)
num_breaks = 20
ess = {}
for t in ekeys:
breaks = np.split(euclid[t]['samples'][:, [-vidx]], num_breaks, axis=0)
k = 'euclid-{}'.format(t)
ess[k] = []
for i, b in enumerate(breaks):
metrics = summarize(b)
m = metrics['ess'].min() / (euclid[t]['time'] / num_breaks)
ess[k].append(m)
ax.violinplot([ess[k] for k in ess.keys()], showmeans=True, showmedians=True, showextrema=False)
ess = {}
for t in rkeys:
breaks = np.split(rmn[t]['samples'][:, [-vidx]], num_breaks, axis=0)
k = 'rmn-{}'.format(t)
ess[k] = []
for i, b in enumerate(breaks):
metrics = summarize(b)
m = metrics['ess'].min() / (rmn[t]['time'] / num_breaks)
ess[k].append(m)
vpb = ax.violinplot([ess[k] for k in ess.keys()], positions=np.arange(len(rkeys)) + 2, showmeans=True, showmedians=True, showextrema=False)
ax.set_xticks(np.arange(1, len(labels) + 1))
ax.set_xticklabels(['' for l in labels])
ax.set_xticklabels(labels)
ax.set_xlim(0.25, len(labels) + 0.75)
for tick in ax.get_xticklabels():
tick.set_rotation(90)
ax.axvline(len(ekeys) + 0.5, color='black', linestyle='--')
ax.set_xlabel('')
ax.set_ylabel('ESS / Sec.', fontsize=20)
ax.tick_params(axis='x', labelsize=20)
ax.tick_params(axis='y', labelsize=20)
ax.grid(linestyle=':')
fig.tight_layout()
fig.savefig(os.path.join('images', 'minimum-ess-per-second-{}.pdf'.format(vidx)))
labels = ['Thresh. {:.0e}'.format(t) for t in rkeys]
fig = plt.figure()
ax = fig.add_subplot(111)
num_breaks = 20
ess = {}
for t in rkeys:
breaks = np.split(rmn[t]['samples'][:, [-vidx]], num_breaks, axis=0)
k = 'rmn-{}'.format(t)
ess[k] = []
for i, b in enumerate(breaks):
metrics = summarize(b)
m = metrics['ess'].min() / (rmn[t]['time'] / num_breaks)
ess[k].append(m)
vpb = ax.violinplot([ess[k] for k in ess.keys()], positions=np.arange(len(rkeys)) + 1, showmeans=True, showmedians=True, showextrema=False)
ess = {}
for t in rkeys:
breaks = np.split(nm_rmn[t]['samples'][:, [-vidx]], num_breaks, axis=0)
k = 'rmn-{}'.format(t)
ess[k] = []
for i, b in enumerate(breaks):
metrics = summarize(b)
m = metrics['ess'].min() / (nm_rmn[t]['time'] / num_breaks)
ess[k].append(m)
vpc = ax.violinplot([ess[k] for k in ess.keys()], positions=np.arange(len(rkeys)) + 1, showmeans=True, showmedians=True, showextrema=False)
ess = {}
for t in rkeys:
breaks = np.split(nb_rmn[t]['samples'][:, [-vidx]], num_breaks, axis=0)
k = 'rmn-{}'.format(t)
ess[k] = []
for i, b in enumerate(breaks):
metrics = summarize(b)
m = metrics['ess'].min() / (nb_rmn[t]['time'] / num_breaks)
ess[k].append(m)
vpd = ax.violinplot([ess[k] for k in ess.keys()], positions=np.arange(len(rkeys)) + 1, showmeans=True, showmedians=True, showextrema=False)
ax.set_xticks(np.arange(1, len(labels) + 1))
ax.set_xticklabels(['' for l in labels])
ax.set_xticklabels(labels)
ax.set_xlim(0.25, len(labels) + 0.75)
for tick in ax.get_xticklabels():
tick.set_rotation(90)
ax.set_xlabel('')
ax.set_ylabel('ESS / Sec.', fontsize=20)
ax.tick_params(axis='x', labelsize=20)
ax.tick_params(axis='y', labelsize=20)
ax.grid(linestyle=':')
if vidx == 1:
ax.legend([vpb["bodies"][0], vpc["bodies"][0], vpd["bodies"][0]], [r'Fixed Point', r'Newton (Mom.)', r'Newton (Mom. and Pos.)'], fontsize=16, loc='upper left')
fig.tight_layout()
fig.savefig(os.path.join('images', 'minimum-ess-per-second-vs-newton-{}.pdf'.format(vidx)))
def kolmogorov_smirnov():
euclid = euclidean_samples()[100000]
rmn = riemannian_samples()[100000]
nm_rmn = riemannian_samples(True)[100000]
nb_rmn = riemannian_samples(True, True)[100000]
iid = iid_samples()
num_iid_ks = 100
iid_ks = np.zeros(num_iid_ks)
x, y = iid[0], iid[1]
for i in range(num_iid_ks):
u = np.random.normal(size=x.shape[-1])
u = u / np.linalg.norm(u)
iid_ks[i] = spst.ks_2samp(x@u, y@u).statistic
print(iid_ks)
summarize(x)
summarize(y)
summarize(rmn[1e-8]['samples'])
print(list(rmn.keys()))
ekeys = sorted(euclid.keys(), reverse=False)
rkeys = sorted(rmn.keys(), reverse=False)
labels = ['I.I.D.'] + ['Euclid. {}'.format(t) for t in ekeys] + ['Thresh. {:.0e}'.format(t) for t in rkeys]
fig = plt.figure(figsize=(10, 4))
ax = fig.add_subplot(111)
ax.violinplot([np.log10(iid_ks)], showmeans=True, showmedians=True, showextrema=False)
ess = {}
for t in ekeys:
k = 'euclid-{}'.format(t)
ess[k] = np.log10(euclid[t]['ks'])
vpa = ax.violinplot([ess[k] for k in ess.keys()], positions=np.array([2.0]), showmeans=True, showmedians=True, showextrema=False)
ess = {}
for t in rkeys:
k = 'rmn-{}'.format(t)
ess[k] = np.log10(rmn[t]['ks'])
vpb = ax.violinplot([ess[k] for k in ess.keys()], positions=np.arange(len(rkeys)) + 3, showmeans=True, showmedians=True, showextrema=False)
ax.set_xticks(np.arange(1, len(labels) + 1))
ax.set_xticklabels(['' for l in labels])
ax.set_xticklabels(labels, rotation=90, ha='right', fontsize=16)
ax.set_xlim(0.25, len(labels) + 0.75)
ax.axvline(len(ekeys) + 1.5, color='black', linestyle='--')
ax.set_xlabel('')
ax.set_ylabel('KS Statistic', fontsize=16)
ax.tick_params(axis='y', labelsize=16)
ax.grid(linestyle=':')
fig.tight_layout()
fig.savefig(os.path.join('images', 'kolmogorov-smirnov.pdf'))
labels = ['Thresh. {:.0e}'.format(t) for t in rkeys]
fig = plt.figure()
ax = fig.add_subplot(111)
ess = {}
for t in rkeys:
k = 'rmn-{}'.format(t)
ess[k] = np.log10(rmn[t]['ks'])
vpb = ax.violinplot([ess[k] for k in ess.keys()], positions=np.arange(len(rkeys)) + 1, showmeans=True, showmedians=True, showextrema=False)
ess = {}
for t in rkeys:
k = 'rmn-{}'.format(t)
ess[k] = np.log10(nm_rmn[t]['ks'])
vpc = ax.violinplot([ess[k] for k in ess.keys()], positions=np.arange(len(rkeys)) + 1, showmeans=True, showmedians=True, showextrema=False)
ess = {}
for t in rkeys:
k = 'rmn-{}'.format(t)
ess[k] = np.log10(nb_rmn[t]['ks'])
vpd = ax.violinplot([ess[k] for k in ess.keys()], positions=np.arange(len(rkeys)) + 1, showmeans=True, showmedians=True, showextrema=False)
ax.set_xticks(np.arange(1, len(labels) + 1))
ax.set_xticklabels(['' for l in labels])
ax.set_xticklabels(labels, rotation=90, ha='right', fontsize=24)
ax.set_xlim(0.25, len(labels) + 0.75)
ax.set_xlabel('')
ax.set_ylabel('KS Statistic', fontsize=30)
ax.tick_params(axis='y', labelsize=24)
ax.grid(linestyle=':')
fig.tight_layout()
fig.savefig(os.path.join('images', 'kolmogorov-smirnov-vs-newton.pdf'))
def mmd():
euclid = euclidean_samples()[100000]
rmn = riemannian_samples()[100000]
ekeys = sorted(euclid.keys(), reverse=False)
rkeys = sorted(rmn.keys(), reverse=False)
num_thresholds = len(rkeys)
thresholds = np.array(rkeys)
emmd = np.log10(np.abs(np.array([euclid[k]['mmd'] for k in ekeys])))
rmmd = np.log10(np.abs(np.array([rmn[k]['mmd'] for k in rkeys])))
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(rmmd, '.-')
for v in emmd:
ax.axhline(v, color='k')
ax.xaxis.set_tick_params(direction='out')
ax.xaxis.set_ticks_position('bottom')
ax.set_xticks(np.arange(0, num_thresholds))
ax.set_xticklabels(['{:.0f}'.format(np.log10(t)) for t in thresholds], fontsize=24)
ax.tick_params(axis='y', labelsize=24)
ax.grid(linestyle=':')
ax.set_xlabel(r'$\log_{10}$ Threshold', fontsize=30)
ax.set_ylabel(r'$\log_{10}|\mathrm{MMD}^2|$ Estimate', fontsize=30)
fig.tight_layout()
fig.savefig(os.path.join('images', 'mmd.pdf'))
def wasserstein_sliced():
euclid = euclidean_samples()[100000]
rmn = riemannian_samples()[100000]
ekeys = sorted(euclid.keys(), reverse=False)
rkeys = sorted(rmn.keys(), reverse=False)
num_thresholds = len(rkeys)
thresholds = np.array(rkeys)
esw = np.log10(np.abs(np.array([euclid[k]['sw'] for k in ekeys])))
rsw = np.log10(np.abs(np.array([rmn[k]['sw'] for k in rkeys])))
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(rsw, '.-')
for v in esw:
ax.axhline(v, color='k')
ax.xaxis.set_tick_params(direction='out')
ax.xaxis.set_ticks_position('bottom')
ax.set_xticks(np.arange(0, num_thresholds))
ax.set_xticklabels(['{:.0f}'.format(np.log10(t)) for t in thresholds], fontsize=24)
ax.tick_params(axis='y', labelsize=24)
ax.grid(linestyle=':')
ax.set_xlabel(r'$\log_{10}$ Threshold', fontsize=30)
ax.set_ylabel(r'$\log_{10}$ Sliced Wasserstein', fontsize=30)
fig.tight_layout()
fig.savefig(os.path.join('images', 'sw.pdf'))
def volume_preservation():
euclid = euclidean_samples()
rmn = riemannian_samples()
num_thresholds = 9
thresholds = np.logspace(-num_thresholds, -1, num_thresholds)
dat = [rmn[100000][t]['jacdet'][1e-5] for t in thresholds]
dat = [_[~np.isnan(_)] for _ in dat]
fig = plt.figure()
ax = fig.add_subplot(111)
ax.boxplot(dat, notch=True)
ax.grid(linestyle=':')
ax.xaxis.set_tick_params(direction='out')
ax.xaxis.set_ticks_position('bottom')
ax.set_xticks(np.arange(1, num_thresholds + 1))
ax.set_xticklabels(['{:.0f}'.format(np.log10(t)) for t in thresholds], fontsize=24)
ax.tick_params(axis='y', labelsize=24)
ax.set_xlim(0.25, len(thresholds) + 0.75)
ax.set_xlabel('$\log_{10}$ Threshold', fontsize=30)
ax.set_ylabel('$\log_{10}$ Vol. Pres. Err.', fontsize=30)
fig.tight_layout()
fig.savefig(os.path.join('images', 'jacobian-determinant.pdf'))
fig = plt.figure()
ax = fig.add_subplot(111)
bp = ax.boxplot(dat, notch=True, patch_artist=True)
for patch in bp['boxes']:
patch.set(facecolor='tab:blue')
nm_rmn = riemannian_samples(True)
dat = [nm_rmn[100000][t]['jacdet'][1e-5] for t in thresholds]
dat = [_[~np.isnan(_)] for _ in dat]
nm_bp = ax.boxplot(dat, notch=True, patch_artist=True)
for patch in nm_bp['boxes']:
patch.set(facecolor='tab:red')
nb_rmn = riemannian_samples(True, True)
dat = [nb_rmn[100000][t]['jacdet'][1e-5] for t in thresholds]
dat = [_[~np.isnan(_)] for _ in dat]
nb_bp = ax.boxplot(dat, notch=True, patch_artist=True)
for patch in nb_bp['boxes']:
patch.set(facecolor='tab:green')
ax.grid(linestyle=':')
ax.xaxis.set_tick_params(direction='out')
ax.xaxis.set_ticks_position('bottom')
ax.set_xticks(np.arange(1, num_thresholds + 1))
ax.set_xticklabels(['{:.0f}'.format(np.log10(t)) for t in thresholds], fontsize=24)
ax.tick_params(axis='y', labelsize=24)
ax.set_xlim(0.25, len(thresholds) + 0.75)
ax.set_xlabel('$\log_{10}$ Threshold', fontsize=30)
ax.set_ylabel('$\log_{10}$ Vol. Pres. Err.', fontsize=30)
fig.tight_layout()
fig.savefig(os.path.join('images', 'jacobian-determinant-vs-newton.pdf'))
perturb = sorted(rmn[100000][1e-9]['jacdet'].keys())
num_perturb = len(perturb)
dat = [rmn[100000][1e-9]['jacdet'][p] for p in perturb]
dat = [_[~np.isnan(_)] for _ in dat]
fig = plt.figure()
ax = fig.add_subplot(111)
ax.boxplot(dat, notch=True)
ax.grid(linestyle=':')
ax.xaxis.set_tick_params(direction='out')
ax.xaxis.set_ticks_position('bottom')
ax.set_xticks(np.arange(1, num_perturb + 1))
ax.set_xticklabels(['{:.0f}'.format(np.log10(t)) for t in perturb], fontsize=24)
ax.tick_params(axis='y', labelsize=24)
ax.set_xlim(0.25, num_perturb + 0.75)
ax.set_xlabel('$\log_{10}$ Perturbation', fontsize=30)
ax.set_ylabel('$\log_{10}$ Volume Preservation Error', fontsize=20)
fig.tight_layout()
fig.savefig(os.path.join('images', 'perturbation.pdf'))
def reversibility():
euclid = euclidean_samples()
rmn = riemannian_samples()
num_thresholds = 9
thresholds = np.logspace(-num_thresholds, -1, num_thresholds)
dat = [rmn[100000][t]['absrev'] for t in thresholds]
dat = [_[~np.isnan(_)] for _ in dat]
fig = plt.figure()
ax = fig.add_subplot(111)
ax.boxplot(dat, notch=True)
ax.grid(linestyle=':')
ax.xaxis.set_tick_params(direction='out')
ax.xaxis.set_ticks_position('bottom')
ax.set_xticks( | np.arange(1, num_thresholds + 1) | numpy.arange |
import numpy as np
import cvxpy as cx
import torch
import torch.nn.functional as F
from torch.autograd import Variable as V
def rms_calib_err(confidence, correct, p='2', beta=100):
# beta is target bin size
idxs = np.argsort(confidence)
confidence = confidence[idxs]
correct = correct[idxs]
bins = [[i * beta, (i + 1) * beta] for i in range(len(confidence) // beta)]
bins[-1] = [bins[-1][0], len(confidence)]
cerr = 0
total_examples = len(confidence)
for i in range(len(bins) - 1):
bin_confidence = confidence[bins[i][0]:bins[i][1]]
bin_correct = correct[bins[i][0]:bins[i][1]]
num_examples_in_bin = len(bin_confidence)
if num_examples_in_bin > 0:
difference = np.abs(np.nanmean(bin_confidence) - np.nanmean(bin_correct))
if p == '2':
cerr += num_examples_in_bin / total_examples * np.square(difference)
elif p == '1':
cerr += num_examples_in_bin / total_examples * difference
elif p == 'infty' or p == 'infinity' or p == 'max':
cerr = | np.maximum(cerr, difference) | numpy.maximum |
from labelmodels.label_model import ClassConditionalLabelModel, LearningConfig, init_random
import numpy as np
from scipy import sparse
import torch
from torch import nn
class HMM(ClassConditionalLabelModel):
"""A generative label model that treats a sequence of true class labels as a
Markov chain, as in a hidden Markov model, and treats all labeling functions
as conditionally independent given the corresponding true class label, as
in a Naive Bayes model.
Proposed for crowdsourced sequence annotations in: <NAME>, <NAME>, <NAME>, <NAME>, and <NAME>. Aggregating and Predicting
Sequence Labels from Crowd Annotations. In Annual Meeting of the Association
for Computational Linguistics, 2017.
"""
def __init__(self, num_classes, num_lfs, init_acc=.9, acc_prior=1,
balance_prior=1):
"""Constructor.
Initializes labeling function accuracies using optional argument and all
other model parameters uniformly.
:param num_classes: number of target classes, i.e., binary
classification = 2
:param num_lfs: number of labeling functions to model
:param init_acc: initial estimated labeling function accuracy, must
be a float in [0,1]
:param acc_prior: strength of regularization of estimated labeling
function accuracies toward their initial values
"""
super().__init__(num_classes, num_lfs, init_acc, acc_prior)
self.start_balance = nn.Parameter(torch.zeros([num_classes]))
self.transitions = nn.Parameter(torch.zeros([num_classes, num_classes]))
self.balance_prior = balance_prior
def forward(self, votes, seq_starts):
"""
Computes log likelihood of sequence of labeling function outputs for
each (sequence) example in batch.
For efficiency, this function prefers that votes is an instance of
scipy.sparse.coo_matrix. You can avoid a conversion by passing in votes
with this class.
:param votes: m x n matrix in {0, ..., k}, where m is the sum of the
lengths of the sequences in the batch, n is the number of
labeling functions and k is the number of classes
:param seq_starts: vector of length l of row indices in votes indicating
the start of each sequence, where l is the number of
sequences in the batch. So, votes[seq_starts[i]] is
the row vector of labeling function outputs for the
first element in the ith sequence
:return: vector of length l, where element is the log-likelihood of the
corresponding sequence of outputs in votes
"""
jll = self._get_labeling_function_likelihoods(votes)
norm_start_balance = self._get_norm_start_balance()
norm_transitions = self._get_norm_transitions()
for i in range(0, votes.shape[0]):
if i in seq_starts:
jll[i] += norm_start_balance
else:
joint_class_pair = jll[i-1, :].clone().unsqueeze(1)
joint_class_pair = joint_class_pair.repeat(1, self.num_classes)
joint_class_pair += norm_transitions
jll[i] += joint_class_pair.logsumexp(0)
seq_ends = [x - 1 for x in seq_starts] + [votes.shape[0]-1]
seq_ends.remove(-1)
mll = torch.logsumexp(jll[seq_ends], dim=1)
return mll
def estimate_label_model(self, votes, seq_starts, config=None):
"""Estimates the parameters of the label model based on observed
labeling function outputs.
Note that a minibatch's size refers to the number of sequences in the
minibatch.
:param votes: m x n matrix in {0, ..., k}, where m is the sum of the
lengths of the sequences in the data, n is the number of
labeling functions and k is the number of classes
:param seq_starts: vector of length l of row indices in votes indicating
the start of each sequence, where l is the number of
sequences in the batch. So, votes[seq_starts[i]] is
the row vector of labeling function outputs for the
first element in the ith sequence
:param config: optional LearningConfig instance. If None, initialized
with default constructor
"""
if config is None:
config = LearningConfig()
# Initializes random seed
init_random(config.random_seed)
# Converts to CSR and integers to standardize input
votes = sparse.csr_matrix(votes, dtype=np.int)
seq_starts = np.array(seq_starts, dtype=np.int)
batches = self._create_minibatches(
votes, seq_starts, config.batch_size, shuffle_seqs=True)
self._do_estimate_label_model(batches, config)
def get_most_probable_labels(self, votes, seq_starts):
"""
Computes the most probable underlying sequence of labels given function
outputs
:param votes: m x n matrix in {0, ..., k}, where m is the sum of the
lengths of the sequences in the data, n is the number of
labeling functions and k is the number of classes
:param seq_starts: vector of length l of row indices in votes indicating
the start of each sequence, where l is the number of
sequences in the batch. So, votes[seq_starts[i]] is
the row vector of labeling function outputs for the
first element in the ith sequence
:return: vector of length m, where element is the most likely predicted labels
"""
# Converts to CSR and integers to standardize input
votes = sparse.csr_matrix(votes, dtype=np.int)
seq_starts = np.array(seq_starts, dtype=np.int)
out = np.ndarray((votes.shape[0],), dtype=np.int)
out_prob = np.ndarray((votes.shape[0],), dtype=object)
offset = 0
for votes, seq_starts in self._create_minibatches(votes, seq_starts, 32):
jll = self._get_labeling_function_likelihoods(votes)
norm_start_balance = self._get_norm_start_balance()
norm_transitions = self._get_norm_transitions()
T = votes.shape[0]
bt = torch.zeros([T, self.num_classes])
bts = torch.zeros([T, self.num_classes, self.num_classes])
for i in range(0, T):
if i in seq_starts:
jll[i] += norm_start_balance
else:
p = jll[i-1].clone().unsqueeze(1).repeat(
1, self.num_classes) + norm_transitions
jll[i] += torch.max(p, dim=0)[0]
bt[i, :] = torch.argmax(p, dim=0)
bts[i, :, :] = p
jll = torch.exp(jll)
seq_ends = [x - 1 for x in seq_starts] + [votes.shape[0] - 1]
res = []
res_prob = []
j = T-1
while j >= 0:
if j in seq_ends:
res.append(torch.argmax(jll[j, :]).item())
res_prob.append(jll[j,:].detach().numpy())
if j in seq_starts:
j -= 1
continue
res.append(int(bt[j, res[-1]].item()))
res_prob.append(torch.exp(bts[j,:,res[-1]]).detach().numpy())
j -= 1
res = [x + 1 for x in res]
res.reverse()
res_prob.reverse()
for i in range(len(res)):
out[offset + i] = res[i]
out_prob[offset + i] = res_prob[i]
offset += len(res)
return out, out_prob
def get_label_distribution(self, votes, seq_starts):
"""Returns the unary and pairwise marginals over true labels estimated
by the model.
:param votes: m x n matrix in {0, ..., k}, where m is the sum of the
lengths of the sequences in the data, n is the number of
labeling functions and k is the number of classes
:param seq_starts: vector of length l of row indices in votes indicating
the start of each sequence, where l is the number of
sequences in the batch. So, votes[seq_starts[i]] is
the row vector of labeling function outputs for the
first element in the ith sequence
:return: p_unary, p_pairwise where p_unary is a m x k matrix representing
the marginal distributions over individual labels, and p_pairwise
is a m x k x k tensor representing pairwise marginals over the
ith and (i+1)th labels. For the last element in a sequence, the
k x k matrix will be all zeros.
"""
# Converts to CSR and integers to standardize input
votes = sparse.csr_matrix(votes, dtype=np.int)
seq_starts = np.array(seq_starts, dtype=np.int)
out_unary = np.zeros((votes.shape[0], self.num_classes))
out_pairwise = np.zeros((votes.shape[0], self.num_classes, self.num_classes))
offset = 0
for votes, seq_starts in self._create_minibatches(votes, seq_starts, 32):
# Computes observation likelihoods and initializes alpha and beta messages
cll = self._get_labeling_function_likelihoods(votes)
alpha = torch.zeros(cll.shape)
beta = torch.zeros(cll.shape)
# Computes alpha
next_seq = 0
for i in range(votes.shape[0]):
if next_seq == len(seq_starts) or i < seq_starts[next_seq]:
# i is not the start of a sequence
temp = alpha[i-1].unsqueeze(1).repeat(1, self.num_classes)
temp = temp + self._get_norm_transitions()
alpha[i] = cll[i] + temp.logsumexp(0)
else:
# i is the start of a sequence
alpha[i] = cll[i] + self._get_norm_start_balance()
next_seq += 1
# Computes beta
this_seq = seq_starts.shape[0] - 1
beta[-1, :] = 1
for i in range(votes.shape[0] - 2, -1, -1):
if i == seq_starts[this_seq] - 1:
# End of sequence
beta[i, :] = 1
this_seq -= 1
else:
temp = beta[i+1] + cll[i+1]
temp = temp.unsqueeze(1).repeat(1, self.num_classes)
temp = temp + self._get_norm_transitions()
beta[i, :] = temp.logsumexp(0)
# Computes p_unary
p_unary = alpha + beta
temp = p_unary.logsumexp(1).unsqueeze(1).repeat(1, self.num_classes)
p_unary = p_unary - temp
for i in range(p_unary.shape[0]):
p = torch.exp(p_unary[i, :] - torch.max(p_unary[i, :]))
out_unary[offset + i, :] = (p / p.sum()).detach()
# Computes p_pairwise
p_pairwise = torch.zeros(
(votes.shape[0], self.num_classes, self.num_classes))
for i in range(p_pairwise.shape[0] - 1):
p_pairwise[i, :, :] = self._get_norm_transitions()
p_pairwise[i] += alpha[i].unsqueeze(1).repeat(1, self.num_classes)
p_pairwise[i] += cll[i+1].unsqueeze(0).repeat(self.num_classes, 1)
p_pairwise[i] += beta[i+1].unsqueeze(0).repeat(self.num_classes, 1)
denom = p_pairwise[i].view(-1).logsumexp(0)
denom = denom.unsqueeze(0).unsqueeze(1)
denom = denom.repeat(self.num_classes, self.num_classes)
p_pairwise[i] -= denom
out_pairwise[offset + i, :, :] = torch.exp(p_pairwise[i]).detach()
offset += votes.shape[0]
return out_unary, out_pairwise
def get_start_balance(self):
"""Returns the model's estimated class balance for the start of a
sequence
:return: a NumPy array with one element in [0,1] for each target class,
representing the estimated prior probability that the first
element in an example sequence has that label
"""
return np.exp(self._get_norm_start_balance().detach().numpy())
def get_transition_matrix(self):
"""Returns the model's estimated transition distribution from class
label to class label in a sequence.
:return: a k x k Numpy array, in which each element i, j is the
probability p(c_{t+1} = j + 1 | c_{t} = i + 1)
"""
return np.exp(self._get_norm_transitions().detach().numpy())
def _create_minibatches(self, votes, seq_starts, batch_size, shuffle_seqs=False):
# Computes explicit seq ends so that we can shuffle the sequences
seq_ends = np.ndarray((seq_starts.shape[0],), dtype=np.int)
for i in range(1, seq_starts.shape[0]):
seq_ends[i-1] = seq_starts[i] - 1
seq_ends[-1] = votes.shape[0] - 1
# Shuffles the sequences by shuffling the start and end index vectors
if shuffle_seqs:
index = np.arange(np.shape(seq_starts)[0])
np.random.shuffle(index)
seq_starts = seq_starts[index]
seq_ends = seq_ends[index]
# Splits seq_starts
seq_start_batches = [np.array(
seq_starts[i * batch_size: ((i + 1) * batch_size)],
copy=True)
for i in range(int(np.ceil(len(seq_starts) / batch_size)))
]
seq_start_batches[-1] = | np.concatenate((seq_start_batches[-1], [votes.shape[0]])) | numpy.concatenate |
import sys
import numpy as np
import pandas as pd
from optparse import OptionParser
import os
from scipy.stats import entropy
from scipy import signal
import scipy.stats as spstats
import fnmatch
from datetime import datetime
from scipy.stats import skew
from scipy.stats import kurtosis
from scipy.stats import t
from scipy.optimize import fsolve
import scipy.special as sc
# Extracts aggregate features per run from raw eye tracking and oculomotor event data, and builds a single feature matrix for use as input to train and validate a predictive model. If the feature matrix file already exists from a prior run of getFeatureMatrix(), you can save time by specifying useExisting=True to load it directly from the file rather than recomputing it from scratch.
# Research was sponsored by the United States Air Force Research Laboratory and the
# United States Air Force Artificial Intelligence Accelerator and was accomplished
# under Cooperative Agreement Number FA8750-19-2-1000. The views and conclusions
# contained in this document are those of the authors and should not be interpreted
# as representing the official policies, either expressed or implied, of the United
# States Air Force or the U.S. Government. The U.S. Government is authorized to
# reproduce and distribute reprints for Government purposes notwithstanding any
# copyright notation herein.
# def main():
# parser = OptionParser()
# parser.add_option('-d', '--dataDir', action="store", dest="dataDir", default=None, help="The top level data directory containing all the raw signal files for each subject.")
# parser.add_option('-o', '--outFilePath', action="store", dest="outFilePath", default=None, help="File to write full feature matrix.");
# (options, args) = parser.parse_args()
# getFeatureMatrix(options.dataDir, options.outFilePath);
def getFeatureMatrix(dataDir, filePath, useExisting):
if useExisting:
if os.path.exists(filePath):
print("Found precomputed feature matrix.")
featMatDF = pd.read_csv(filePath)
print("Loaded into a dataFrame.")
return featMatDF
else:
print(
"Cannot use existing feature matrix because specified file was not found. Recomputing it from scratch."
)
subjDirs = [f.path for f in os.scandir(dataDir) if f.is_dir()]
dfHeader = [
"Subject",
"Session",
"Run",
"OverallGazeEntropyLX",
"psdMaxLX",
"psdFreqOfMaxLX",
"OverallGazeEntropyLY",
"psdMaxLY",
"psdFreqOfMaxLY",
"OverallGazeEntropyLZ",
"psdMaxLZ",
"psdFreqOfMaxLZ",
"OverallGazeEntropyRX",
"psdMaxRX",
"psdFreqOfMaxRX",
"OverallGazeEntropyRY",
"psdMaxRY",
"psdFreqOfMaxRY",
"OverallGazeEntropyRZ",
"psdMaxRZ",
"psdFreqOfMaxRZ",
"EyesClosedFractionL",
"EyesClosedFractionR",
"PupilDiamMeanL",
"PupilDiamStdevL",
"PupilDiamSkewL",
"PupilDiamKurtL",
"PupilDiamMeanR",
"PupilDiamStdevR",
"PupilDiamSkewR",
"PupilDiamKurtR",
"FixDurMean",
"FixDurStdev",
"FixDurSkew",
"FixDurKurt",
"FixDensityMean",
"FixDensityStdev",
"FixDensitySkew",
"FixDensityKurt",
"SacMainSeqMean",
"SacMainSeqStdev",
"SacPeakVelMean",
"SacPeakVelStdev",
]
# walks through the directory structure of the raw data
featMat = []
ctr = 1
for subjd in subjDirs:
sessDirs = [f.path for f in os.scandir(subjd) if f.is_dir()]
print(
"Processing subject "
+ str(ctr)
+ " of "
+ str(len(subjDirs))
+ ": "
+ os.path.basename(subjd)
)
ctr = ctr + 1
for sessd in sessDirs:
runDirs = [f.path for f in os.scandir(sessd) if f.is_dir()]
for rund in runDirs:
dataFiles = [f.path for f in os.scandir(rund) if f.is_file()]
toks = rund.split(os.path.sep)
subj = toks[-3]
sess = toks[-2]
run = toks[-1]
rawEyeFile = fnmatch.filter(dataFiles, "*lslhtcviveeye*.csv")
dfraw = pd.read_csv(rawEyeFile[0])
timeStr = dfraw["time_s"]
datalen = len(timeStr)
if datalen < 10:
continue
# if there is even one corrupted date-time string, skip this whole run.
try:
timesMillis = [convertTimeStrToMillis(f) for f in timeStr]
except ValueError:
print(
"corrupted timestamp string, skipping run = "
+ run
+ ", subj = "
+ subj
+ ", sess = "
+ sess
)
continue
ocuEvtsFile = fnmatch.filter(dataFiles, "*_ocuevts_*.csv")
if len(ocuEvtsFile) < 1:
print(
"No oculomotor events file found for run "
+ run
+ ", subj = "
+ subj
+ ", sess = "
+ sess
)
continue
try:
dfocu = pd.read_csv(ocuEvtsFile[0])
except pd.errors.EmptyDataError:
print("Empty oculomotor events file. Skipping.")
continue
if dfocu.shape[0] < 10:
continue
gazeFeats = extractRawEyeFeats(dfraw, timesMillis)
ocuEvtFeats = extractOcuEvtFeats(dfraw, dfocu)
dfrow = [subj, sess, run]
dfrow = dfrow + gazeFeats + ocuEvtFeats
featMat.append(dfrow)
featMatDF = pd.DataFrame(featMat, columns=dfHeader)
if filePath != None:
print("Saving feature matrix to file.")
featMatDF.to_csv(filePath)
print("Processing complete. Returning feature matrix data frame.")
return featMatDF
def convertTimeStrToMillis(timeStr):
millisec = float(timeStr) * 1000
return millisec
def extractRawEyeFeats(df, timesMillis):
diffTimes = np.diff(timesMillis)
fs = np.mean(1.0 / diffTimes)
gazeFeatsLX = getSpectralFeatures(df["gaze_direction_l_x_mm"].values, fs)
gazeFeatsLY = getSpectralFeatures(df["gaze_direction_l_y_mm"].values, fs)
gazeFeatsLZ = getSpectralFeatures(df["gaze_direction_l_z_mm"].values, fs)
gazeFeatsRX = getSpectralFeatures(df["gaze_direction_r_x_mm"].values, fs)
gazeFeatsRY = getSpectralFeatures(df["gaze_direction_r_y_mm"].values, fs)
gazeFeatsRZ = getSpectralFeatures(df["gaze_direction_r_z_mm"].values, fs)
eyeClosedFracL = getFracTimeEyeClosed(df["eye_openness_l"].values, 0.5)
eyeClosedFracR = getFracTimeEyeClosed(df["eye_openness_r"].values, 0.5)
pupilFeatsL = getPupilFeatures(df["pupil_diameter_l_mm"].values)
pupilFeatsR = getPupilFeatures(df["pupil_diameter_r_mm"].values)
eyeFeatsAll = (
gazeFeatsLX
+ gazeFeatsLY
+ gazeFeatsLZ
+ gazeFeatsRX
+ gazeFeatsRY
+ gazeFeatsRZ
+ [eyeClosedFracL, eyeClosedFracR]
+ pupilFeatsL
+ pupilFeatsR
)
return eyeFeatsAll
def getFracTimeEyeClosed(eoSignal, thresh):
closedSamples = np.where(eoSignal <= thresh)
timeEyeClosed = np.max(closedSamples[0].shape)
fracTimeEyeClosed = timeEyeClosed / np.max(eoSignal.shape)
return fracTimeEyeClosed
def getPupilFeatures(pdSignal):
meanPD = np.mean(pdSignal)
stdevPD = np.std(pdSignal)
skewPD = skew(pdSignal)
kurtPD = kurtosis(pdSignal)
return [meanPD, stdevPD, skewPD, kurtPD]
# compute the overall spectral entropy of a continuous-valued signal, as well as the peak of the power spectral density.
def getSpectralFeatures(rawSignal, fs):
f, psd = signal.welch(rawSignal, fs)
# defaults to: hanning window, 256 samples per segment. Returns mean across segments.
psdMaxPower = max(psd)
psdMaxPowerIdx = np.argmax(psd)
psdFreqOfMax = f[psdMaxPowerIdx]
# Spectral Entropy is defined to be the Shannon Entropy of the power spectral density of the data.
# Step 1: Normalize the PSD by dividing it by the total PSD sum
normPSD = psd / sum(psd)
# Step 2: Calculate power spectral entropy
overallEntropy = -np.sum(normPSD * np.log2(psd))
return [overallEntropy, psdMaxPower, psdFreqOfMax]
# Extract features pertaining to oculomotor events: fixations and saccades.
def extractOcuEvtFeats(dfRawEye, dfOcuEvt):
eoSignal = dfRawEye["eye_openness_l"].values
eyeOpenIdxs = np.where(eoSignal > 0.5)
eoIdxs = eyeOpenIdxs[0]
fixFeats = getFixationFeats(dfOcuEvt, dfRawEye, eoIdxs[:-2])
sacFeats = getSaccadeFeats(dfOcuEvt, dfRawEye, eoIdxs[:-2])
return fixFeats + sacFeats
# Computes aggregate statistics of fixation durations and densities across each run.
def getFixationFeats(dfOcuEvt, dfRawEye, eoIdxs):
fixSeq = dfOcuEvt["FixationSeq"].values
timeCol = dfOcuEvt["Timestamp"].values
gazeX = dfRawEye["gaze_direction_l_x_mm"].values
gazeY = dfRawEye["gaze_direction_l_y_mm"].values
gazeZ = dfRawEye["gaze_direction_l_z_mm"].values
fixEO = fixSeq[eoIdxs]
timeEO = timeCol[eoIdxs]
fixDurs = getFixDurations(fixEO, timeEO)
fixDens = getFixDensities(
fixEO, timeEO, gazeX[eoIdxs], gazeY[eoIdxs], gazeZ[eoIdxs]
)
meanFixDur = np.mean(fixDurs)
stdevFixDur = np.std(fixDurs)
skewFixDur = skew(fixDurs)
kurtFixDur = kurtosis(fixDurs)
meanFixDen = np.mean(fixDens)
stdevFixDen = np.std(fixDens)
skewFixDen = skew(fixDens)
kurtFixDen = kurtosis(fixDens)
return [
meanFixDur,
stdevFixDur,
skewFixDur,
kurtFixDur,
meanFixDen,
stdevFixDen,
skewFixDen,
kurtFixDen,
]
def getFixDurations(fixEO, timeEO):
fixDurs = []
uniqueFixNums = set(fixEO)
for fn in uniqueFixNums:
if fn < 0:
continue
curFixIdxsArr = np.where(fixEO == fn)
curFixIdxs = curFixIdxsArr[0]
curFixTimes = timeEO[curFixIdxs]
startTime = curFixTimes[0]
endTime = curFixTimes[-1]
curFixDur = endTime - startTime
fixDurs.append(curFixDur)
return fixDurs
def getFixDensities(fixEO, timeEO, gazeEOx, gazeEOy, gazeEOz):
fixDens = []
uniqueFixNums = set(fixEO)
for fn in uniqueFixNums:
if fn < 0:
continue
curFixIdxsArr = np.where(fixEO == fn)
curFixIdxs = curFixIdxsArr[0]
curFixTimes = timeEO[curFixIdxs]
startTime = curFixTimes[0]
endTime = curFixTimes[-1]
curFixDen = computeDispersion(
gazeEOx[curFixIdxs], gazeEOy[curFixIdxs], gazeEOz[curFixIdxs]
)
fixDens.append(curFixDen)
return fixDens
def computeDispersion(gazeX, gazeY, gazeZ):
centroidX = np.mean(gazeX)
centroidY = np.mean(gazeY)
centroidZ = np.mean(gazeZ)
offsetsXsq = np.square(gazeX - centroidX)
offsetsYsq = np.square(gazeY - centroidY)
offsetsZsq = np.square(gazeZ - centroidZ)
dispersion = np.sqrt(
np.mean(offsetsXsq) + np.mean(offsetsYsq) + np.mean(offsetsZsq)
)
return dispersion
def getSaccadeFeats(dfOcuEvt, dfRawEye, eoIdxs):
sacSeq = dfOcuEvt["SaccadeSeq"].values
timeCol = dfOcuEvt["Timestamp"].values
gazeX = dfRawEye["gaze_direction_l_x_mm"].values
gazeY = dfRawEye["gaze_direction_l_y_mm"].values
gazeZ = dfRawEye["gaze_direction_l_z_mm"].values
sacEO = sacSeq[eoIdxs]
timeEO = timeCol[eoIdxs]
sacFeats = computeSacMetrics(
sacEO, timeEO, gazeX[eoIdxs], gazeY[eoIdxs], gazeZ[eoIdxs]
)
return sacFeats
# Computes aggregate statistics of saccade main sequence and peak velocity across each run.
def computeSacMetrics(sacEO, timeEO, gazeEOx, gazeEOy, gazeEOz):
sacAmpls = []
sacPkVels = []
sacDurs = []
uniqueSacNums = set(sacEO)
for sn in uniqueSacNums:
if sn < 0:
continue
curSacIdxsArr = np.where(sacEO == sn)
curSacIdxs = curSacIdxsArr[0]
if len(curSacIdxs) < 2:
continue
curSacTimes = timeEO[curSacIdxs]
startTime = curSacTimes[0]
endTime = curSacTimes[-1]
curSacDur = endTime - startTime
curSacGazeX = gazeEOx[curSacIdxs]
curSacGazeY = gazeEOy[curSacIdxs]
curSacGazeZ = gazeEOz[curSacIdxs]
xvel = np.diff(curSacGazeX)
yvel = np.diff(curSacGazeY)
zvel = np.diff(curSacGazeZ)
curSacAmpl = np.sqrt(
np.square(curSacGazeX[-1] - curSacGazeX[0])
+ np.square(curSacGazeY[-1] - curSacGazeY[0])
+ np.square(curSacGazeZ[-1] - curSacGazeZ[0])
)
curSacVels = np.sqrt(
np.square(xvel) + | np.square(yvel) | numpy.square |
# import some libraries
import numpy as np
import pandas as pd
import statsmodels.api as sm
import random
from scipy.stats import t, f
import matplotlib.pyplot as plt
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
import torch.utils.data as data
from sklearn import metrics
from sklearn import decomposition
from sklearn import manifold
import matplotlib.pyplot as plt
import numpy as np
from scipy import stats
import copy
import random
import time
SEED = 1234
random.seed(SEED)
np.random.seed(SEED)
torch.manual_seed(SEED)
torch.cuda.manual_seed(SEED)
# Generate the simulated data
# Initialize seed and parameters
# number of data points
n_S = 1000000
n_T = int(0.001 * n_S)
M = 14
# Model parameters
a = np.asarray([[1.1, -0.1, 0, 0.1, 0, 0.2, 0, 0.1, -0.1, 0, 0, 0.1, -0.1, 0.2, -0.2]])
b = (-1) * np.asarray([[0.5, 0.1, -0.1, 0, 0, 0, 0, 0.2, 0.1, 0.2, 0, 0.2, -0.1, -0.2, 0]])
# independent variable in Sorce domain
mu_S = np.repeat(1, M)
cov_S = 0.2 * np.identity(M, dtype=float)
X0_S = np.random.multivariate_normal(mu_S, cov_S, n_S)
p_S = np.random.uniform(low=0.2, high=2.0, size=n_S)
# add column of ones for intercept
X_S = sm.add_constant(X0_S)
print(X_S.shape)
print(a.shape)
# dependent variable (i.e., demand ) in Sorce domain
d_S = a @ X_S.T+ (b @ X_S.T) * p_S + np.random.normal(0,0.1, n_S)
# revenue
r_S = d_S * p_S
# independent variable in Target domain
#mu_T = np.repeat(0, M)
#cov_T = 0.05 * np.identity(M, dtype=float)
#X0_T = np.random.multivariate_normal(mu_T, cov_T, n_T)
df_T = 10
X0_T = stats.chi2.rvs(df_T, size=(n_T,M))
p_T = np.random.uniform(low=0.2, high=2.0, size=n_T)
# add column of ones for intercept
X_T = sm.add_constant(X0_T)
X_T[:,8:]=0
print(X_T.shape)
print(a.shape)
# dependent variable (i.e., demand ) in Target domain
d_T = a @ X_T.T+ (b @ X_T.T) * p_T + np.random.normal(0,0.1, n_T)
# revenue
r_T = d_T * p_T
def rescale(d_S):
return (d_S-d_S.min())/(d_S.max()-d_S.min())
#print(d_S.min(), d_S.max())
d_S =rescale(d_S)
#raise ValueError
d_T=rescale(d_T)
p_S = rescale(p_S)
p_T =rescale(p_T)
print(X_T.shape,p_T.shape)
print(d_S.max(),d_S.min())
#res = stats.linregress(np.concatenate((X_T,np.expand_dims(p_T,axis=1)),axis=1),d_T.T)
d_S=torch.tensor(d_S).transpose(0,1).float()
p_S=torch.tensor(p_S).unsqueeze(1).float()
x_S=torch.tensor(X_S).float()
d_T=torch.tensor(d_T).transpose(0,1).float()
p_T=torch.tensor(p_T).unsqueeze(1).float()
x_T=torch.tensor(X_T).float()
d_S = torch.cat([d_S,torch.zeros_like(d_S)],dim=-1)
d_T = torch.cat([d_T,torch.ones_like(d_T)],dim=-1)
d= torch.cat([d_S,d_T], dim=0)
p= torch.cat([p_S,p_T], dim=0)
x= torch.cat([x_S,x_T], dim=0)
print(d.shape ,p.shape, x.shape)
pdS_dataset = data.TensorDataset(torch.cat([p_S,x_S],dim=-1), d_S)
pdT_dataset = data.TensorDataset(torch.cat([p_T,x_T],dim=-1), d_T)
VALID_RATIO = 0.8
n_train_examples = int(d_S.shape[0] * VALID_RATIO)
n_valid_examples = (d_S.shape[0] - n_train_examples)//2
n_test_examples = (d_S.shape[0] - n_train_examples)//2
pdS_train, pdS_valid, pdS_test= data.random_split(pdS_dataset,
[n_train_examples, n_valid_examples,n_test_examples])
VALID_RATIO = 0.8
n_train_examples = int(d_T.shape[0] * VALID_RATIO)
n_valid_examples = (d_T.shape[0] - n_train_examples)//2
n_test_examples = (d_T.shape[0] - n_train_examples)//2
pdT_train, pdT_valid, pdT_test= data.random_split(pdT_dataset,
[n_train_examples, n_valid_examples,n_test_examples])
pd_train = data.ConcatDataset([pdS_train,pdT_train])
pd_valid = pdT_valid
pd_test = pdT_test
import torch
import numpy as np
import math
def _flatten(sequence):
flat = [p.contiguous().view(-1) for p in sequence]
return torch.cat(flat) if len(flat) > 0 else torch.tensor([])
def compute_cc_weights(nb_steps):
lam = np.arange(0, nb_steps + 1, 1).reshape(-1, 1)
lam = np.cos((lam @ lam.T) * math.pi / nb_steps)
lam[:, 0] = .5
lam[:, -1] = .5 * lam[:, -1]
lam = lam * 2 / nb_steps
W = np.arange(0, nb_steps + 1, 1).reshape(-1, 1)
W[np.arange(1, nb_steps + 1, 2)] = 0
W = 2 / (1 - W ** 2)
W[0] = 1
W[ | np.arange(1, nb_steps + 1, 2) | numpy.arange |
# Copyright 2015 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Tests for tensorflow.ops.ops."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
import tensorflow as tf
from tensorflow.python.framework import random_seed
from tensorflow.python.ops import init_ops
# Returns true iff the two initializers produce the same tensor to
# within a tiny tolerance.
def identicaltest(tc, init1, init2, use_gpu):
"""Tests if two initializations are identical to within tiny tolerances.
Args:
tc: An instance of TensorFlowTestCase.
init1: An Initializer that generates a tensor of a given shape
init2: An Initializer that generates a tensor of a given shape
use_gpu: Use gpu if true.
Returns:
True or False as determined by test.
"""
num = 100
with tc.test_session(use_gpu=use_gpu, graph=tf.Graph()):
t1 = init1([num]).eval()
with tc.test_session(use_gpu=use_gpu, graph=tf.Graph()):
t2 = init2([num]).eval()
return | np.allclose(t1, t2, rtol=1e-15, atol=1e-15) | numpy.allclose |
"""
Goal - Calculate distance travelled by each fish
Date - Mar 11 2021
"""
import os
import pathlib
from pprint import pprint
import numpy as np
from scipy import stats
from scipy.spatial import distance
import matplotlib.pyplot as plt
from matplotlib.pyplot import figure
import trajectorytools as tt
import trajectorytools.plot as ttplot
import trajectorytools.socialcontext as ttsocial
from trajectorytools.constants import dir_of_data
import csv
import pickle
import argparse
import pandas as pd
def position(tr): #shape returns tr.s.shape
return(tr.s)
def speed(tr): #speed(tr).shape returns tr.speed.shape - 2
v = (position(tr)[2:] - position(tr)[:-2]) / 2
b = | np.linalg.norm(v, axis=-1) | numpy.linalg.norm |
# This module tests data directly from the pangeo google cloud storage.
# Tests are meant to be more high level and also serve to document known problems (see skip statements).
import pytest
import xarray as xr
import numpy as np
from cmip6_preprocessing.tests.cloud_test_utils import (
full_specs,
xfail_wrapper,
all_models,
data,
diagnose_doubles,
)
from cmip6_preprocessing.preprocessing import combined_preprocessing
from cmip6_preprocessing.grids import combine_staggered_grid
pytest.importorskip("gcsfs")
print(f"\n\n\n\n$$$$$$$ All available models: {all_models()}$$$$$$$\n\n\n\n")
# manually combine all pytest parameters, so that I have very fine grained control over
# which combination of parameters is expected to fail.
########################### Most basic test #########################
expected_failures = [
("AWI-ESM-1-1-LR", "thetao", "historical", "gn"),
("AWI-ESM-1-1-LR", "thetao", "ssp585", "gn"),
("AWI-CM-1-1-MR", "thetao", "historical", "gn"),
("AWI-CM-1-1-MR", "thetao", "ssp585", "gn"),
# TODO: would be nice to have a "*" matching...
("CESM2-FV2", "thetao", "historical", "gn"),
("CESM2-FV2", "thetao", "ssp585", "gn"),
]
@pytest.mark.parametrize(
"source_id,variable_id,experiment_id,grid_label",
xfail_wrapper(full_specs(), expected_failures),
)
def test_check_dim_coord_values_wo_intake(
source_id, variable_id, experiment_id, grid_label
):
# there must be a better way to build this at the class level and then tear it down again
# I can probably get this done with fixtures, but I dont know how atm
ds, cat = data(source_id, variable_id, experiment_id, grid_label, False)
if ds is None:
pytest.skip(
f"No data found for {source_id}|{variable_id}|{experiment_id}|{grid_label}"
)
##### Check for dim duplicates
# check all dims for duplicates
# for di in ds.dims:
# for now only test a subset of the dims. TODO: Add the bounds once they
# are cleaned up.
for di in ["x", "y", "lev", "time"]:
if di in ds.dims:
diagnose_doubles(ds[di].load().data)
assert len(ds[di]) == len(np.unique(ds[di]))
if di != "time": # these tests do not make sense for decoded time
assert ~np.all(np.isnan(ds[di]))
assert np.all(ds[di].diff(di) >= 0)
assert ds.lon.min().load() >= 0
assert ds.lon.max().load() <= 360
if "lon_bounds" in ds.variables:
assert ds.lon_bounds.min().load() >= 0
assert ds.lon_bounds.max().load() <= 360
assert ds.lat.min().load() >= -90
assert ds.lat.max().load() <= 90
# make sure lon and lat are 2d
assert len(ds.lon.shape) == 2
assert len(ds.lat.shape) == 2
expected_failures = [
("AWI-ESM-1-1-LR", "thetao", "historical", "gn"),
("AWI-ESM-1-1-LR", "thetao", "ssp585", "gn"),
("AWI-CM-1-1-MR", "thetao", "historical", "gn"),
("AWI-CM-1-1-MR", "thetao", "ssp585", "gn"),
# TODO: would be nice to have a "*" matching...
("CESM2-FV2", "thetao", "historical", "gn"),
("CESM2-FV2", "thetao", "ssp585", "gn"),
(
"IPSL-CM6A-LR",
"thetao",
"historical",
"gn",
), # IPSL has an issue with `lev` dims concatting
("IPSL-CM6A-LR", "o2", "historical", "gn"),
("NorESM2-MM", "thetao", "historical", "gn"),
("NorESM2-MM", "thetao", "historical", "gr"),
]
@pytest.mark.parametrize(
"source_id,variable_id,experiment_id,grid_label",
xfail_wrapper(full_specs(), expected_failures),
)
def test_check_dim_coord_values(source_id, variable_id, experiment_id, grid_label):
# there must be a better way to build this at the class level and then tear it down again
# I can probably get this done with fixtures, but I dont know how atm
ds, cat = data(source_id, variable_id, experiment_id, grid_label, True)
if ds is None:
pytest.skip(
f"No data found for {source_id}|{variable_id}|{experiment_id}|{grid_label}"
)
##### Check for dim duplicates
# check all dims for duplicates
# for di in ds.dims:
# for now only test a subset of the dims. TODO: Add the bounds once they
# are cleaned up.
for di in ["x", "y", "lev", "time"]:
if di in ds.dims:
diagnose_doubles(ds[di].load().data)
assert len(ds[di]) == len(np.unique(ds[di]))
if di != "time": # these tests do not make sense for decoded time
assert ~np.all( | np.isnan(ds[di]) | numpy.isnan |
import numpy as np
from scipy.special import gamma
from copy import deepcopy
class arfima(object):
def __init__(self, Ap = [], Aq = [], d = 0, infit=100):
self.Ap = Ap
self.Aq = Aq
self.order = d
self.infit = infit
if not isinstance(Ap, list):
raise TypeError('Ap has to be entered in a single list form')
if not isinstance(Aq, list):
raise TypeError('Aq has to be entered in a single list form')
if d < -0.5 or d>0.5:
raise Exception('d has to be in the range of [-0.5, 0.5]')
def gen(self, T = 1000, noise_var = 1):
p = len(self.Ap)
q = len(self.Aq)
et = np.random.randn(T,) * np.sqrt(noise_var)
if self.order == 0:
if p == 0 and q == 0:
return et
if p == 0:
Aq = np.array([1] + self.Aq)
moving_average_ = | np.convolve(et, Aq) | numpy.convolve |
# Copyright 2019 <NAME>.
#
# This file is part of Mi3-GPU.
#
# Mi3-GPU is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, version 3 of the License.
#
# Mi3-GPU is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with Mi3-GPU. If not, see <http://www.gnu.org/licenses/>.
#
#Contact: allan.haldane _AT_ gmail.com
import scipy
import numpy as np
from numpy.random import RandomState
import pyopencl as cl
import pyopencl.array as cl_array
import os, time, warnings
import textwrap
from utils import printsome
import collections
cf = cl.mem_flags
rng_buf_mul = 1024
################################################################################
os.environ['PYOPENCL_COMPILER_OUTPUT'] = '0'
os.environ['PYOPENCL_NO_CACHE'] = '1'
os.environ["CUDA_CACHE_DISABLE"] = '1'
def printPlatform(log, p, n=0):
log("Platform {} '{}':".format(n, p.name))
log(" Vendor: {}".format(p.vendor))
log(" Version: {}".format(p.version))
exts = ("\n" + " "*16).join(textwrap.wrap(p.extensions, 80-16))
log(" Extensions: {}".format(exts))
def printDevice(log, d):
log(" Device '{}':".format(d.name))
log(" Vendor: {}".format(d.vendor))
log(" Version: {}".format(d.version))
log(" Driver Version: {}".format(d.driver_version))
log(" Max Clock Frequency: {}".format(d.max_clock_frequency))
log(" Max Compute Units: {}".format(d.max_compute_units))
log(" Max Work Group Size: {}".format(d.max_work_group_size))
log(" Global Mem Size: {}".format(d.global_mem_size))
log(" Global Mem Cache Size: {}".format(d.global_mem_cache_size))
log(" Local Mem Size: {}".format(d.local_mem_size))
log(" Max Constant Buffer Size: {}".format(d.max_constant_buffer_size))
def printGPUs(log):
for n,p in enumerate(cl.get_platforms()):
printPlatform(log, p, n)
for d in p.get_devices():
printDevice(log, d)
log("")
################################################################################
# The GPU performs two main types of computation: MCMC runs, and perturbed
# coupling updates. MCMCGPU methods are asynchronous on the host.
# Functions that return data do not return the data directly, but return a
# FutureBuf object. The data may be obtained by FutureBuf.read(), which is
# blocking.
# The gpu has two sequence buffers: A "small" buffer for MCMC gpu generation,
# and an optional "large buffer" for combined sequence sets.
# The opencl queue is created as an out-of-order queue, and so kernel order is
# managed by the MCMCGPU class itself. By default, it makes all opencl
# commands wait until the last command is finished, but all methods also
# have a wait_for argument to override this. `None` means wait until the last
# command is done, or it can be a list of opencl events to wait for. Set it
# to the empty list [] to run immediately.
# Note that in openCL implementations there is generally a limit on the number
# of queued commands allowed in a context. If you reach the limit, all queues
# will block until a kernel finishes. So we must be careful not to fill up a
# single queue before others, so do `for i in range(100): for g in gpus:
# g.command()` instead of `for g in gpus: for i in range(100): g.command()` as
# the latter may fill the first gpu's queue, blocking the rest.
# See CL_DEVICE_QUEUE_ON_DEVICE_MAX_SIZE and CL_DEVICE_MAX_ON_DEVICE_EVENTS
# Note that on some systems there is a watchdog timer that kills any kernel
# that runs for too long. You will get a CL_OUT_OF_RESOURCES error if this
# happens, which occurs when the *following* kernel is run.
class FutureBuf:
def __init__(self, buffer, event, postprocess=None):
self.buffer = buffer
self.event = event
self.postfunc = postprocess
self.shape = buffer.shape
self.dtype = buffer.dtype
def read(self):
self.event.wait()
if self.postfunc != None:
return self.postfunc(self.buffer)
return self.buffer
class MCMCGPU:
def __init__(self, gpuinfo, L, q, nseq, wgsize, outdir,
vsize, seed, profile=False):
if nseq%512 != 0:
raise ValueError("nwalkers/ngpus must be a multiple of 512")
# this guarantees that all kernel access to seqmem is coalesced and
# simplifies the histogram kernels
self.L = L
self.q = q
self.nPairs = L*(L-1)//2
self.events = collections.deque()
self.SWORDS = ((L-1)//4+1) #num words needed to store a sequence
self.SBYTES = (4*self.SWORDS) #num bytes needed to store a sequence
self.nseq = {'main': nseq}
self.nwalkers = nseq
device, gpunum, ctx, prg = gpuinfo
self.gpunum = gpunum
self.ctx = ctx
self.prg = prg
self.device = device
self.wgsize = wgsize
self.nhist, self.histws = histogram_heuristic(q)
# sanity checks (should be checked elsewhere before this)
if nseq%wgsize != 0:
raise Exception("nseq per GPU must be a multiple of wgsize")
if wgsize < q*q:
raise Exception("wgsize cannot be less than q*q")
self.logfn = os.path.join(outdir, 'gpu-{}.log'.format(gpunum))
with open(self.logfn, "wt") as f:
printDevice(f.write, device)
self.mcmcprg = prg.metropolis
self.rngstate = RandomState(seed)
#setup opencl for this device
self.log("Getting CL Queue")
qprop = cl.command_queue_properties.OUT_OF_ORDER_EXEC_MODE_ENABLE
self.profile = profile
if profile:
qprop |= cl.command_queue_properties.PROFILING_ENABLE
self.queue = cl.CommandQueue(ctx, device=device, properties=qprop)
self.log("\nOpenCL Device Compilation Log:")
self.log(self.prg.get_build_info(device, cl.program_build_info.LOG))
maxwgs = self.mcmcprg.get_work_group_info(
cl.kernel_work_group_info.WORK_GROUP_SIZE, device)
self.log("Max MCMC WGSIZE: {}".format(maxwgs))
self.initted = []
self.bufs = {}
self.buf_spec = {}
self.seqbufs = {}
self.Ebufs = {}
self.largebufs = []
# setup essential buffers
nPairs, SWORDS = self.nPairs, self.SWORDS
j_pad = 3*self.wgsize
self._setupBuffer( 'J', '<f4', (nPairs, q*q), pad=j_pad)
self._setupBuffer('Junpacked', '<f4', (L*L, q*q), pad=j_pad)
self._setupBuffer( 'bi', '<f4', (nPairs, q*q)),
self._setupBuffer( 'bicount', '<u4', (nPairs, q*q)),
self._setupBuffer( 'seq main', '<u4', (SWORDS, self.nseq['main'])),
self._setupBuffer('seqL main', '<u4', (L, self.nseq['main']//4)),
self._setupBuffer( 'E main', '<f4', (self.nseq['main'],)),
self.unpackedJ = False #use to keep track of whether J is unpacked
self.repackedSeqT = {'main': False}
self.lastevt = None
def log(self, msg):
#logs are rare, so just open the file every time
with open(self.logfn, "at") as f:
print("{: 10.3f}".format(time.process_time()), msg, file=f)
def logevt(self, name, evt, nbytes=None):
self.lastevt = evt
# don't save events if not profiling.
# note that saved events use up memory - free it using logprofile
if self.profile:
if len(self.events)%1000 == 0 and len(self.events) != 0:
self.log("Warning: Over {} profiling events are not flushed "
"(using up memory)".format(len(self.events)))
if nbytes:
self.events.append((evt, name, nbytes))
else:
self.events.append((evt, name))
return evt
def _evtlist(self, evts):
if evts is None:
return []
elif isinstance(evts, cl.Event):
return [evts]
else:
return evts
def _waitevt(self, evts=None):
if evts is None and self.lastevt is not None:
return [self.lastevt]
return self._evtlist(evts)
def logProfile(self):
if not self.profile:
return
def isComplete(e):
return (e.command_execution_status ==
cl.command_execution_status.COMPLETE)
with open(self.logfn, "at") as f:
while len(self.events) != 0 and isComplete(self.events[0][0]):
dat = self.events.popleft()
evt, name, size = dat[0],dat[1],(dat[2] if len(dat)==3 else '')
print("EVT", name, evt.profile.start, evt.profile.end,
size, file=f)
def _setupBuffer(self, bufname, buftype, bufshape, pad=None,
flags=cf.READ_WRITE):
flags = flags | cf.ALLOC_HOST_PTR
nelem = int(np.product(bufshape))
if pad:
nelem = nelem + pad
size = np.dtype(buftype).itemsize * nelem
buf = cl.Buffer(self.ctx, flags, size=size)
self.bufs[bufname] = buf
self.buf_spec[bufname] = (buftype, bufshape, flags)
# add it to convenience dicts if applicable
names = bufname.split()
if len(names) > 1:
bufs = {'seq': self.seqbufs, 'E': self.Ebufs}
if names[0] in bufs:
bufs[names[0]][names[1]] = buf
def require(self, *reqs):
for r in reqs:
if r not in self.initted:
raise Exception("{} not initialized".format(r))
def _initcomponent(self, cmp):
if cmp in self.initted:
raise Exception("Already initialized {}".format(cmp))
self.initted.append(cmp)
def initMCMC(self, nsteps, rng_offset, rng_span):
self._initcomponent('MCMC')
# rngstates should be size of mwc64xvec2_state_t
self.nsteps = nsteps
self._setupBuffer('rngstates', '<2u8', (self.nseq['main'],)),
self._setupBuffer( 'Bs', '<f4', (self.nseq['main'],)),
self._setupBuffer( 'randpos', '<u4', (self.nsteps*rng_buf_mul,))
self.randpos_offset = rng_buf_mul*self.nsteps
self.setBuf('Bs', np.ones(self.nseq['main'], dtype='<f4'))
self._initMCMC_RNG(rng_offset, rng_span)
self.nsteps = int(nsteps)
def initLargeBufs(self, nseq_large):
self._initcomponent('Large')
self.nseq['large'] = nseq_large
self._setupBuffer( 'seq large', '<u4', (self.SWORDS, nseq_large))
self._setupBuffer( 'seqL large', '<u4', (self.L, nseq_large//4)),
self._setupBuffer( 'E large', '<f4', (nseq_large,))
self._setupBuffer('weights large', '<f4', (nseq_large,))
self.largebufs.extend(['seq large', 'seqL large', 'E large',
'weights large'])
self.nstoredseqs = 0
# it is important to zero out the large seq buffer, because
# if it is partially full we may need to compute energy
# over the padding sequences at the end to get a full wg.
buf = self.bufs['seq large']
self.fillBuf('seq large', 0)
self.repackedSeqT['large'] = False
def initSubseq(self):
self.require('Large')
self._initcomponent('Subseq')
self._setupBuffer('markpos', '<u1', (self.SBYTES,), flags=cf.READ_ONLY)
self.markPos(np.zeros(self.SBYTES, '<u1'))
## we may want to select replicas at a particular temperature
#def initMarkSeq(self):
# self._initcomponent('Markseq')
# self._setupBuffer( 'markseqs', '<i4', (self.nseq['main'],))
# self.setBuf('markseqs', np.arange(self.nseq['main'], dtype='<i4'))
# self.nmarks = self.nseq['main']
def initJstep(self):
self._initcomponent('Jstep')
nPairs, q = self.nPairs, self.q
self._setupBuffer( 'dJ', '<f4', (nPairs, q*q))
self._setupBuffer('bi target', '<f4', (nPairs, q*q))
self._setupBuffer( 'Creg', '<f4', (nPairs, q*q))
self._setupBuffer( 'Xlambdas', '<f4', (nPairs,))
self._setupBuffer( 'neff', '<f4', (1,))
self._setupBuffer( 'weights', '<f4', (self.nseq['main'],))
def packSeqs_4(self, seqs):
"""
Converts seqs to 4-byte uint format on CPU, padded to 32bits, assumes
little endian. Each row's bytes are
a0 a1 a2 a3 b0 b1 b2 b3 c0 c1 c2 c3 ...
for sequences a, b, c, so each uint32 correaponds to 4 seq bytes.
"""
if seqs.dtype != np.dtype('<u1'):
raise Exception("seqs must have u1 dtype")
bseqs = np.zeros((seqs.shape[0], self.SBYTES), dtype='<u1', order='C')
bseqs[:,:self.L] = seqs
mem = np.zeros((self.SWORDS, seqs.shape[0]), dtype='<u4', order='C')
for i in range(self.SWORDS):
mem[i,:] = bseqs.view(np.uint32)[:,i]
return mem
def unpackSeqs_4(self, mem):
""" reverses packSeqs_4 (on CPU)"""
bseqs = np.zeros((mem.shape[1], self.SBYTES), dtype='<u1', order='C')
for i in range(self.SWORDS): #undo memory rearrangement
bseqs.view(np.uint32)[:,i] = mem[i,:]
return bseqs[:,:self.L]
def repackseqs_T(self, bufname, wait_for=None):
"""
On GPU, copies the seq buffer (in 4-byte format) to a seqL buffer
in "transpose" format, which is just the usual CPU sequence buffer
but transposed.
"""
self.log("repackseqs_T")
nseq = self.nseq[bufname]
inseq_dev = self.bufs['seq ' + bufname]
outseq_dev = self.bufs['seqL ' + bufname]
self.repackedSeqT[bufname] = True
return self.logevt('repackseqs_T',
self.prg.unpackseqs1(self.queue, (self.SWORDS*256,), (256,),
inseq_dev, np.uint32(nseq),
outseq_dev, np.uint32(nseq//4),
wait_for=self._waitevt(wait_for)))
def unpackJ(self, wait_for=None):
"""convert J from format where every row is a unique ij pair (L choose 2
rows) to format with every pair, all orders (L^2 rows)."""
# quit if J already loaded/unpacked
if self.unpackedJ:
return wait_for
self.log("unpackJ")
q, nPairs = self.q, self.nPairs
self.unpackedJ = True
return self.logevt('unpackJ',
self.prg.unpackfV(self.queue, (nPairs*q*q,), (q*q,),
self.bufs['J'], self.bufs['Junpacked'],
wait_for=self._waitevt(wait_for)))
def _initMCMC_RNG(self, rng_offset, rng_span, wait_for=None):
self.require('MCMC')
self.log("initMCMC_RNG")
# Idea is we want to divide the rng stream into non-overlapping chunks
# for each walker. This GPU was given a span of rng_span, so divide it
# by number of walkers (times 2 since each rng call advances by 2 for
# vec2).
# Read mwc64 docs for more info. mwc64 doc says each walker's stream
# offset is (rng_offset + walker_span*(get_global_id(0)*vectorSize +
# vecind)) where vectorSize is 2. Note that rng_offset is not
# multiplied by 2!
rng_offset = np.uint64(rng_offset)
nwalkers = np.uint64(self.nseq['main'])
v2 = np.uint64(2)
# walker span is the # of rng calls assigned per walker
walker_span = np.uint64(rng_span)//(v2*nwalkers) # factor of 2 for vec2
self.log("RNG offset: {} walker-span: {} nwalkers {}".format(
rng_offset, walker_span, nwalkers))
# Warning: It is very important that the walker rng stream offsets
# across gpus are all distinct, or else some walkers will be highly
# correlated. Touch this code with care.
assert(walker_span*v2*nwalkers <= rng_span)
wgsize = self.wgsize
while wgsize > nwalkers:
wgsize = wgsize//2
return self.logevt('initMCMC_RNG',
self.prg.initRNG2(self.queue, (nwalkers,), (wgsize,),
self.bufs['rngstates'],
np.uint64(rng_offset), walker_span,
wait_for=self._waitevt(wait_for)))
def updateRngPos(self, wait_evt=None):
self.randpos_offset = self.randpos_offset + self.nsteps
rng_evt = None
bufsize = rng_buf_mul*self.nsteps
if self.randpos_offset >= bufsize:
# all gpus use same position-rng series. This way there is no
# difference between running on one gpu vs splitting on multiple
rng = self.rngstate.randint(0, self.L, size=bufsize).astype('u4')
rng_evt = self.setBuf('randpos', rng, wait_for=wait_evt)
self.randpos_offset = 0
return np.uint32(self.randpos_offset), rng_evt
def runMCMC(self, wait_for=None):
"""Performs a single round of mcmc sampling (nsteps MC steps)"""
t1 = time.time()
self.require('MCMC')
self.log("runMCMC")
wait_evt = self._waitevt(wait_for)
nseq = self.nseq['main']
nsteps = self.nsteps
wait_unpack = self.unpackJ(wait_for=wait_evt)
rngoffset, wait_rng = self.updateRngPos(wait_evt)
wait = self._evtlist(wait_unpack) + self._evtlist(wait_rng)
self.repackedSeqT['main'] = False
return self.logevt('mcmc',
self.mcmcprg(self.queue, (nseq,), (self.wgsize,),
self.bufs['Junpacked'], self.bufs['rngstates'],
rngoffset, self.bufs['randpos'], np.uint32(nsteps),
self.Ebufs['main'], self.bufs['Bs'],
self.seqbufs['main'],
wait_for=wait))
def measureFPerror(self, log, nloops=3):
log("Measuring FP Error")
for n in range(nloops):
self.runMCMC()
e1 = self.getBuf('E main').read()
self.calcEnergies('main')
e2 = self.getBuf('E main').read()
log("Run", n, "Error:", np.mean((e1-e2)**2))
log(' Final E MC', printsome(e1), '...')
log(" Final E rc", printsome(e2), '...')
seqs = self.getBuf('seq main').read()
J = self.getBuf('J').read()
e3 = getEnergies(seqs, J)
log(" Exact E", e3[:5])
log(" Error:", np.mean([float((a-b)**2) for a,b in zip(e1, e3)]))
def calcBicounts(self, seqbufname, wait_for=None):
self.log("calcBicounts " + seqbufname)
L, q, nPairs, nhist = self.L, self.q, self.nPairs, self.nhist
if seqbufname == 'main':
nseq = self.nseq[seqbufname]
buflen = nseq
else:
nseq = self.nstoredseqs
buflen = self.nseq[seqbufname]
seq_dev = self.seqbufs[seqbufname]
localhist = cl.LocalMemory(nhist*q*q*np.dtype(np.uint32).itemsize)
return self.logevt('calcBicounts',
self.prg.countBivariate(self.queue, (nPairs*nhist,), (nhist,),
self.bufs['bicount'],
np.uint32(nseq), seq_dev, np.uint32(buflen), localhist,
wait_for=self._waitevt(wait_for)))
def bicounts_to_bimarg(self, seqbufname='main', wait_for=None):
self.log("bicounts_to_bimarg ")
q, nPairs = self.q, self.nPairs
if seqbufname == 'main':
nseq = self.nseq['main']
else:
nseq = self.nstoredseqs
nworkunits = self.wgsize*((nPairs*q*q-1)//self.wgsize+1)
return self.logevt('bicounts_to_bimarg',
self.prg.bicounts_to_bimarg(self.queue,
(nworkunits,), (self.wgsize,),
self.bufs['bicount'], self.bufs['bi'], np.uint32(nseq),
wait_for=self._waitevt(wait_for)))
def calcEnergies(self, seqbufname, Jbufname='J', wait_for=None):
self.log("calcEnergies " + seqbufname)
energies_dev = self.Ebufs[seqbufname]
seq_dev = self.seqbufs[seqbufname]
buflen = self.nseq[seqbufname]
if seqbufname == 'main':
nseq = self.nseq[seqbufname]
else:
nseq = self.nstoredseqs
# pad to be a multiple of wgsize (uses dummy seqs at end)
nseq = nseq + ((self.wgsize - nseq) % self.wgsize)
return self.logevt('getEnergies',
self.prg.getEnergies(self.queue, (nseq,), (self.wgsize,),
self.bufs[Jbufname], seq_dev, np.uint32(buflen),
energies_dev, wait_for=self._waitevt(wait_for)))
def weightedMarg(self, seqbufname='main', wait_for=None):
self.require('Jstep')
self.log("weightedMarg")
q, L, nPairs = self.q, self.L, self.nPairs
nhist, histws = self.nhist, self.histws
if seqbufname == 'main':
nseq = self.nseq[seqbufname]
buflen = nseq//4
weights_dev = self.bufs['weights']
else:
nseq = self.nstoredseqs
buflen = self.nseq[seqbufname]//4
weights_dev = self.bufs['weights large']
# pad to be a multiple of 512 (uses dummy seqs at end)
nseq = nseq + ((512 - nseq) % 512)
# XXX find correct padding here
if not self.repackedSeqT[seqbufname]:
wait_for = self.repackseqs_T(seqbufname,
wait_for=self._waitevt(wait_for))
seq_dev = self.bufs['seqL ' + seqbufname]
return self.logevt('weightedMarg',
self.prg.weightedMarg(self.queue, (nPairs*histws,), (histws,),
self.bufs['bi'], weights_dev,
np.uint32(nseq), seq_dev, np.uint32(buflen),
wait_for=self._waitevt(wait_for)))
def renormalize_bimarg(self, wait_for=None):
self.log("renormalize_bimarg")
q, nPairs = self.q, self.nPairs
return self.logevt('renormalize_bimarg',
self.prg.renormalize_bimarg(self.queue, (nPairs*q*q,), (q*q,),
self.bufs['bi'], wait_for=self._waitevt(wait_for)))
def addBiBuffer(self, bufname, otherbuf, wait_for=None):
# used for combining results from different gpus, where otherbuf is a
# buffer "belonging" to another gpu
self.log("addbuf")
selfbuf = self.bufs[bufname]
if selfbuf.size != otherbuf.size:
raise Exception('Tried to add bufs of different sizes')
q, nPairs = self.q, self.nPairs
nworkunits = self.wgsize*((nPairs*q*q-1)//self.wgsize+1)
return self.logevt('addbuf',
self.prg.addBiBufs(self.queue, (nworkunits,), (self.wgsize,),
selfbuf, otherbuf, wait_for=self._waitevt(wait_for)))
def updateJ(self, gamma, pc, Jbuf='dJ', wait_for=None):
self.require('Jstep')
self.log("updateJ")
q, nPairs = self.q, self.nPairs
#find next highest multiple of wgsize, for num work units
nworkunits = self.wgsize*((nPairs*q*q-1)//self.wgsize+1)
bibuf = self.bufs['bi']
Jin = Jout = self.bufs[Jbuf]
self.unpackedJ = False
return self.logevt('updateJ',
self.prg.updatedJ(self.queue, (nworkunits,), (self.wgsize,),
self.bufs['bi target'], bibuf,
np.float32(gamma), np.float32(pc), Jin, Jout,
wait_for=self._waitevt(wait_for)))
def reg_l1z(self, gamma, pc, lJ, wait_for=None):
self.require('Jstep')
self.log("reg_l1z")
q, nPairs = self.q, self.nPairs
bibuf = self.bufs['bi']
self.unpackedJ = None
return self.logevt('reg_l1z',
self.prg.reg_l1z(self.queue, (nPairs*q*q,), (q*q,),
bibuf, np.float32(gamma), np.float32(pc),
np.float32(lJ), self.bufs['J'], self.bufs['dJ'],
wait_for=self._waitevt(wait_for)))
def reg_l2z(self, gamma, pc, lJ, wait_for=None):
self.require('Jstep')
self.log("reg_l2z")
q, nPairs = self.q, self.nPairs
bibuf = self.bufs['bi']
self.unpackedJ = None
return self.logevt('reg_l2z',
self.prg.reg_l2z(self.queue, (nPairs*q*q,), (q*q,),
bibuf, np.float32(gamma), np.float32(pc),
np.float32(lJ),
self.bufs['J'], self.bufs['dJ'],
wait_for=self._waitevt(wait_for)))
def reg_X(self, gamma, pc, wait_for=None):
self.require('Jstep')
self.log("reg X")
q, nPairs = self.q, self.nPairs
bibuf = self.bufs['bi']
self.unpackedJ = None
return self.logevt('reg_X',
self.prg.reg_X(self.queue, (nPairs*q*q,), (q*q,),
bibuf, self.bufs['Creg'],
np.float32(gamma), np.float32(pc),
self.bufs['J'], self.bufs['dJ'],
wait_for=self._waitevt(wait_for)))
def reg_ddE(self, gamma, pc, lam, wait_for=None):
self.require('Jstep')
self.log("reg ddE")
q, nPairs = self.q, self.nPairs
bibuf = self.bufs['bi']
self.unpackedJ = None
return self.logevt('reg_ddE',
self.prg.reg_ddE(self.queue, (nPairs*q*q,), (q*q,),
bibuf, np.float32(gamma), np.float32(pc),
np.float32(lam),
self.bufs['J'], self.bufs['dJ'],
wait_for=self._waitevt(wait_for)))
def getBuf(self, bufname, truncateLarge=True, wait_for=None):
"""get buffer data. truncateLarge means only return the
computed part of the large buffer (rest may be uninitialized)"""
self.log("getBuf " + bufname)
bufspec = self.buf_spec[bufname]
buftype, bufshape = bufspec[0], bufspec[1]
mem = np.zeros(bufshape, dtype=buftype)
evt = cl.enqueue_copy(self.queue, mem, self.bufs[bufname],
is_blocking=False, wait_for=self._waitevt(wait_for))
self.logevt('getBuf', evt, mem.nbytes)
if bufname.split()[0] == 'seq':
if bufname in self.largebufs and truncateLarge:
nret = self.nstoredseqs
return FutureBuf(mem, evt,
lambda b: self.unpackSeqs_4(b)[:nret,:])
return FutureBuf(mem, evt, self.unpackSeqs_4)
if bufname in self.largebufs and truncateLarge:
nret = self.nstoredseqs
return FutureBuf(mem, evt, lambda b: b[:nret])
return FutureBuf(mem, evt)
def setBuf(self, bufname, buf, wait_for=None):
self.log("setBuf " + bufname)
# device-to-device copies skip all the checks
if isinstance(buf, cl.Buffer):
evt = cl.enqueue_copy(self.queue, self.bufs[bufname], buf,
wait_for=self._waitevt(wait_for))
self.logevt('setBuf', evt, buf.size)
if bufname.split()[0] == 'J':
self.unpackedJ = None
return evt
if bufname.split()[0] == 'seq':
buf = self.packSeqs_4(buf)
bufspec = self.buf_spec[bufname]
buftype, bufshape = bufspec[0], bufspec[1]
if not isinstance(buf, np.ndarray):
buf = array(buf, dtype=buftype)
if np.dtype(buftype) != buf.dtype:
raise ValueError("Buffer dtype mismatch.Expected {}, got {}".format(
np.dtype(buftype), buf.dtype))
if bufshape != buf.shape and not (bufshape == (1,) or buf.size == 1):
raise ValueError("Buffer size mismatch. Expected {}, got {}".format(
bufshape, buf.shape))
evt = cl.enqueue_copy(self.queue, self.bufs[bufname], buf,
is_blocking=False, wait_for=self._waitevt(wait_for))
self.logevt('setBuf', evt, buf.nbytes)
#unset packedJ flag if we modified that J buf
if bufname.split()[0] == 'J':
self.unpackedJ = None
if bufname == 'seq large':
self.nstoredseqs = bufshape[1]
if bufname.split()[0] == 'seq':
self.repackedSeqT[bufname.split()[1]] = False
return evt
def fillBuf(self, bufname, val, wait_for=None):
self.log("fillBuf " + bufname)
buf = self.bufs[bufname]
buftype = np.dtype(self.buf_spec[bufname][0]).type
self.logevt('fill_buffer',
cl.enqueue_fill_buffer(self.queue, buf, buftype(val), 0, buf.size,
wait_for=self._waitevt()))
def markPos(self, marks, wait_for=None):
self.require('Subseq')
marks = marks.astype('<u1')
if len(marks) == self.L:
marks.resize(self.SBYTES)
return self.setBuf('markpos', marks, wait_for=wait_for)
def fillSeqs(self, startseq, seqbufname='main', wait_for=None):
#write a kernel function for this?
self.log("fillSeqs " + seqbufname)
nseq = self.nseq[seqbufname]
self.setBuf('seq '+seqbufname, np.tile(startseq, (nseq,1)),
wait_for=wait_for)
def storeSeqs(self, seqs=None, wait_for=None):
"""
If seqs is None, stores main to large seq buffer. Otherwise
stores seqs to large buffer
"""
self.require('Large')
offset = self.nstoredseqs
self.log("storeSeqs " + str(offset))
if seqs is not None:
nseq, L = seqs.shape
if L != self.L:
raise Exception(
"Sequences have wrong length: {} vs {}".format(L, self.L))
if offset + nseq > self.nseq['large']:
raise Exception("cannot store seqs past end of large buffer")
assert(seqs.dtype == np.dtype('u1'))
buf = self.packSeqs_4(seqs)
w, h = self.buf_spec['seq large'][1] # L/4, nseq
# for some reason, rectangular copies in pyOpencl use opposite axis
# order from numpy, and need indices in bytes not elements, so we
# have to switch all this around. buf is uint32, or 4 bytes.
evt = cl.enqueue_copy(self.queue, self.seqbufs['large'], buf,
buffer_origin=(4*offset, 0),
host_origin=(0, 0),
region=(4*buf.shape[1], buf.shape[0]),
buffer_pitches=(4*h, w),
host_pitches=(4*buf.shape[1], buf.shape[0]),
is_blocking=False,
wait_for=self._waitevt(wait_for))
else:
nseq = self.nseq['main']
if offset + nseq > self.nseq['large']:
raise Exception("cannot store seqs past end of large buffer")
evt = self.prg.storeSeqs(self.queue, (nseq,), (self.wgsize,),
self.seqbufs['main'], self.seqbufs['large'],
np.uint32(self.nseq['large']), np.uint32(offset),
wait_for=self._waitevt(wait_for))
self.nstoredseqs += nseq
self.repackedSeqT['large'] = False
return self.logevt('storeSeqs', evt)
def clearLargeSeqs(self):
self.require('Large')
self.nstoredseqs = 0
self.repackedSeqT['large'] = False
def restoreSeqs(self, wait_for=None):
self.require('Large')
self.log("restoreSeqs " + str(offset))
nseq = self.nseq['main']
if offset + nseq > self.nseq['large']:
raise Exception("cannot get seqs past end of large buffer")
if self.nstoredseqs < nseq:
raise Exception("not enough seqs stored in large buffer")
self.repackedSeqT['main'] = False
return self.logevt('restoreSeqs',
self.prg.restoreSeqs(self.queue, (nseq,), (self.wgsize,),
self.seqbufs['main'], self.seqbufs['large'],
| np.uint32(self.nseq['large']) | numpy.uint32 |
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