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# 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]) | numpy.array |
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
from load_rider_id_results import df
# Plot parameters for Latex output
params = {'backend': 'ps',
'axes.labelsize': 10,
'text.fontsize': 10,
'legend.fontsize': 8,
'xtick.labelsize': 8,
'ytick.labelsize': 8,
'text.usetex': True,
'figure.dpi': 200,
}
plt.rcParams.update(params)
# Create a histogram of the speeds
fig, ax = plt.subplots(1, 1, squeeze=True)
fig.set_size_inches(5, 5)
ax.hist(df['speed'], bins=40, range=(0, 10), align='mid')
ax.set_xlabel('Speed m/s')
ax.set_ylabel('Runs')
ax.set_xticks( | np.linspace(0, 10, 21) | numpy.linspace |
# -*- coding: utf-8 -*-
# -----------------------------------------------------------------------------
# Copyright (c) 2014, <NAME>. All rights reserved.
# Distributed under the terms of the new BSD License.
# -----------------------------------------------------------------------------
import unittest
import numpy as np
from vispy.gloo import Texture1D, Texture2D, Texture3D, TextureAtlas
from vispy.testing import requires_pyopengl, run_tests_if_main, assert_raises
# here we test some things that will be true of all Texture types:
Texture = Texture2D
# ----------------------------------------------------------------- Texture ---
class TextureTest(unittest.TestCase):
# No data, no dtype : forbidden
# ---------------------------------
def test_init_none(self):
self.assertRaises(ValueError, Texture)
# Data only
# ---------------------------------
def test_init_data(self):
data = np.zeros((10, 10, 3), dtype=np.uint8)
T = Texture(data=data, interpolation='linear', wrapping='repeat')
assert T._shape == (10, 10, 3)
assert T._interpolation == ('linear', 'linear')
assert T._wrapping == ('repeat', 'repeat')
# Setting data and shape
# ---------------------------------
def test_init_dtype_shape(self):
T = Texture((10, 10))
assert T._shape == (10, 10, 1)
self.assertRaises(ValueError, Texture, shape=(10, 10),
data=np.zeros((10, 10), np.float32))
# Set data with store
# ---------------------------------
def test_setitem_all(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture(data=data)
T[...] = np.ones((10, 10, 1))
glir_cmd = T._glir.clear()[-1]
assert glir_cmd[0] == 'DATA'
assert np.allclose(glir_cmd[3], np.ones((10, 10, 1)))
# Set data without store
# ---------------------------------
def test_setitem_all_no_store(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture(data=data)
T[...] = np.ones((10, 10), np.uint8)
assert np.allclose(data, np.zeros((10, 10)))
# Set a single data
# ---------------------------------
def test_setitem_single(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture(data=data)
T[0, 0, 0] = 1
glir_cmd = T._glir.clear()[-1]
assert glir_cmd[0] == 'DATA'
assert np.allclose(glir_cmd[3], np.array([1]))
# We apparently support this
T[8:3, 3] = 1
# Set some data
# ---------------------------------
def test_setitem_partial(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture(data=data)
T[5:, 5:] = 1
glir_cmd = T._glir.clear()[-1]
assert glir_cmd[0] == 'DATA'
assert np.allclose(glir_cmd[3], np.ones((5, 5)))
# Set non contiguous data
# ---------------------------------
def test_setitem_wrong(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture(data=data)
# with self.assertRaises(ValueError):
# T[::2, ::2] = 1
s = slice(None, None, 2)
self.assertRaises(IndexError, T.__setitem__, (s, s), 1)
self.assertRaises(IndexError, T.__setitem__, (-100, 3), 1)
self.assertRaises(TypeError, T.__setitem__, ('foo', 'bar'), 1)
# Set properties
def test_set_texture_properties(self):
T = Texture((10, 10))
# Interpolation
T.interpolation = 'nearest'
assert T.interpolation == 'nearest'
T.interpolation = 'linear'
assert T.interpolation == 'linear'
T.interpolation = ['linear'] * 2
assert T.interpolation == 'linear'
T.interpolation = ['linear', 'nearest']
assert T.interpolation == ('linear', 'nearest')
# Wrong interpolation
iset = Texture.interpolation.fset
self.assertRaises(ValueError, iset, T, ['linear'] * 3)
self.assertRaises(ValueError, iset, T, True)
self.assertRaises(ValueError, iset, T, [])
self.assertRaises(ValueError, iset, T, 'linearios')
# Wrapping
T.wrapping = 'clamp_to_edge'
assert T.wrapping == 'clamp_to_edge'
T.wrapping = 'repeat'
assert T.wrapping == 'repeat'
T.wrapping = 'mirrored_repeat'
assert T.wrapping == 'mirrored_repeat'
T.wrapping = 'repeat', 'repeat'
assert T.wrapping == 'repeat'
T.wrapping = 'repeat', 'clamp_to_edge'
assert T.wrapping == ('repeat', 'clamp_to_edge')
# Wrong wrapping
wset = Texture.wrapping.fset
self.assertRaises(ValueError, wset, T, ['repeat'] * 3)
self.assertRaises(ValueError, wset, T, True)
self.assertRaises(ValueError, wset, T, [])
self.assertRaises(ValueError, wset, T, 'repeatos')
# --------------------------------------------------------------- Texture2D ---
class Texture2DTest(unittest.TestCase):
# Note: put many tests related to (re)sizing here, because Texture
# is not really aware of shape.
# Shape extension
# ---------------------------------
def test_init(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture2D(data=data)
assert 'Texture2D' in repr(T)
assert T._shape == (10, 10, 1)
assert T.glsl_type == ('uniform', 'sampler2D')
# Width & height
# ---------------------------------
def test_width_height(self):
data = np.zeros((10, 20), dtype=np.uint8)
T = Texture2D(data=data)
assert T.width == 20
assert T.height == 10
# Resize
# ---------------------------------
def test_resize(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture2D(data=data)
T.resize((5, 5))
assert T.shape == (5, 5, 1)
glir_cmd = T._glir.clear()[-1]
assert glir_cmd[0] == 'SIZE'
# Wong arg
self.assertRaises(ValueError, T.resize, (5, 5), 4)
# Resize with bad shape
# ---------------------------------
def test_resize_bad_shape(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture2D(data=data)
# with self.assertRaises(ValueError):
# T.resize((5, 5, 5))
self.assertRaises(ValueError, T.resize, (5,))
self.assertRaises(ValueError, T.resize, (5, 5, 5))
self.assertRaises(ValueError, T.resize, (5, 5, 5, 1))
# Resize not resizable
# ---------------------------------
def test_resize_unresizable(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture2D(data=data, resizable=False)
# with self.assertRaises(RuntimeError):
# T.resize((5, 5))
self.assertRaises(RuntimeError, T.resize, (5, 5))
# Set oversized data (-> resize)
# ---------------------------------
def test_set_oversized_data(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture2D(data=data)
T.set_data(np.ones((20, 20), np.uint8))
assert T.shape == (20, 20, 1)
glir_cmds = T._glir.clear()
assert glir_cmds[-2][0] == 'SIZE'
assert glir_cmds[-1][0] == 'DATA'
# Set undersized data
# ---------------------------------
def test_set_undersized_data(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture2D(data=data)
T.set_data(np.ones((5, 5), np.uint8))
assert T.shape == (5, 5, 1)
glir_cmds = T._glir.clear()
assert glir_cmds[-2][0] == 'SIZE'
assert glir_cmds[-1][0] == 'DATA'
# Set misplaced data
# ---------------------------------
def test_set_misplaced_data(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture2D(data=data)
# with self.assertRaises(ValueError):
# T.set_data(np.ones((5, 5)), offset=(8, 8))
self.assertRaises(ValueError, T.set_data,
np.ones((5, 5)), offset=(8, 8))
# Set misshaped data
# ---------------------------------
def test_set_misshaped_data_2D(self):
data = np.zeros((10, 10), dtype=np.uint8)
T = Texture2D(data=data)
# with self.assertRaises(ValueError):
# T.set_data(np.ones((10, 10)))
self.assertRaises(ValueError, T.set_data, np.ones((10,)))
self.assertRaises(ValueError, T.set_data, | np.ones((5, 5, 5, 1)) | numpy.ones |
# PyVot Python Variational Optimal Transportation
# Author: <NAME> <<EMAIL>>
# Date: April 28th 2020
# Licence: MIT
import os
import sys
import torch
import numpy as np
import matplotlib
from mpl_toolkits import mplot3d
matplotlib.use('Agg')
import matplotlib.pyplot as plt
sys.path.append(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
from vot_torch import VWB
import imageio
| np.random.seed(19) | numpy.random.seed |
"""
Aggregations.
| Copyright 2017-2021, Voxel51, Inc.
| `voxel51.com <https://voxel51.com/>`_
|
"""
import numpy as np
import eta.core.utils as etau
from fiftyone.core.expressions import ViewField as F
import fiftyone.core.media as fom
import fiftyone.core.utils as fou
class Aggregation(object):
"""Abstract base class for all aggregations.
:class:`Aggregation` instances represent an aggregation or reduction
of a :class:`fiftyone.core.collections.SampleCollection` instance.
Args:
field_name: the name of the field to operate on
expr (None): an optional
:class:`fiftyone.core.expressions.ViewExpression` or
`MongoDB expression <https://docs.mongodb.com/manual/meta/aggregation-quick-reference/#aggregation-expressions>`_
to apply to the field before aggregating
"""
def __init__(self, field_name, expr=None):
self._field_name = field_name
self._expr = expr
@property
def field_name(self):
"""The field name being computed on."""
return self._field_name
@property
def expr(self):
"""The :class:`fiftyone.core.expressions.ViewExpression` or MongoDB
expression that will be applied to the field before aggregating, if any.
"""
return self._expr
def to_mongo(self, sample_collection):
"""Returns the MongoDB aggregation pipeline for this aggregation.
Args:
sample_collection: the
:class:`fiftyone.core.collections.SampleCollection` to which
the aggregation is being applied
Returns:
a MongoDB aggregation pipeline (list of dicts)
"""
raise NotImplementedError("subclasses must implement to_mongo()")
def parse_result(self, d):
"""Parses the output of :meth:`to_mongo`.
Args:
d: the result dict
Returns:
the aggregation result
"""
raise NotImplementedError("subclasses must implement parse_result()")
def default_result(self):
"""Returns the default result for this aggregation.
Returns:
the aggregation result
"""
raise NotImplementedError("subclasses must implement default_result()")
def _parse_field_and_expr(
self, sample_collection, auto_unwind=True, allow_missing=False
):
return _parse_field_and_expr(
sample_collection,
self._field_name,
self._expr,
auto_unwind,
allow_missing,
)
class AggregationError(Exception):
"""An error raised during the execution of an :class:`Aggregation`."""
pass
class Bounds(Aggregation):
"""Computes the bounds of a numeric field of a collection.
``None``-valued fields are ignored.
This aggregation is typically applied to *numeric* field types (or lists of
such types):
- :class:`fiftyone.core.fields.IntField`
- :class:`fiftyone.core.fields.FloatField`
Examples::
import fiftyone as fo
from fiftyone import ViewField as F
dataset = fo.Dataset()
dataset.add_samples(
[
fo.Sample(
filepath="/path/to/image1.png",
numeric_field=1.0,
numeric_list_field=[1, 2, 3],
),
fo.Sample(
filepath="/path/to/image2.png",
numeric_field=4.0,
numeric_list_field=[1, 2],
),
fo.Sample(
filepath="/path/to/image3.png",
numeric_field=None,
numeric_list_field=None,
),
]
)
#
# Compute the bounds of a numeric field
#
aggregation = fo.Bounds("numeric_field")
bounds = dataset.aggregate(aggregation)
print(bounds) # (min, max)
#
# Compute the a bounds of a numeric list field
#
aggregation = fo.Bounds("numeric_list_field")
bounds = dataset.aggregate(aggregation)
print(bounds) # (min, max)
#
# Compute the bounds of a transformation of a numeric field
#
aggregation = fo.Bounds("numeric_field", expr=2 * (F() + 1))
bounds = dataset.aggregate(aggregation)
print(bounds) # (min, max)
Args:
field_name: the name of the field to operate on
expr (None): an optional
:class:`fiftyone.core.expressions.ViewExpression` or
`MongoDB expression <https://docs.mongodb.com/manual/meta/aggregation-quick-reference/#aggregation-expressions>`_
to apply to the field before aggregating
"""
def default_result(self):
"""Returns the default result for this aggregation.
Returns:
``(None, None)``
"""
return None, None
def parse_result(self, d):
"""Parses the output of :meth:`to_mongo`.
Args:
d: the result dict
Returns:
the ``(min, max)`` bounds
"""
return d["min"], d["max"]
def to_mongo(self, sample_collection):
path, pipeline, _ = self._parse_field_and_expr(sample_collection)
pipeline.append(
{
"$group": {
"_id": None,
"min": {"$min": "$" + path},
"max": {"$max": "$" + path},
}
}
)
return pipeline
class Count(Aggregation):
"""Counts the number of field values in a collection.
``None``-valued fields are ignored.
If no field is provided, the samples themselves are counted.
Examples::
import fiftyone as fo
dataset = fo.Dataset()
dataset.add_samples(
[
fo.Sample(
filepath="/path/to/image1.png",
predictions=fo.Detections(
detections=[
fo.Detection(label="cat"),
fo.Detection(label="dog"),
]
),
),
fo.Sample(
filepath="/path/to/image2.png",
predictions=fo.Detections(
detections=[
fo.Detection(label="cat"),
fo.Detection(label="rabbit"),
fo.Detection(label="squirrel"),
]
),
),
fo.Sample(
filepath="/path/to/image3.png",
predictions=None,
),
]
)
#
# Count the number of samples in the dataset
#
aggregation = fo.Count()
count = dataset.aggregate(aggregation)
print(count) # the count
#
# Count the number of samples with `predictions`
#
aggregation = fo.Count("predictions")
count = dataset.aggregate(aggregation)
print(count) # the count
#
# Count the number of objects in the `predictions` field
#
aggregation = fo.Count("predictions.detections")
count = dataset.aggregate(aggregation)
print(count) # the count
#
# Count the number of samples with more than 2 predictions
#
expr = (F("detections").length() > 2).if_else(F("detections"), None)
aggregation = fo.Count("predictions", expr=expr)
count = dataset.aggregate(aggregation)
print(count) # the count
Args:
field_name (None): the name of the field to operate on. If none is
provided, the samples themselves are counted
expr (None): an optional
:class:`fiftyone.core.expressions.ViewExpression` or
`MongoDB expression <https://docs.mongodb.com/manual/meta/aggregation-quick-reference/#aggregation-expressions>`_
to apply to the field before aggregating
"""
def __init__(self, field_name=None, expr=None):
super().__init__(field_name, expr=expr)
def default_result(self):
"""Returns the default result for this aggregation.
Returns:
``0``
"""
return 0
def parse_result(self, d):
"""Parses the output of :meth:`to_mongo`.
Args:
d: the result dict
Returns:
the count
"""
return d["count"]
def to_mongo(self, sample_collection):
if self._field_name is None:
return [{"$count": "count"}]
path, pipeline, _ = self._parse_field_and_expr(sample_collection)
if sample_collection.media_type != fom.VIDEO or path != "frames":
pipeline.append({"$match": {"$expr": {"$gt": ["$" + path, None]}}})
pipeline.append({"$count": "count"})
return pipeline
class CountValues(Aggregation):
"""Counts the occurrences of field values in a collection.
This aggregation is typically applied to *countable* field types (or lists
of such types):
- :class:`fiftyone.core.fields.BooleanField`
- :class:`fiftyone.core.fields.IntField`
- :class:`fiftyone.core.fields.StringField`
Examples::
import fiftyone as fo
dataset = fo.Dataset()
dataset.add_samples(
[
fo.Sample(
filepath="/path/to/image1.png",
tags=["sunny"],
predictions=fo.Detections(
detections=[
fo.Detection(label="cat"),
fo.Detection(label="dog"),
]
),
),
fo.Sample(
filepath="/path/to/image2.png",
tags=["cloudy"],
predictions=fo.Detections(
detections=[
fo.Detection(label="cat"),
fo.Detection(label="rabbit"),
]
),
),
fo.Sample(
filepath="/path/to/image3.png",
predictions=None,
),
]
)
#
# Compute the tag counts in the dataset
#
aggregation = fo.CountValues("tags")
counts = dataset.aggregate(aggregation)
print(counts) # dict mapping values to counts
#
# Compute the predicted label counts in the dataset
#
aggregation = fo.CountValues("predictions.detections.label")
counts = dataset.aggregate(aggregation)
print(counts) # dict mapping values to counts
#
# Compute the predicted label counts after some normalization
#
expr = F().map_values({"cat": "pet", "dog": "pet"}).upper()
aggregation = fo.CountValues("predictions.detections.label", expr=expr)
counts = dataset.aggregate(aggregation)
print(counts) # dict mapping values to counts
Args:
field_name: the name of the field to operate on
expr (None): an optional
:class:`fiftyone.core.expressions.ViewExpression` or
`MongoDB expression <https://docs.mongodb.com/manual/meta/aggregation-quick-reference/#aggregation-expressions>`_
to apply to the field before aggregating
"""
def default_result(self):
"""Returns the default result for this aggregation.
Returns:
``{}``
"""
return {}
def parse_result(self, d):
"""Parses the output of :meth:`to_mongo`.
Args:
d: the result dict
Returns:
a dict mapping values to counts
"""
return {i["k"]: i["count"] for i in d["result"]}
def to_mongo(self, sample_collection):
path, pipeline, _ = self._parse_field_and_expr(sample_collection)
pipeline += [
{"$group": {"_id": "$" + path, "count": {"$sum": 1}}},
{
"$group": {
"_id": None,
"result": {"$push": {"k": "$_id", "count": "$count"}},
}
},
]
return pipeline
class Distinct(Aggregation):
"""Computes the distinct values of a field in a collection.
``None``-valued fields are ignored.
This aggregation is typically applied to *countable* field types (or lists
of such types):
- :class:`fiftyone.core.fields.BooleanField`
- :class:`fiftyone.core.fields.IntField`
- :class:`fiftyone.core.fields.StringField`
Examples::
import fiftyone as fo
dataset = fo.Dataset()
dataset.add_samples(
[
fo.Sample(
filepath="/path/to/image1.png",
tags=["sunny"],
predictions=fo.Detections(
detections=[
fo.Detection(label="cat"),
fo.Detection(label="dog"),
]
),
),
fo.Sample(
filepath="/path/to/image2.png",
tags=["sunny", "cloudy"],
predictions=fo.Detections(
detections=[
fo.Detection(label="cat"),
fo.Detection(label="rabbit"),
]
),
),
fo.Sample(
filepath="/path/to/image3.png",
predictions=None,
),
]
)
#
# Get the distinct tags in a dataset
#
aggregation = fo.Distinct("tags")
values = dataset.aggregate(aggregation)
print(values) # list of distinct values
#
# Get the distinct predicted labels in a dataset
#
aggregation = fo.Distinct("predictions.detections.label")
values = dataset.aggregate(aggregation)
print(values) # list of distinct values
#
# Get the distinct predicted labels after some normalization
#
expr = F().map_values({"cat": "pet", "dog": "pet"}).upper()
aggregation = fo.Distinct("predictions.detections.label", expr=expr)
values = dataset.aggregate(aggregation)
print(values) # list of distinct values
Args:
field_name: the name of the field to operate on
expr (None): an optional
:class:`fiftyone.core.expressions.ViewExpression` or
`MongoDB expression <https://docs.mongodb.com/manual/meta/aggregation-quick-reference/#aggregation-expressions>`_
to apply to the field before aggregating
"""
def default_result(self):
"""Returns the default result for this aggregation.
Returns:
``[]``
"""
return []
def parse_result(self, d):
"""Parses the output of :meth:`to_mongo`.
Args:
d: the result dict
Returns:
a sorted list of distinct values
"""
return sorted(d["values"])
def to_mongo(self, sample_collection):
path, pipeline, _ = self._parse_field_and_expr(sample_collection)
pipeline += [
{"$match": {"$expr": {"$gt": ["$" + path, None]}}},
{"$group": {"_id": None, "values": {"$addToSet": "$" + path}}},
]
return pipeline
class HistogramValues(Aggregation):
"""Computes a histogram of the field values in a collection.
This aggregation is typically applied to *numeric* field types (or
lists of such types):
- :class:`fiftyone.core.fields.IntField`
- :class:`fiftyone.core.fields.FloatField`
Examples::
import numpy as np
import matplotlib.pyplot as plt
import fiftyone as fo
samples = []
for idx in range(100):
samples.append(
fo.Sample(
filepath="/path/to/image%d.png" % idx,
numeric_field=np.random.randn(),
numeric_list_field=list(np.random.randn(10)),
)
)
dataset = fo.Dataset()
dataset.add_samples(samples)
def plot_hist(counts, edges):
counts = np.asarray(counts)
edges = np.asarray(edges)
left_edges = edges[:-1]
widths = edges[1:] - edges[:-1]
plt.bar(left_edges, counts, width=widths, align="edge")
#
# Compute a histogram of a numeric field
#
aggregation = fo.HistogramValues("numeric_field", bins=50)
counts, edges, other = dataset.aggregate(aggregation)
plot_hist(counts, edges)
plt.show(block=False)
#
# Compute the histogram of a numeric list field
#
aggregation = fo.HistogramValues("numeric_list_field", bins=50)
counts, edges, other = dataset.aggregate(aggregation)
plot_hist(counts, edges)
plt.show(block=False)
#
# Compute the histogram of a transformation of a numeric field
#
aggregation = fo.HistogramValues(
"numeric_field", expr=2 * (F() + 1), bins=50
)
counts, edges, other = dataset.aggregate(aggregation)
plot_hist(counts, edges)
plt.show(block=False)
Args:
field_name: the name of the field to operate on
expr (None): an optional
:class:`fiftyone.core.expressions.ViewExpression` or
`MongoDB expression <https://docs.mongodb.com/manual/meta/aggregation-quick-reference/#aggregation-expressions>`_
to apply to the field before aggregating
bins (None): can be either an integer number of bins to generate or a
monotonically increasing sequence specifying the bin edges to use.
By default, 10 bins are created. If ``bins`` is an integer and no
``range`` is specified, bin edges are automatically computed from
the bounds of the field
range (None): a ``(lower, upper)`` tuple specifying a range in which to
generate equal-width bins. Only applicable when ``bins`` is an
integer or ``None``
auto (False): whether to automatically choose bin edges in an attempt
to evenly distribute the counts in each bin. If this option is
chosen, ``bins`` will only be used if it is an integer, and the
``range`` parameter is ignored
"""
def __init__(
self, field_name, expr=None, bins=None, range=None, auto=False
):
super().__init__(field_name, expr=expr)
self._bins = bins
self._range = range
self._auto = auto
self._num_bins = None
self._edges = None
self._edges_last_used = None
self._parse_args()
def default_result(self):
"""Returns the default result for this aggregation.
Returns:
a tuple of
- counts: ``[]``
- edges: ``[]``
- other: ``0``
"""
return [], [], 0
def parse_result(self, d):
"""Parses the output of :meth:`to_mongo`.
Args:
d: the result dict
Returns:
a tuple of
- counts: a list of counts in each bin
- edges: an increasing list of bin edges of length
``len(counts) + 1``. Note that each bin is treated as having an
inclusive lower boundary and exclusive upper boundary,
``[lower, upper)``, including the rightmost bin
- other: the number of items outside the bins
"""
if self._auto:
return self._parse_result_auto(d)
return self._parse_result_edges(d)
def to_mongo(self, sample_collection):
path, pipeline, _ = self._parse_field_and_expr(sample_collection)
if self._auto:
pipeline.append(
{
"$bucketAuto": {
"groupBy": "$" + path,
"buckets": self._num_bins,
"output": {"count": {"$sum": 1}},
}
}
)
else:
if self._edges is not None:
edges = self._edges
else:
edges = self._compute_bin_edges(sample_collection)
self._edges_last_used = edges
pipeline.append(
{
"$bucket": {
"groupBy": "$" + path,
"boundaries": edges,
"default": "other", # counts documents outside of bins
"output": {"count": {"$sum": 1}},
}
}
)
pipeline.append({"$group": {"_id": None, "bins": {"$push": "$$ROOT"}}})
return pipeline
def _parse_args(self):
if self._bins is None:
bins = 10
else:
bins = self._bins
if self._auto:
if etau.is_numeric(bins):
self._num_bins = bins
else:
self._num_bins = 10
return
if not etau.is_numeric(bins):
# User-provided bin edges
self._edges = list(bins)
return
if self._range is not None:
# Linearly-spaced bins within `range`
self._edges = list(
np.linspace(self._range[0], self._range[1], bins + 1)
)
else:
# Compute bin edges from bounds
self._num_bins = bins
def _compute_bin_edges(self, sample_collection):
bounds = sample_collection.bounds(self._field_name, expr=self._expr)
if any(b is None for b in bounds):
bounds = (-1, -1)
return list(
np.linspace(bounds[0], bounds[1] + 1e-6, self._num_bins + 1)
)
def _parse_result_edges(self, d):
_edges_array = np.array(self._edges_last_used)
edges = list(_edges_array)
counts = [0] * (len(edges) - 1)
other = 0
for di in d["bins"]:
left = di["_id"]
if left == "other":
other = di["count"]
else:
idx = | np.abs(_edges_array - left) | numpy.abs |
#------------------------------------------------------------------------------
# Copyright (C) 1996-2010 Power System Engineering Research Center (PSERC)
# Copyright (C) 2007-2010 <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.
#------------------------------------------------------------------------------
""" Defines a DC OPF solver and an AC OPF solver.
Based on dcopf_solver.m and mipsopf_solver.m from MATPOWER by <NAME>,
developed at Cornell. See U{http://www.pserc.cornell.edu/matpower/} for more
information.
"""
#------------------------------------------------------------------------------
# Imports:
#------------------------------------------------------------------------------
import logging
from numpy import \
array, pi, polyder, polyval, exp, conj, Inf, ones, r_, zeros, asarray
from scipy.sparse import lil_matrix, csr_matrix, hstack, vstack
from case import REFERENCE
from generator import POLYNOMIAL, PW_LINEAR
#from pdipm import pdipm, pdipm_qp
from pips import pips, qps_pips
#------------------------------------------------------------------------------
# Constants:
#------------------------------------------------------------------------------
SFLOW = "Sflow"
PFLOW = "Pflow"
IFLOW = "Iflow"
#------------------------------------------------------------------------------
# Logging:
#------------------------------------------------------------------------------
logger = logging.getLogger(__name__)
#------------------------------------------------------------------------------
# "_Solver" class:
#------------------------------------------------------------------------------
class _Solver(object):
""" Defines a base class for many solvers.
"""
def __init__(self, om):
#: Optimal power flow model.
self.om = om
#: Number of equality constraints.
self._nieq = 0
def solve(self):
""" Solves optimal power flow and returns a results dict.
"""
raise NotImplementedError
def _unpack_model(self, om):
""" Returns data from the OPF model.
"""
buses = om.case.connected_buses
branches = om.case.online_branches
gens = om.case.online_generators
cp = om.get_cost_params()
# Bf = om._Bf
# Pfinj = om._Pfinj
return buses, branches, gens, cp
def _dimension_data(self, buses, branches, generators):
""" Returns the problem dimensions.
"""
ipol = [i for i, g in enumerate(generators)
if g.pcost_model == POLYNOMIAL]
ipwl = [i for i, g in enumerate(generators)
if g.pcost_model == PW_LINEAR]
nb = len(buses)
nl = len(branches)
# Number of general cost vars, w.
nw = self.om.cost_N
# Number of piece-wise linear costs.
if "y" in [v.name for v in self.om.vars]:
ny = self.om.get_var_N("y")
else:
ny = 0
# Total number of control variables of all types.
nxyz = self.om.var_N
return ipol, ipwl, nb, nl, nw, ny, nxyz
def _linear_constraints(self, om):
""" Returns the linear problem constraints.
"""
A, l, u = om.linear_constraints() # l <= A*x <= u
# Indexes for equality, greater than (unbounded above), less than
# (unbounded below) and doubly-bounded box constraints.
# ieq = flatnonzero( abs(u - l) <= EPS )
# igt = flatnonzero( (u >= 1e10) & (l > -1e10) )
# ilt = flatnonzero( (l <= -1e10) & (u < 1e10) )
# ibx = flatnonzero( (abs(u - l) > EPS) & (u < 1e10) & (l > -1e10) )
# Zero-sized sparse matrices not supported. Assume equality
# constraints exist.
## AA = A[ieq, :]
## if len(ilt) > 0:
## AA = vstack([AA, A[ilt, :]], "csr")
## if len(igt) > 0:
## AA = vstack([AA, -A[igt, :]], "csr")
## if len(ibx) > 0:
## AA = vstack([AA, A[ibx, :], -A[ibx, :]], "csr")
#
# if len(ieq) or len(igt) or len(ilt) or len(ibx):
# sig_idx = [(1, ieq), (1, ilt), (-1, igt), (1, ibx), (-1, ibx)]
# AA = vstack([sig * A[idx, :] for sig, idx in sig_idx if len(idx)])
# else:
# AA = None
#
# bb = r_[u[ieq, :], u[ilt], -l[igt], u[ibx], -l[ibx]]
#
# self._nieq = ieq.shape[0]
#
# return AA, bb
return A, l, u
def _var_bounds(self):
""" Returns bounds on the optimisation variables.
"""
x0 = array([])
xmin = array([])
xmax = array([])
for var in self.om.vars:
x0 = r_[x0, var.v0]
xmin = r_[xmin, var.vl]
xmax = r_[xmax, var.vu]
return x0, xmin, xmax
def _initial_interior_point(self, buses, generators, xmin, xmax, ny):
""" Selects an interior initial point for interior point solver.
"""
Va = self.om.get_var("Va")
va_refs = [b.v_angle * pi / 180.0 for b in buses
if b.type == REFERENCE]
x0 = (xmin + xmax) / 2.0
x0[Va.i1:Va.iN + 1] = va_refs[0] # Angles set to first reference angle.
if ny > 0:
yvar = self.om.get_var("y")
# Largest y-value in CCV data
c = []
for g in generators:
if g.pcost_model == PW_LINEAR:
for _, y in g.p_cost:
c.append(y)
x0[yvar.i1:yvar.iN + 1] = max(c) * 1.1
return x0
#------------------------------------------------------------------------------
# "DCOPFSolver" class:
#------------------------------------------------------------------------------
class DCOPFSolver(_Solver):
""" Defines a solver for DC optimal power flow [3].
Based on dcopf_solver.m from MATPOWER by <NAME>, developed at PSERC
Cornell. See U{http://www.pserc.cornell.edu/matpower/} for more info.
"""
def __init__(self, om, opt=None):
""" Initialises a new DCOPFSolver instance.
"""
super(DCOPFSolver, self).__init__(om)
# TODO: Implement user-defined costs.
self.N = None
self.H = None
self.Cw = zeros((0, 0))
self.fparm = zeros((0, 0))
#: Solver options (See pips.py for futher details).
self.opt = {} if opt is None else opt
def solve(self):
""" Solves DC optimal power flow and returns a results dict.
"""
base_mva = self.om.case.base_mva
Bf = self.om._Bf
Pfinj = self.om._Pfinj
# Unpack the OPF model.
bs, ln, gn, cp = self._unpack_model(self.om)
# Compute problem dimensions.
ipol, ipwl, nb, nl, nw, ny, nxyz = self._dimension_data(bs, ln, gn)
# Split the constraints in equality and inequality.
AA, ll, uu = self._linear_constraints(self.om)
# Piece-wise linear components of the objective function.
Npwl, Hpwl, Cpwl, fparm_pwl, any_pwl = self._pwl_costs(ny, nxyz, ipwl)
# Quadratic components of the objective function.
Npol, Hpol, Cpol, fparm_pol, polycf, npol = \
self._quadratic_costs(gn, ipol, nxyz, base_mva)
# Combine pwl, poly and user costs.
NN, HHw, CCw, ffparm = \
self._combine_costs(Npwl, Hpwl, Cpwl, fparm_pwl, any_pwl,
Npol, Hpol, Cpol, fparm_pol, npol, nw)
# Transform quadratic coefficients for w into coefficients for X.
HH, CC, C0 = self._transform_coefficients(NN, HHw, CCw, ffparm, polycf,
any_pwl, npol, nw)
# Bounds on the optimisation variables.
_, xmin, xmax = self._var_bounds()
# Select an interior initial point for interior point solver.
x0 = self._initial_interior_point(bs, gn, xmin, xmax, ny)
# Call the quadratic/linear solver.
s = self._run_opf(HH, CC, AA, ll, uu, xmin, xmax, x0, self.opt)
# Compute the objective function value.
Va, Pg = self._update_solution_data(s, HH, CC, C0)
# Set case result attributes.
self._update_case(bs, ln, gn, base_mva, Bf, Pfinj, Va, Pg, s["lmbda"])
return s
def _pwl_costs(self, ny, nxyz, ipwl):
""" Returns the piece-wise linear components of the objective function.
"""
any_pwl = int(ny > 0)
if any_pwl:
y = self.om.get_var("y")
# Sum of y vars.
Npwl = csr_matrix((ones(ny), (zeros(ny), array(ipwl) + y.i1)))
Hpwl = csr_matrix((1, 1))
Cpwl = array([1])
fparm_pwl = array([[1., 0., 0., 1.]])
else:
Npwl = None#zeros((0, nxyz))
Hpwl = None#array([])
Cpwl = array([])
fparm_pwl = zeros((0, 4))
return Npwl, Hpwl, Cpwl, fparm_pwl, any_pwl
def _quadratic_costs(self, generators, ipol, nxyz, base_mva):
""" Returns the quadratic cost components of the objective function.
"""
npol = len(ipol)
rnpol = range(npol)
gpol = [g for g in generators if g.pcost_model == POLYNOMIAL]
if [g for g in gpol if len(g.p_cost) > 3]:
logger.error("Order of polynomial cost greater than quadratic.")
iqdr = [i for i, g in enumerate(generators)
if g.pcost_model == POLYNOMIAL and len(g.p_cost) == 3]
ilin = [i for i, g in enumerate(generators)
if g.pcost_model == POLYNOMIAL and len(g.p_cost) == 2]
polycf = zeros((npol, 3))
if npol > 0:
if len(iqdr) > 0:
polycf[iqdr, :] = array([list(g.p_cost)
for g in generators])#[iqdr, :].T
if len(ilin) > 0:
polycf[ilin, 1:] = array([list(g.p_cost[:2])
for g in generators])#[ilin, :].T
# Convert to per-unit.
polycf = polycf * array([base_mva**2, base_mva, 1])
Pg = self.om.get_var("Pg")
Npol = csr_matrix((ones(npol), (rnpol, Pg.i1 + array(ipol))),
(npol, nxyz))
Hpol = csr_matrix((2 * polycf[:, 0], (rnpol, rnpol)), (npol, npol))
Cpol = polycf[:, 1]
fparm_pol = (ones(npol) * array([[1], [0], [0], [1]])).T
else:
Npol = Hpol = None
Cpol = array([])
fparm_pol = zeros((0, 4))
return Npol, Hpol, Cpol, fparm_pol, polycf, npol
def _combine_costs(self, Npwl, Hpwl, Cpwl, fparm_pwl, any_pwl,
Npol, Hpol, Cpol, fparm_pol, npol, nw):
""" Combines pwl, polynomial and user-defined costs.
"""
NN = vstack([n for n in [Npwl, Npol] if n is not None], "csr")
if (Hpwl is not None) and (Hpol is not None):
Hpwl = hstack([Hpwl, csr_matrix((any_pwl, npol))])
Hpol = hstack([csr_matrix((npol, any_pwl)), Hpol])
# if H is not None:
# H = hstack([csr_matrix((nw, any_pwl+npol)), H])
HHw = vstack([h for h in [Hpwl, Hpol] if h is not None], "csr")
CCw = r_[Cpwl, Cpol]
ffparm = r_[fparm_pwl, fparm_pol]
return NN, HHw, CCw, ffparm
def _transform_coefficients(self, NN, HHw, CCw, ffparm, polycf,
any_pwl, npol, nw):
""" Transforms quadratic coefficients for w into coefficients for x.
"""
nnw = any_pwl + npol + nw
M = csr_matrix((ffparm[:, 3], (range(nnw), range(nnw))))
MR = M * ffparm[:, 2] # FIXME: Possibly column 1.
HMR = HHw * MR
MN = M * NN
HH = MN.T * HHw * MN
CC = MN.T * (CCw - HMR)
# Constant term of cost.
C0 = 1./2. * MR.T * HMR + sum(polycf[:, 2])
return HH, CC, C0[0]
def _run_opf(self, HH, CC, AA, ll, uu, xmin, xmax, x0, opt):
""" Solves the either quadratic or linear program.
"""
N = self._nieq
if HH.nnz > 0:
solution = qps_pips(HH, CC, AA, ll, uu, xmin, xmax, x0, opt)
else:
solution = qps_pips(None, CC, AA, ll, uu, xmin, xmax, x0, opt)
return solution
def _update_solution_data(self, s, HH, CC, C0):
""" Returns the voltage angle and generator set-point vectors.
"""
x = s["x"]
Va_v = self.om.get_var("Va")
Pg_v = self.om.get_var("Pg")
Va = x[Va_v.i1:Va_v.iN + 1]
Pg = x[Pg_v.i1:Pg_v.iN + 1]
# f = 0.5 * dot(x.T * HH, x) + dot(CC.T, x)
s["f"] = s["f"] + C0
# Put the objective function value in the solution.
# solution["f"] = f
return Va, Pg
def _update_case(self, bs, ln, gn, base_mva, Bf, Pfinj, Va, Pg, lmbda):
""" Calculates the result attribute values.
"""
Pmis = self.om.get_lin_constraint("Pmis")
Pf = self.om.get_lin_constraint("Pf")
Pt = self.om.get_lin_constraint("Pt")
Pg_v = self.om.get_var("Pg")
mu_l = lmbda["mu_l"]
mu_u = lmbda["mu_u"]
lower = lmbda["lower"]
upper = lmbda["upper"]
for i, bus in enumerate(bs):
bus.v_angle = Va[i] * 180.0 / pi
bus.p_lmbda = (mu_u[Pmis.i1:Pmis.iN + 1][i] -
mu_l[Pmis.i1:Pmis.iN + 1][i]) / base_mva
for l, branch in enumerate(ln):
branch.p_from = (Bf * Va + Pfinj)[l] * base_mva
branch.p_to = -branch.p_from
branch.mu_s_from = mu_u[Pf.i1:Pf.iN + 1][l] / base_mva
branch.mu_s_to = mu_u[Pt.i1:Pt.iN + 1][l] / base_mva
for k, generator in enumerate(gn):
generator.p = Pg[k] * base_mva
generator.mu_pmin = lower[Pg_v.i1:Pg_v.iN + 1][k] / base_mva
generator.mu_pmax = upper[Pg_v.i1:Pg_v.iN + 1][k] / base_mva
#------------------------------------------------------------------------------
# "PIPSSolver" class:
#------------------------------------------------------------------------------
class PIPSSolver(_Solver):
""" Solves AC optimal power flow using a primal-dual interior point method.
Based on mipsopf_solver.m from MATPOWER by <NAME>, developed at
PSERC Cornell. See U{http://www.pserc.cornell.edu/matpower/} for more info.
"""
def __init__(self, om, flow_lim=SFLOW, opt=None):
""" Initialises a new PIPSSolver instance.
"""
super(PIPSSolver, self).__init__(om)
#: Quantity to limit for branch flow constraints ("S", "P" or "I").
self.flow_lim = flow_lim
#: Options for the PIPS.
self.opt = {} if opt is None else opt
def _ref_bus_angle_constraint(self, buses, Va, xmin, xmax):
""" Adds a constraint on the reference bus angles.
"""
refs = [bus._i for bus in buses if bus.type == REFERENCE]
Varefs = array([b.v_angle for b in buses if b.type == REFERENCE])
xmin[Va.i1 - 1 + refs] = Varefs
xmax[Va.iN - 1 + refs] = Varefs
return xmin, xmax
def solve(self):
""" Solves AC optimal power flow.
"""
case = self.om.case
self._base_mva = case.base_mva
# TODO: Find an explanation for this value.
self.opt["cost_mult"] = 1e-4
# Unpack the OPF model.
self._bs, self._ln, self._gn, _ = self._unpack_model(self.om)
# Compute problem dimensions.
self._ipol, _, self._nb, self._nl, _, self._ny, self._nxyz = \
self._dimension_data(self._bs, self._ln, self._gn)
# Compute problem dimensions.
self._ng = len(self._gn)
# gpol = [g for g in gn if g.pcost_model == POLYNOMIAL]
# Linear constraints (l <= A*x <= u).
A, l, u = self.om.linear_constraints()
# AA, bb = self._linear_constraints(self.om)
_, xmin, xmax = self._var_bounds()
# Select an interior initial point for interior point solver.
x0 = self._initial_interior_point(self._bs, self._gn, xmin, xmax, self._ny)
# Build admittance matrices.
self._Ybus, self._Yf, self._Yt = case.Y
# Optimisation variables.
self._Pg = self.om.get_var("Pg")
self._Qg = self.om.get_var("Qg")
self._Va = self.om.get_var("Va")
self._Vm = self.om.get_var("Vm")
# Adds a constraint on the reference bus angles.
# xmin, xmax = self._ref_bus_angle_constraint(bs, Va, xmin, xmax)
# Solve using Python Interior Point Solver (PIPS).
s = self._solve(x0, A, l, u, xmin, xmax)
Vang, Vmag, Pgen, Qgen = self._update_solution_data(s)
self._update_case(self._bs, self._ln, self._gn, self._base_mva,
self._Yf, self._Yt, Vang, Vmag, Pgen, Qgen, s["lmbda"])
return s
def _solve(self, x0, A, l, u, xmin, xmax):
""" Solves using Python Interior Point Solver (PIPS).
"""
s = pips(self._costfcn, x0, A, l, u, xmin, xmax,
self._consfcn, self._hessfcn, self.opt)
return s
def _f(self, x, user_data=None):
""" Evaluates the objective function.
"""
p_gen = x[self._Pg.i1:self._Pg.iN + 1] # Active generation in p.u.
q_gen = x[self._Qg.i1:self._Qg.iN + 1] # Reactive generation in p.u.
# Polynomial cost of P and Q.
xx = r_[p_gen, q_gen] * self._base_mva
if len(self._ipol) > 0:
f = sum([g.total_cost(xx[i]) for i,g in enumerate(self._gn)])
else:
f = 0
# Piecewise linear cost of P and Q.
if self._ny:
y = self.om.get_var("y")
self._ccost = csr_matrix((ones(self._ny),
(range(y.i1, y.iN + 1), zeros(self._ny))),
shape=(self._nxyz, 1)).T
f = f + self._ccost * x
else:
self._ccost = zeros((1, self._nxyz))
# TODO: Generalised cost term.
return f
def _df(self, x, user_data=None):
""" Evaluates the cost gradient.
"""
p_gen = x[self._Pg.i1:self._Pg.iN + 1] # Active generation in p.u.
q_gen = x[self._Qg.i1:self._Qg.iN + 1] # Reactive generation in p.u.
# Polynomial cost of P and Q.
xx = r_[p_gen, q_gen] * self._base_mva
iPg = range(self._Pg.i1, self._Pg.iN + 1)
iQg = range(self._Qg.i1, self._Qg.iN + 1)
# Polynomial cost of P and Q.
df_dPgQg = zeros((2 * self._ng, 1)) # w.r.t p.u. Pg and Qg
# df_dPgQg[ipol] = matrix([g.poly_cost(xx[i], 1) for g in gpol])
# for i, g in enumerate(gn):
# der = polyder(list(g.p_cost))
# df_dPgQg[i] = polyval(der, xx[i]) * base_mva
for i in self._ipol:
p_cost = list(self._gn[i].p_cost)
df_dPgQg[i] = \
self._base_mva * polyval(polyder(p_cost), xx[i])
df = zeros((self._nxyz, 1))
df[iPg] = df_dPgQg[:self._ng]
df[iQg] = df_dPgQg[self._ng:self._ng + self._ng]
# Piecewise linear cost of P and Q.
df = df + self._ccost.T
# TODO: Generalised cost term.
return asarray(df).flatten()
def _d2f(self, x):
""" Evaluates the cost Hessian.
"""
d2f_dPg2 = lil_matrix((self._ng, 1)) # w.r.t p.u. Pg
d2f_dQg2 = lil_matrix((self._ng, 1)) # w.r.t p.u. Qg]
for i in self._ipol:
p_cost = list(self._gn[i].p_cost)
d2f_dPg2[i, 0] = polyval(polyder(p_cost, 2),
self._Pg.v0[i] * self._base_mva) * self._base_mva**2
# for i in ipol:
# d2f_dQg2[i] = polyval(polyder(list(gn[i].p_cost), 2),
# Qg.v0[i] * base_mva) * base_mva**2
i = r_[range(self._Pg.i1, self._Pg.iN + 1),
range(self._Qg.i1, self._Qg.iN + 1)]
d2f = csr_matrix((vstack([d2f_dPg2, d2f_dQg2]).toarray().flatten(),
(i, i)), shape=(self._nxyz, self._nxyz))
return d2f
def _gh(self, x):
""" Evaluates the constraint function values.
"""
Pgen = x[self._Pg.i1:self._Pg.iN + 1] # Active generation in p.u.
Qgen = x[self._Qg.i1:self._Qg.iN + 1] # Reactive generation in p.u.
for i, gen in enumerate(self._gn):
gen.p = Pgen[i] * self._base_mva # active generation in MW
gen.q = Qgen[i] * self._base_mva # reactive generation in MVAr
# Rebuild the net complex bus power injection vector in p.u.
Sbus = self.om.case.getSbus(self._bs)
Vang = x[self._Va.i1:self._Va.iN + 1]
Vmag = x[self._Vm.i1:self._Vm.iN + 1]
V = Vmag * exp(1j * Vang)
# Evaluate the power flow equations.
mis = V * conj(self._Ybus * V) - Sbus
# Equality constraints (power flow).
g = r_[mis.real, # active power mismatch for all buses
mis.imag] # reactive power mismatch for all buses
# Inequality constraints (branch flow limits).
# (line constraint is actually on square of limit)
flow_max = array([(l.rate_a / self._base_mva)**2 for l in self._ln])
# FIXME: There must be a more elegant method for this.
for i, v in enumerate(flow_max):
if v == 0.0:
flow_max[i] = Inf
if self.flow_lim == IFLOW:
If = self._Yf * V
It = self._Yt * V
# Branch current limits.
h = r_[(If * conj(If)) - flow_max,
(It * conj(It)) - flow_max]
else:
i_fbus = [e.from_bus._i for e in self._ln]
i_tbus = [e.to_bus._i for e in self._ln]
# Complex power injected at "from" bus (p.u.).
Sf = V[i_fbus] * | conj(self._Yf * V) | numpy.conj |
import numpy as np
import matplotlib.pyplot as plt
import Neurapse
from Neurapse.Synapses import *
from Neurapse.utils.SpikeTrains import *
from Neurapse.Networks import *
from Neurapse.utils.CURRENTS import *
#usage : DRN_Const problem 2 and 3
def DRN_Const_driver(N, exci_frac, connect_frac):
N_exci = int(N*exci_frac)
N_inhi = N - N_exci
# Constructing the network
exci_neuron_id = range(N_exci)
inhi_neuron_id = range(N_exci, N)
Fanout = []
W = []
Tau = []
w0 = 3000
gamma = 0.77 #for problem 3
gamma = 1# for problem 2
for i in exci_neuron_id:
a = []
for z in range(N):
if z!=i:
a.append(z)
tempFL = []
tempWL = []
tempTL = []
for j in range(int(connect_frac*N)):
t = np.random.choice(a)
tempFL.append(t)
tempWL.append(gamma*w0)
tempTL.append( | np.random.uniform(1e-3, 20e-3) | numpy.random.uniform |
#!/usr/bin/env python
"""
Perform the Mann-Whitney U test, the Kolmogorov-Smirnov test, and the Student's
t-test for the following ensembles:
- GPU double precision (reference & control)
- CPU double precision
- GPU single precision
- GPU double precision with additional explicit diffusion
Make sure to compile the cpp files for the Mann-Whitney U test and the
Kolmogorov-Smirnov test first before running this script (see mannwhitneyu.cpp
and kolmogorov_smirnov.cpp).
Copyright (c) 2021 ETH Zurich, <NAME>
MIT License
"""
import numpy as np
import xarray as xr
import pickle
import mannwhitneyu as mwu
import kolmogorov_smirnov as ks
rpert = 'e4' # prefix
n_runs = 50 # total number of runs
n_sel = 100 # how many times we randomly select runs
alpha = 0.05 # significance level
nm = 20 # members per ensemble
u_crit = 127 # nm = 20
t_crit = 2.024 # nm = 20
replace = False # to bootstrap or not to bootstrap
nbins = 100 # Kolmogorov-Smirnov
# Some arrays to make life easier
tests = ['mwu', 'ks', 't']
comparisons = ['c', 'cpu', 'sp', 'diff']
# Variable
variables = ['t_850hPa', 'fi_500hPa', 'u_10m', 't_2m', 'precip', 'asob_t',
'athb_t', 'ps']
path_gpu = '../data/10d_gpu_cpu_sp_diff/gpu_dycore/'
path_cpu = '../data/10d_gpu_cpu_sp_diff/cpu_nodycore/'
path_gpu_sp = '../data/10d_gpu_cpu_sp_diff/gpu_dycore_sp/'
path_gpu_diff = '../data/10d_gpu_cpu_sp_diff/gpu_dycore_diff/'
# Final rejection rates
rej_rates = {}
for comp in comparisons:
rej_rates[comp] = {}
for vname in variables:
rej_rates[comp][vname] = {}
runs_r = {}
runs_c = {}
runs_cpu = {}
runs_sp = {}
runs_diff = {}
# Load data for gpu (reference and control) and cpu
for i in range(n_runs):
i_str_r = str(i).zfill(4)
i_str_c = str(i+n_runs).zfill(4)
fname_r = path_gpu + rpert + '_' + i_str_r + '.nc'
fname_c = path_gpu + rpert + '_' + i_str_c + '.nc'
fname_cpu = path_cpu + rpert + '_' + i_str_r + '.nc'
fname_sp = path_gpu_sp + rpert + '_' + i_str_r + '.nc'
fname_diff = path_gpu_diff + rpert + '_' + i_str_r + '.nc'
runs_r[i] = {}
runs_c[i] = {}
runs_cpu[i] = {}
runs_sp[i] = {}
runs_diff[i] = {}
runs_r[i]['dset'] = xr.open_dataset(fname_r)
runs_c[i]['dset'] = xr.open_dataset(fname_c)
runs_cpu[i]['dset'] = xr.open_dataset(fname_cpu)
runs_sp[i]['dset'] = xr.open_dataset(fname_sp)
runs_diff[i]['dset'] = xr.open_dataset(fname_diff)
# Test for each variable
for vname in variables:
print("----------------------------")
print("Working on " + vname + " ...")
print("----------------------------")
# initialize arrays
nt, ny, nx = runs_r[0]['dset'][vname].shape
values_r = np.zeros((nt, ny, nx, nm))
values_c = np.zeros((nt, ny, nx, nm))
values_cpu = np.zeros((nt, ny, nx, nm))
values_sp = np.zeros((nt, ny, nx, nm))
values_diff = np.zeros((nt, ny, nx, nm))
# For the results
results = {}
for test in tests:
results[test] = {}
for comp in comparisons:
results[test][comp] = np.zeros((n_sel, nt))
# Do test multiple times with random selection of ensemble members
for s in range(n_sel):
if ((s+1) % 10 == 0):
print(str(s+1) + " / " + str(n_sel))
# Pick random samples for comparison
idxs_r = np.random.choice(np.arange(n_runs), nm, replace=replace)
idxs_c = np.random.choice(np.arange(n_runs), nm, replace=replace)
idxs_cpu = np.random.choice(np.arange(n_runs), nm, replace=replace)
idxs_sp = np.random.choice(np.arange(n_runs), nm, replace=replace)
idxs_diff = np.random.choice(np.arange(n_runs), nm, replace=replace)
# ============================================================
# Mann-Whitney U test
# ============================================================
test = 'mwu'
# Put together arrays
for i in range(nm):
values_r[:,:,:,i] = runs_r[idxs_r[i]]['dset'][vname].values
values_c[:,:,:,i] = runs_c[idxs_c[i]]['dset'][vname].values
values_cpu[:,:,:,i] = runs_cpu[idxs_cpu[i]]['dset'][vname].values
values_sp[:,:,:,i] = runs_sp[idxs_sp[i]]['dset'][vname].values
values_diff[:,:,:,i] = runs_diff[idxs_diff[i]]['dset'][vname].values
# Call test
reject_c = mwu.mwu(values_r, values_c, u_crit)
reject_cpu = mwu.mwu(values_r, values_cpu, u_crit)
reject_sp = mwu.mwu(values_r, values_sp, u_crit)
reject_diff = mwu.mwu(values_r, values_diff, u_crit)
results[test]['c'][s] = np.mean(reject_c, axis=(1,2))
results[test]['cpu'][s] = | np.mean(reject_cpu, axis=(1,2)) | numpy.mean |
from unittest import TestCase
import numpy as np
from bladex import CustomProfile, NacaProfile, ProfileBase
def create_custom_profile():
"""
xup_coordinates, yup_coordinates, xdown_coordinates, ydown_coordinates
"""
xup = | np.linspace(-1.0, 1.0, 5) | numpy.linspace |
import json
import numpy as np
import cv2
from utils.experiments.patches import extract_patches
import time
import sys
import pdb
class Shapes():
def name(self):
return 'shapes'
def __init__(self, opt):
self.WIN_SIZE = opt.WIN_SIZE
self.IGNORE_LABEL = opt.IGNORE_LABEL
self.LABEL_PATH = opt.EXEMPLAR_LABEL_PATH
self.INST_PATH = opt.EXEMPLAR_INST_PATH
self.IMAGE_PATH = opt.EXEMPLAR_IMAGE_PATH
self.TOP_K = opt.TOP_K
self.RES_F = opt.RES_F
self.SHAPE_THRESH = opt.SHAPE_THRESH
self.IS_PARTS = opt.IS_PARTS
self.PARTS_WIN = opt.PARTS_WIN
self.PARTS_SIZE = opt.PARTS_SIZE
self.FIN_SIZE = opt.FIN_SIZE
self.PAT_HEIGHT = opt.PAT_HEIGHT
self.PAT_WIDTH = opt.PAT_WIDTH
self.PAT_NBD = opt.PAT_NBD
self.PAT_LOC = self.get_pat_loc()
# load annotations --
with open(opt.COCO_ANNOTATIONS_PATH) as f:
annotations = json.load(f)
label_data = np.zeros((len(annotations), 6))
for i in range(0, len(annotations)):
label_data[i, 0] = annotations[i]["id"]
label_data[i, 1:4] = annotations[i]["color"]
label_data[i, 4] = annotations[i]["isthing"]
label_data[i, 5] = label_data[i, 1] + \
label_data[i, 2]*256 + \
label_data[i, 3]*65536
self.label_data = label_data
self.label_dict = {}
for annotation in annotations:
self.label_dict[tuple(annotation["color"])
] = np.array([annotation["id"]])
def convert_colors_to_labels_old(self, INPUT_MAP):
semantic_map = np.int32(INPUT_MAP[:, :, 0]) + \
np.int32(INPUT_MAP[:, :, 1])*256 + \
np.int32(INPUT_MAP[:, :, 2])*65536
label_data = self.label_data
#print("Shape", INPUT_MAP.shape)
#print np.unique(INPUT_MAP, axis=1)
unique_points = np.unique(semantic_map)
#print unique_points
LABEL_MAP = np.zeros((np.size(INPUT_MAP, 0), np.size(INPUT_MAP, 1)))
for i in range(0, len(unique_points)):
if(unique_points[i] == self.IGNORE_LABEL):
continue
ith_loc_id = label_data[:, 5] == unique_points[i]
#print ith_loc_id
LABEL_MAP[semantic_map == unique_points[i]
] = label_data[ith_loc_id, 0]
return LABEL_MAP
def convert_colors_to_labels(self, INPUT_MAP):
# Get all unique pixels in input
unique_pixels = np.unique(INPUT_MAP.reshape(-1, 3), axis=0)
# Create a blank matrix with same dimensions
LABEL_MAP = np.zeros((INPUT_MAP.shape[:-1]))
#pdb.set_trace()
for upixel in unique_pixels:
label_of_pixel = self.label_dict.get(
tuple(upixel), np.array([self.IGNORE_LABEL]))
# print("LOP", label_of_pixel)
condition = np.all(INPUT_MAP == upixel, 2)
LABEL_MAP[condition] = label_of_pixel
#pdb.set_trace()
return LABEL_MAP
def get_query_shapes(self, LABEL_MAP, INST_MAP):
instances = INST_MAP[:, :, 0]*10 + \
INST_MAP[:, :, 1]*100 + \
INST_MAP[:, :, 2]*1000
category_list = np.unique(LABEL_MAP)
category_list = category_list[category_list != self.IGNORE_LABEL]
query_shapes = {}
iter_ = 0
#pdb.set_trace()
for n in range(0, len(category_list)):
# for each semantic label map --
nth_label_map = np.int16(LABEL_MAP)
nth_label_map[nth_label_map != category_list[n]] = -1
nth_label_map[nth_label_map == category_list[n]] = 1
nth_label_map[nth_label_map == -1] = 0
# ---------------------------------------------------
# check if this category belongs to things or stuff--
is_thing = self.label_data[self.label_data[:, 0]
== category_list[n], 4]
if(is_thing != 1):
[n_r, n_c] = np.nonzero(nth_label_map)
y1 = np.amin(n_r)
y2 = np.amax(n_r)
x1 = np.amin(n_c)
x2 = np.amax(n_c)
comp_shape = nth_label_map[y1:y2, x1:x2]
comp_context = LABEL_MAP[y1:y2, x1:x2]
ar = np.size(
comp_context, 0)/(float(np.size(comp_context, 1)) + sys.float_info.epsilon)
# -- get the comp-list
query_shapes[iter_] = {}
query_shapes[iter_]['comp_shape'] = comp_shape
query_shapes[iter_]['comp_context'] = comp_context
query_shapes[iter_]['shape_label'] = category_list[n]
query_shapes[iter_]['ar'] = ar
query_shapes[iter_]['bbox'] = [y1, x1, y2, x2]
query_shapes[iter_]['dim'] = [
np.size(nth_label_map, 0), np.size(nth_label_map, 1)]
iter_ = iter_ + 1
else:
nth_inst_map = np.empty_like(instances)
np.copyto(nth_inst_map, instances)
nth_inst_map[nth_inst_map == 0] = -1
nth_inst_map[nth_label_map == 0] = -1
nth_inst_ids = np.unique(nth_inst_map)
nth_inst_ids = nth_inst_ids[nth_inst_ids != -1]
for m in range(0, len(nth_inst_ids)):
mth_inst_map = np.empty_like(nth_inst_map)
np.copyto(mth_inst_map, nth_inst_map)
mth_inst_map[mth_inst_map != nth_inst_ids[m]] = -1
mth_inst_map[mth_inst_map == nth_inst_ids[m]] = 1
mth_inst_map[mth_inst_map == -1] = 0
# --
[m_r, m_c] = np.nonzero(mth_inst_map)
y1 = np.amin(m_r)
y2 = np.amax(m_r)
x1 = np.amin(m_c)
x2 = np.amax(m_c)
comp_shape = mth_inst_map[y1:y2, x1:x2]
comp_context = LABEL_MAP[y1:y2, x1:x2]
ar = np.size(
comp_context, 0)/(float(np.size(comp_context, 1)) + sys.float_info.epsilon)
# -- comp_list data
query_shapes[iter_] = {}
query_shapes[iter_]['comp_shape'] = comp_shape
query_shapes[iter_]['comp_context'] = comp_context
query_shapes[iter_]['shape_label'] = category_list[n]
query_shapes[iter_]['ar'] = ar
query_shapes[iter_]['bbox'] = [y1, x1, y2, x2]
query_shapes[iter_]['dim'] = [
np.size(nth_label_map, 0), np.size(nth_label_map, 1)]
iter_ = iter_ + 1
return query_shapes
def get_exemplar_shapes(self, EXEMPLAR_MATCHES):
exemplar_shapes = {}
iter_ = 0
for i in range(0, len(EXEMPLAR_MATCHES)):
LABEL_MAP = cv2.imread(self.LABEL_PATH + EXEMPLAR_MATCHES[i][0].decode('UTF-8'))
LABEL_MAP = np.int16(LABEL_MAP[:, :, 0])
INST_MAP = np.int32(cv2.imread(
self.INST_PATH + EXEMPLAR_MATCHES[i][0].decode('UTF-8')))
EXEMPLAR_IMAGE = cv2.imread(self.IMAGE_PATH +
(EXEMPLAR_MATCHES[i][0]).decode('UTF-8').replace('.png', '.jpg'))
instances = INST_MAP[:, :, 0]*10 + \
INST_MAP[:, :, 1]*100 + \
INST_MAP[:, :, 2]*1000
category_list = np.unique(LABEL_MAP)
category_list = category_list[category_list != self.IGNORE_LABEL]
for n in range(0, len(category_list)):
# for each semantic label map --
nth_label_map = np.empty_like(LABEL_MAP)
np.copyto(nth_label_map, LABEL_MAP)
nth_label_map[nth_label_map != category_list[n]] = -1
nth_label_map[nth_label_map == category_list[n]] = 1
nth_label_map[nth_label_map == -1] = 0
# ---------------------------------------------------
# check if this category belongs to things or stuff--
is_thing = self.label_data[self.label_data[:, 0]
== category_list[n], 4]
if(is_thing != 1):
[n_r, n_c] = np.nonzero(nth_label_map)
y1 = np.amin(n_r)
y2 = np.amax(n_r)
x1 = np.amin(n_c)
x2 = np.amax(n_c)
comp_shape = nth_label_map[y1:y2, x1:x2]
comp_context = LABEL_MAP[y1:y2, x1:x2]
comp_rgb = np.empty_like(EXEMPLAR_IMAGE[y1:y2, x1:x2, :])
np.copyto(comp_rgb, EXEMPLAR_IMAGE[y1:y2, x1:x2, :])
comp_rgb[:, :, 0] = comp_rgb[:, :, 0] * comp_shape
comp_rgb[:, :, 1] = comp_rgb[:, :, 1] * comp_shape
comp_rgb[:, :, 2] = comp_rgb[:, :, 2] * comp_shape
ar = np.size(
comp_context, 0)/(float(np.size(comp_context, 1)) + sys.float_info.epsilon)
# -- get the comp-list
exemplar_shapes[iter_] = {}
exemplar_shapes[iter_]['comp_shape'] = comp_shape
exemplar_shapes[iter_]['comp_context'] = comp_context
exemplar_shapes[iter_]['comp_rgb'] = comp_rgb
exemplar_shapes[iter_]['org_rgb'] = EXEMPLAR_IMAGE[y1:y2, x1:x2, :]
exemplar_shapes[iter_]['shape_label'] = category_list[n]
exemplar_shapes[iter_]['ar'] = ar
exemplar_shapes[iter_]['bbox'] = [y1, x1, y2, x2]
exemplar_shapes[iter_]['dim'] = [
np.size(nth_label_map, 0), np.size(nth_label_map, 1)]
iter_ = iter_ + 1
else:
nth_inst_map = np.empty_like(instances)
np.copyto(nth_inst_map, instances)
nth_inst_map[nth_inst_map == 0] = -1
nth_inst_map[nth_label_map == 0] = -1
nth_inst_ids = np.unique(nth_inst_map)
nth_inst_ids = nth_inst_ids[nth_inst_ids != -1]
for m in range(0, len(nth_inst_ids)):
mth_inst_map = np.empty_like(nth_inst_map)
np.copyto(mth_inst_map, nth_inst_map)
mth_inst_map[mth_inst_map != nth_inst_ids[m]] = -1
mth_inst_map[mth_inst_map == nth_inst_ids[m]] = 1
mth_inst_map[mth_inst_map == -1] = 0
# --
[m_r, m_c] = np.nonzero(mth_inst_map)
y1 = np.amin(m_r)
y2 = np.amax(m_r)
x1 = np.amin(m_c)
x2 = np.amax(m_c)
comp_shape = mth_inst_map[y1:y2, x1:x2]
comp_context = LABEL_MAP[y1:y2, x1:x2]
comp_rgb = np.empty_like(
EXEMPLAR_IMAGE[y1:y2, x1:x2, :])
| np.copyto(comp_rgb, EXEMPLAR_IMAGE[y1:y2, x1:x2, :]) | numpy.copyto |
import torch
from gcn_lib.dense import DilatedKNN2d
from gcn_lib.dense.torch_vertex1d import MLP1dLayer, GraphConv1d, DenseGraphBlock1d, ResGraphBlock1d, PlainGraphBlock1d
from torch.nn import Sequential as Seq
import numpy as np
class DeepGCN(torch.nn.Module):
def __init__(self, config, lbl_values, ign_lbls):
super(DeepGCN, self).__init__()
in_channels = config.in_channels
n_classes = config.n_classes
channels = config.n_filters
block = config.block
conv = config.conv
k = config.k
self.k = k
act = config.act
norm = config.norm
bias = config.bias
stochastic = config.stochastic
epsilon = config.epsilon
dropout = config.dropout
self.n_blocks = config.n_blocks
c_growth = 0
# self.knn = DilatedKNN2d(k, 1, stochastic, epsilon)
self.head = GraphConv1d(in_channels, channels, conv, act, norm, bias, k)
if block.lower() == 'res':
self.backbone = Seq(*[ResGraphBlock1d(channels, conv, act, norm, bias, k)
for _ in range(self.n_blocks - 1)])
elif block.lower() == 'plain':
self.backbone = Seq(*[PlainGraphBlock1d(channels, conv, act, norm, bias, k)
for _ in range(self.n_blocks - 1)])
elif block.lower() == 'dense':
c_growth = channels
self.backbone = Seq(*[DenseGraphBlock1d(channels + i * c_growth, c_growth, conv, act, norm, bias, k)
for i in range(self.n_blocks - 1)])
else:
raise NotImplementedError
fusion_dims = int(channels * self.n_blocks + c_growth * ((1 + self.n_blocks - 1) * (self.n_blocks - 1) / 2))
self.fusion_block = MLP1dLayer([fusion_dims, 1024], act, norm, bias)
self.prediction = Seq(*[MLP1dLayer([fusion_dims+1024, 512], act, norm, bias),
MLP1dLayer([512, 256], act, norm, bias, drop=dropout),
MLP1dLayer([256, n_classes], None, None, bias)])
self.model_init()
# List of valid labels (those not ignored in loss)
self.valid_labels = np.sort([c for c in lbl_values if c not in ign_lbls])
# Choose segmentation loss
if len(config.class_w) > 0:
class_w = torch.from_numpy( | np.array(config.class_w, dtype=np.float32) | numpy.array |
import json
import os
import sys
import tempfile
from collections import namedtuple
from pathlib import Path
import numpy as np
import pandas as pd
import pytest
from morphio.vasculature import Vasculature
from numpy import testing as npt
from pandas import testing as pdt
from vascpy import SectionVasculature
from vascpy import conversion as tested
np.set_printoptions(threshold=sys.maxsize)
from vascpy.exceptions import VasculatureAPIError
from vascpy.point_vasculature import PointGraph
DATAPATH = Path(__file__).parent / "data"
class MockSection:
__slots__ = "id", "type", "points", "diameters", "successors", "predecessors"
def __init__(self, sid, points, diameters):
self.id = sid
self.type = 1
self.points = points
self.diameters = diameters
self.successors = []
self.predecessors = []
def __str__(self):
return "< {} ps: {} ss: {} >".format(
self.id, [s.id for s in self.predecessors], [s.id for s in self.successors]
)
__repr__ = __str__
def test_sections_to_point_connectivity__one_section():
points = np.random.random((5, 3))
diameters = np.random.random(5)
section = MockSection(0, points, diameters)
r_points, r_diameters, r_edge_properties = tested._sections_to_point_connectivity([section])
npt.assert_allclose(points, r_points)
npt.assert_allclose(diameters, r_diameters)
npt.assert_equal(r_edge_properties[:, tested.ColsEdges.BEG_NODE], [0, 1, 2, 3])
npt.assert_equal(r_edge_properties[:, tested.ColsEdges.END_NODE], [1, 2, 3, 4])
npt.assert_equal(r_edge_properties[:, tested.ColsEdges.SECTION_ID], [0, 0, 0, 0])
npt.assert_equal(r_edge_properties[:, tested.ColsEdges.SEGMENT_ID], [0, 1, 2, 3])
npt.assert_equal(r_edge_properties[:, tested.ColsEdges.EDGE_TYPE], [1, 1, 1, 1])
def test_sections_to_point_connectivity__bifurcation():
points1 = np.array([[0.0, 0.0, 0.0], [1.0, 1.0, 1.0], [2.0, 2.0, 2.0]])
diameters1 = np.array([0.0, 1.0, 2.0])
points2 = np.array([[2.0, 2.0, 2.0], [3.0, 3.0, 3.0], [4.0, 4.0, 4.0]])
diameters2 = np.array([2.0, 3.0, 4.0])
points3 = np.array([[2.0, 2.0, 2.0], [5.0, 5.0, 5.0], [6.0, 6.0, 6.0]])
diameters3 = np.array([2.0, 5.0, 6.0])
s1 = MockSection(0, points1, diameters1)
s2 = MockSection(1, points2, diameters2)
s3 = MockSection(2, points3, diameters3)
s1.successors = [s2, s3]
s2.predecessors = [s1]
s3.predecessors = [s1]
sections = [s1, s2, s3]
r_points, r_diameters, r_edge_properties = tested._sections_to_point_connectivity(sections)
npt.assert_allclose(
r_points,
[
[0.0, 0.0, 0.0],
[1.0, 1.0, 1.0],
[2.0, 2.0, 2.0],
[3.0, 3.0, 3.0],
[4.0, 4.0, 4.0],
[5.0, 5.0, 5.0],
[6.0, 6.0, 6.0],
],
)
npt.assert_allclose(r_diameters, [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0])
npt.assert_equal(r_edge_properties[:, tested.ColsEdges.BEG_NODE], [0, 1, 2, 3, 2, 5])
npt.assert_equal(r_edge_properties[:, tested.ColsEdges.END_NODE], [1, 2, 3, 4, 5, 6])
npt.assert_equal(r_edge_properties[:, tested.ColsEdges.SECTION_ID], [0, 0, 1, 1, 2, 2])
npt.assert_equal(r_edge_properties[:, tested.ColsEdges.SEGMENT_ID], [0, 1, 0, 1, 0, 1])
npt.assert_equal(r_edge_properties[:, tested.ColsEdges.EDGE_TYPE], [1, 1, 1, 1, 1, 1])
def test_sections_to_point_connectivity__bifurcation_2():
points1 = np.array([[0.0, 0.0, 0.0], [1.0, 1.0, 1.0], [2.0, 2.0, 2.0]])
diameters1 = np.array([0.0, 1.0, 2.0])
points2 = np.array([[2.0, 2.0, 2.0], [3.0, 3.0, 3.0], [4.0, 4.0, 4.0]])
diameters2 = np.array([2.0, 3.0, 4.0])
points3 = np.array([[2.0, 2.0, 2.0], [5.0, 5.0, 5.0], [6.0, 6.0, 6.0]])
diameters3 = np.array([2.0, 5.0, 6.0])
s1 = MockSection(0, points1, diameters1)
s2 = MockSection(1, points2, diameters2)
s3 = MockSection(2, points3, diameters3)
s1.successors = [s2, s3]
s2.predecessors = [s1]
s3.predecessors = [s1]
sections = [s1, s2, s3]
r_points, r_diameters, r_edge_properties = tested._sections_to_point_connectivity(sections)
npt.assert_allclose(
r_points,
[
[0.0, 0.0, 0.0],
[1.0, 1.0, 1.0],
[2.0, 2.0, 2.0],
[3.0, 3.0, 3.0],
[4.0, 4.0, 4.0],
[5.0, 5.0, 5.0],
[6.0, 6.0, 6.0],
],
)
npt.assert_allclose(r_diameters, [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0])
npt.assert_equal(r_edge_properties[:, tested.ColsEdges.BEG_NODE], [0, 1, 2, 3, 2, 5])
npt.assert_equal(r_edge_properties[:, tested.ColsEdges.END_NODE], [1, 2, 3, 4, 5, 6])
| npt.assert_equal(r_edge_properties[:, tested.ColsEdges.SECTION_ID], [0, 0, 1, 1, 2, 2]) | numpy.testing.assert_equal |
# -*- coding: utf-8 -*-
"""
This file is part of pyCMBS.
(c) 2012- <NAME>
For COPYING and LICENSE details, please refer to the LICENSE file
"""
from unittest import TestCase
import unittest
from nose.tools import assert_raises
import numpy as np
from pycmbs.data import Data
from pycmbs.geostatistic import Geostatistic, Variogram, SphericalVariogram
class TestData(unittest.TestCase):
def setUp(self):
D = Data(None, None)
tmp = np.random.random((55, 20))
D.data = np.ma.array(tmp, mask=tmp!=tmp)
lon = np.arange(-10.,10.) # -10 ... 9
lat = np.arange(-60., 50., 2.) # -60 ... 48
LON, LAT = np.meshgrid(lon, lat)
D.lon = np.ma.array(LON, mask=LON!=LON)
D.lat = np.ma.array(LAT, mask=LAT!=LAT)
self.x = D
def tearDown(self):
pass
def test_invalid_geometry(self):
x = self.x
x.data = np.random.random((5,4,3))
with self.assertRaises(ValueError):
G = Geostatistic(x)
def test_init(self):
with self.assertRaises(ValueError): # missing range bins
G = Geostatistic(self.x)
# 3D is invalid
y = self.x.copy()
y.data = np.random.random((10,20,30))
with self.assertRaises(ValueError): # missing range bins
G = Geostatistic(self.x, lags = np.random.random(10))
y = self.x.copy() # missing 3D
y.data = np.random.random((10,20,30))
with self.assertRaises(ValueError):
G = Geostatistic(self.x)
bins = np.random.random(10)
with self.assertRaises(ValueError):
G = Geostatistic(self.x, lags=bins)
bins = np.arange(10)
G = Geostatistic(self.x, lags=bins)
def test_plot(self):
bins = np.arange(3) / 6.
G = Geostatistic(self.x, lags=bins)
G.set_center_position(0., 0.)
G.plot_semivariogram()
def test_percentiles(self):
bins = np.arange(10)
G = Geostatistic(self.x, lags=bins)
G.set_center_position(5., -20.)
p = [0.05, 0.1, 0.5]
G.plot_percentiles(p, ax=None, logy=False, ref_lags=None)
def test_set_center(self):
bins = np.arange(10)
G = Geostatistic(self.x, lags=bins)
G.set_center_position(5., -20.)
self.assertEqual(G.lon_center, 5.)
self.assertEqual(G.lat_center, -20.)
def test_center_pos(self):
bins = np.arange(10)
G = Geostatistic(self.x, lags=bins)
# forgot to set center
with self.assertRaises(ValueError):
G._get_center_pos()
G.set_center_position(-10., -60.)
i_lat, i_lon = G._get_center_pos()
self.assertEqual(i_lat, 0)
self.assertEqual(i_lon, 0)
G.set_center_position(9., 48.)
i_lat, i_lon = G._get_center_pos()
self.assertEqual(i_lat, 54)
self.assertEqual(i_lon, 19)
G.set_center_position(-10.1, 48.)
i_lat, i_lon = G._get_center_pos()
self.assertEqual(i_lat, 54)
self.assertEqual(i_lon, 0)
def test_get_coordinate_at_distance(self):
bins = np.arange(10)
G = Geostatistic(self.x, lags=bins)
with self.assertRaises(ValueError): # missing center
lon, lat = G.get_coordinates_at_distance(2.5, dist_threshold=1.)
G.set_center_position(5., -20.)
lon, lat = G.get_coordinates_at_distance(2.5, dist_threshold=1.)
def test_variogram_semivariance(self):
V = Variogram()
x = np.random.random(100)
lon = np.random.random(100)*10.-90.
lat = np.random.random(100)*10.-90.
h_km = 20.
dh_km = 2.
# just test if it works; no reference solution yet
g = V._semivariance(x, lon, lat, | np.asarray([h_km]) | numpy.asarray |
import numpy as np
def makeGaussGridByOrder(order):
nAz = 2*(order + 1)
nEl = order + 1
return makeGaussGrid(nAz, nEl + 2)
def makeGaussGrid(resolutionAz, resolutionEl):
az = np.linspace(0, 360, resolutionAz + 1)
el = np.linspace(0, 180, resolutionEl)
# remove last element of azimuth list to avoid 0°/360° ambiguity
az = np.delete(az, resolutionAz)
# remove 0° and 180° from elevation list to avoid multiple north/south poles
el = np.delete(el, [0, resolutionEl - 1])
size = az.size * el.size + 2
grid = | np.zeros(size * 2) | numpy.zeros |
#!/usr/bin/env python
import argparse
import json
import math
import os
import shutil
import xml.etree.ElementTree as ET
import numpy as np
import igibson
from igibson.scenes.igibson_indoor_scene import SCENE_SOURCE
from igibson.utils.assets_utils import (
get_3dfront_scene_path,
get_cubicasa_scene_path,
get_ig_category_path,
get_ig_scene_path,
)
from igibson.utils.utils import parse_config
"""
Script to update all urdfs
for file in ../../igibson/ig_dataset/scenes/*
python scene_converter.py $(basename $file)
"""
config = parse_config(os.path.join(igibson.root_path, "test", "test.yaml"))
missing_models = set(
[
"exercise_equipment",
"curtain",
"garbage_compressor",
"staircase",
"closet",
"ac_engine",
"water_hearter",
"clutter",
"ceiling_lamp",
]
)
def convert_scene(scene_name, scene_source, select_best=False):
if scene_source not in SCENE_SOURCE:
raise ValueError("Unsupported scene source: {}".format(scene_source))
if scene_source == "IG":
scene_dir = get_ig_scene_path(scene_name)
elif scene_source == "CUBICASA":
scene_dir = get_cubicasa_scene_path(scene_name)
else:
scene_dir = get_3dfront_scene_path(scene_name)
scene_file = os.path.join(scene_dir, "urdf", "{}_orig.urdf".format(scene_name))
scene_tree = ET.parse(scene_file)
bbox_dir = os.path.join(scene_dir, "bbox")
os.makedirs(bbox_dir, exist_ok=True)
with open(os.path.join(scene_dir, "misc", "all_objs.json"), "r") as all_objs_file:
all_objs = json.load(all_objs_file)
total = 0
categories = []
for c, obj in enumerate(all_objs):
obj_category = obj["category"].lower()
# print('obj_category:', obj_category)
if obj_category in missing_models:
print("We don't have yet models of ", obj_category)
continue
total += 1
link_name = obj_category + "_" + str(c)
if obj_category not in categories:
categories += [obj_category]
edge_x = obj["edge_x"]
bbox_x = | np.linalg.norm(edge_x) | numpy.linalg.norm |
import pandas as pd
import numpy as np
import logging
import os
import geojson
import math
import itertools
import geopandas as gpd
from geopy.geocoders import Nominatim
from shapely.geometry import Point, Polygon, MultiPolygon, shape
import shapely.ops
from pyproj import Proj
from bs4 import BeautifulSoup
import requests
from abc import ABC, abstractmethod
from .geolocations import *
from .visualizations import *
logging.basicConfig(level=logging.WARNING)
class OpinionNetworkModel(ABC):
""" Abstract base class for network model """
def __init__(self,
probabilities = [.45,.1,.45],
power_law_exponent = 1.5,
openness_to_neighbors = 1.5,
openness_to_influencers = 1.5,
distance_scaling_factor = 1/10,
importance_of_weight = 1.6,
importance_of_distance = 8.5,
include_opinion = True,
include_weight = True,
left_reach = 0.8,
right_reach = 0.8,
threshold = -1
):
"""Returns initialized OpinionNetworkModel.
Inputs:
probabilities: (list) probabilities of each mode; these are the
values "p_0,p_1,p_2" from [1].
power_law_exponent: (float) exponent of power law, must be > 0;
this is "gamma" from [1].
openness_to_neighbors: (float) maximum inter-mode distance that agents
can influence; this is "b" from [1].
openness_to_influencers: (float) distance in opinion space that
mega-influencers can reach; this is "epsilon" from [1].
distance_scaling_factor: (float) Scale distancy by this amount, must
be >0; this is "lambda" from [1].
importance_of_weight: (float) Raise weights to this power, must be > 0;
this is "alpha" from [1].
importance_of_distance: (float) Raise adjusted distance to this power,
must be > 0; this is "delta" from [1].
include_opinion: (boolean) If True, include distance in opinion space
in the probability measure.
include_weight: (boolean) If True, include influencer weight in the
probability measure.
left_reach: (float) this is the proportion of the susceptible population
that the left mega-influencers will actually reach, must be between
0 and 1; this is p_L from [1]
right_reach: (float) this is the proportion of the susceptible population
that the right mega-influencers will actually reach, must be between
0 and 1; this is p_R from [1]
threshold: (int) value below which opinions no longer change.
Outputs:
Fully initialized OpinionNetwork instance.
"""
self.probabilities = probabilities
self.power_law_exponent = power_law_exponent
self.openness_to_neighbors = openness_to_neighbors
self.openness_to_influencers = openness_to_influencers
self.distance_scaling_factor = distance_scaling_factor
self.importance_of_weight = importance_of_weight
self.importance_of_distance = importance_of_distance
self.include_opinion = include_opinion
self.include_weight = include_weight
self.left_reach = left_reach
self.right_reach = right_reach
self.threshold = threshold
self.agent_df = None
self.belief_df = None
self.prob_df = None
self.adjacency_df = None
self.mega_influencer_df = None
self.clustering_coefficient = 0
self.mean_degree = 0
def populate_model(self, num_agents = None, geo_df = None, bounding_box = None, show_plot = False):
""" Fully initialized but untrained OpinionNetworkModel instance.
Input:
num_agents: (int) number of agents to plot.
geo_df: (dataframe) geographic datatframe including county geometry.
bounding_box: (list) list of 4 vertices determining a bounding box
where agents are to be added. If no box is given, agents are added
to a random triangle.
show_plot: (bool) if true then plot is shown.
Output:
OpinionNetworkModel instance.
"""
if bounding_box is None:
agent_df = self.add_random_agents_to_triangle(num_agents = num_agents,
geo_df = geo_df,
show_plot = False)
else:
if geo_df is None:
raise ValueError("If a bounding box is specified, then a "
"geo_df must also be given.")
agent_df = self.add_random_agents_to_triangles(geo_df = geo_df,
bounding_box = bounding_box,
show_plot = False)
logging.info("\n {} agents added.".format(agent_df.shape[0]))
belief_df = self.assign_weights_and_beliefs(agent_df)
logging.info("\n Weights and beliefs assigned.")
prob_df = self.compute_probability_array(belief_df)
adjacency_df = self.compute_adjacency(prob_df)
logging.info("\n Adjacencies computed.")
# Connect mega-influencers
mega_influencer_df = self.connect_mega_influencers(belief_df)
# Compute network statistics.
logging.info("\n Computing network statistics...")
cc, md = self.compute_network_stats(adjacency_df)
logging.info("\n Clustering Coefficient: {}".format(cc))
logging.info("\n Mean Degree: {}".format(md))
self.agent_df = agent_df
self.belief_df = belief_df
self.prob_df = prob_df
self.adjacency_df = adjacency_df
self.mega_influencer_df = mega_influencer_df
self.clustering_coefficient = cc
self.mean_degree = md
if show_plot == True:
self.plot_initial_network()
return None
def plot_initial_network(self):
plot_network(self)
return None
def add_random_agents_to_triangle(self, num_agents, geo_df = None, triangle_object = None,
show_plot = False):
""" Assign N points on a triangle using Poisson point process.
Input:
num_agents: (int) number of agents to add to the triangle. If None,
then agents are added according to density.
geo_df: (dataframe) geographic datatframe including county geometry.
triangle_object: (Polygon) bounded triangular region to be populated.
show_plot: (bool) if true then plot is shown.
Returns:
An num_agents x 2 dataframe of point coordinates.
"""
if triangle_object is None:
# If no triangle is given, initialize triangle with area 1 km^2.
triangle_object = Polygon([[0,0],[1419,0], [1419/2,1419],[0,0]])
# If density is specified, adjust triangle size.
if geo_df is not None:
density = geo_df.loc[0,"density"]
b = 1419 * (num_agents/density) ** (1/2)
triangle_object = Polygon([[0,0],[b,0], [b/2,b],[0,0]])
bnd = list(triangle_object.boundary.coords)
gdf = gpd.GeoDataFrame(geometry = [triangle_object])
# Establish initial CRS
gdf.crs = "EPSG:3857"
# Set CRS to lat/lon
gdf = gdf.to_crs(epsg=4326)
# Extract coordinates
co = list(gdf.loc[0,"geometry"].exterior.coords)
lon, lat = zip(*co)
pa = Proj(
"+proj=aea +lat_1=37.0 +lat_2=41.0 +lat_0=39.0 +lon_0=-106.55")
x, y = pa(lon, lat)
coord_proj = {"type": "Polygon", "coordinates": [zip(x, y)]}
area = shape(coord_proj).area / (10 ** 6) # area in km^2
# Get Vertices
V1 = np.array(bnd[0])
V2 = np.array(bnd[1])
V3 = np.array(bnd[2])
# Sample from uniform distribution on [0,1]
U = np.random.uniform(0,1,num_agents)
V = np.random.uniform(0,1,num_agents)
UU = np.where(U + V > 1, 1-U, U)
VV = np.where(U + V > 1, 1-V, V)
# Shift triangle into origin and and place points.
agents = (UU.reshape(len(UU),-1) * (V2 - V1).reshape(-1,2)) + (
VV.reshape(len(VV),-1) * (V3 - V1).reshape(-1,2))
# Shift points back to original position.
agents = agents + V1.reshape(-1,2)
agent_df = pd.DataFrame(agents, columns = ["x","y"])
if show_plot == True:
plot_agents_on_triangle(triangle_object, agent_df)
return agent_df
def add_random_agents_to_triangles(self, geo_df, bounding_box = None, show_plot = False):
""" Plots county with triangular regions.
Inputs:
geo_df: (dataframe) geographic datatframe including county geometry.
bounding_box: (list) list of 4 vertices determining a bounding box
where agents are to be added. If no box is given, then the
bounding box is taken as the envelope of the county.
show_plot: (bool) if true then plot is shown.
Returns:
Populated triangles in specified county enclosed in the given
bounding box where regions are filled with proper density using a Poisson
point process.
"""
tri_dict = make_triangulation(geo_df)
tri_df = gpd.GeoDataFrame({"geometry":[Polygon(t) for t in tri_dict["geometry"]["coordinates"]]})
# Establish initial CRS
tri_df.crs = "EPSG:3857"
# Set CRS to lat/lon.
tri_df = tri_df.to_crs(epsg=4326)
# Get triangles within bounding box.
if bounding_box is None:
geo_df.crs = "EPSG:3857"
geo_df = geo_df.to_crs(epsg=4326)
sq_df = gpd.GeoDataFrame(geo_df["geometry"])
else:
sq_df = gpd.GeoDataFrame({"geometry":[Polygon(bounding_box)]})
inset = [i for i in tri_df.index if tri_df.loc[i,"geometry"].within(sq_df.loc[0,"geometry"])]
# Load triangle area.
agent_df = pd.DataFrame()
for i in inset:
co = list(tri_df.loc[i,"geometry"].exterior.coords)
lon, lat = zip(*co)
pa = Proj(
"+proj=aea +lat_1=37.0 +lat_2=41.0 +lat_0=39.0 +lon_0=-106.55")
x, y = pa(lon, lat)
coord_proj = {"type": "Polygon", "coordinates": [zip(x, y)]}
area = shape(coord_proj).area / (10 ** 6) # area in km^2
num_agents = int(area * geo_df.loc[0,"density"])
df = pd.DataFrame(columns = ["x","y"])
if num_agents > 0:
df = self.add_random_agents_to_triangle(num_agents,
geo_df = geo_df,
triangle_object = tri_df.loc[i,"geometry"],
show_plot = False)
agent_df = pd.concat([agent_df,df])
agent_df.reset_index(drop = True, inplace = True)
# Plot triangles.
if show_plot == True:
fig, ax = plt.subplots(figsize = (10,10))
tri_df.loc[inset,:].boundary.plot(ax = ax, alpha=1,
linewidth = 3,
edgecolor = COLORS["light_blue"])
ax.scatter(agent_df["x"], agent_df["y"], s = 3)
ax.set_axis_off()
ax.set_aspect(.9)
plt.show()
return agent_df
def assign_weights_and_beliefs(self, agent_df, show_plot = False):
""" Assign weights and beliefs (i.e. modes) accoring to probabilities.
Inputs:
agent_df: (dataframe) xy-coordinates for agents.
show_plot: (bool) if true then plot is shown.
Returns:
Dataframe with xy-coordinates, beliefs, and weights for each point.
"""
belief_df = agent_df.copy()
power_law_exponent = self.power_law_exponent
k = -1/(power_law_exponent)
modes = [i for i in range(len(self.probabilities))]
assert np.sum(np.array(self.probabilities)) == 1, "Probabilities must sum to 1."
belief_df["weight"] = np.random.uniform(0,1,belief_df.shape[0]) ** (k)
belief_df["belief"] = np.random.choice(modes, belief_df.shape[0],
p = self.probabilities)
belief_df["decile"] = pd.qcut(belief_df["weight"], q = 100, labels = [
i for i in range(1,101)])
if show_plot == True:
plot_agents_with_belief_and_weight(belief_df)
return belief_df
def compute_probability_array(self, belief_df):
""" Return dataframe of probability that row n influences column m.
Inputs:
belief_df: (dataframe) xy-coordinats, beliefs and weights of
agents.
Returns:
Dataframe with the probability that agent n influces agent m
in row n column m.
"""
n = belief_df.index.shape[0]
prob_array = np.ones((n,n))
dist_array = np.zeros((n,n))
for i in range(n):
point_i = Point(belief_df.loc[i,"x"],belief_df.loc[i,"y"])
# Get distances from i to each other point.
dist_array[i,:] = [point_i.distance(Point(belief_df.loc[j,"x"],
belief_df.loc[j,"y"])
) for j in belief_df.index]
# Compute the dimensionless distance metric.
diam = dist_array.max().max()
lam = (self.distance_scaling_factor * diam)
delta = -1 * self.importance_of_distance
dist_array = np.where(dist_array == 0,np.nan, dist_array)
dist_array = (1 + (dist_array/lam)) ** delta
prob_array = prob_array * dist_array
# Only allow connections to people close in opinion space.
if self.include_opinion == True:
op_array = | np.zeros((n,n)) | numpy.zeros |
import collections.abc
import os
import numpy as np
import pycuda.driver as cuda
import pycuda.gpuarray as gpuarray
from pycuda.compiler import SourceModule
import pyconrad
import pyconrad.config
from conebeam_projector._utils import divup, ndarray_to_float_tex
_SMALL_VALUE = 1e-12
_ = pyconrad.ClassGetter(
'edu.stanford.rsl.conrad.numerics'
) # type: pyconrad.AutoCompleteConrad
class CudaProjector:
_kernel_backprojection_withvesselmask = None
_module_backprojection = None
_tex_backprojection = None
_kernel_backprojection = None
_kernel_backprojection_withvesselmask = None
_kernel_backprojection_multiplicative = None
_module_forwardprojection = None
_kernel_forwardprojection = None
_tex_forwardprojection = None
def __init__(self):
self.is_configured = False
self._manually_set_normalizer = None
self._init_kernels()
self._num_projections = pyconrad.config.get_geometry().getProjectionStackSize()
self.start_idx = 0
self.forward_projection_stepsize = 1.
self.stop_idx = self._num_projections
self._init_config()
def _init_config(self):
geo = pyconrad.config.get_geometry()
self._voxelSize = (geo.getVoxelSpacingX(),
geo.getVoxelSpacingY(),
geo.getVoxelSpacingZ())
self._volumeSize = (geo.getReconDimensionX(),
geo.getReconDimensionY(),
geo.getReconDimensionZ())
self._origin = (geo.getOriginX(),
geo.getOriginY(),
geo.getOriginZ())
self._volshape = pyconrad.config.get_reco_shape()
self._volumeEdgeMaxPoint = []
for i in range(3):
self._volumeEdgeMaxPoint.append(self._volumeSize[i] -
1. - _SMALL_VALUE)
# self._volumeEdgeMaxPoint.append( self._volumeSize[i] -
# 0.5 - SMALL_VALUE)
self._volumeEdgeMinPoint = []
for i in range(3):
self._volumeEdgeMinPoint.append(-1. + _SMALL_VALUE)
self._projectionMatrices = pyconrad.config.get_projection_matrices()
self._num_projections = geo.getProjectionStackSize()
self._width = geo.getDetectorWidth()
self._height = geo.getDetectorHeight()
self._srcPoint = np.ndarray([3 * self._num_projections], np.float32)
self._invARmatrix = np.ndarray(
[3 * 3 * self._num_projections], np.float32)
for i in range(self._num_projections):
self._computeCanonicalProjectionMatrix(i)
self._inv_AR_matrix_gpu = gpuarray.to_gpu(self._invARmatrix)
self._proj_mats_gpu = gpuarray.to_gpu(self._projectionMatrices)
if self._manually_set_normalizer is None:
self._normalizer = geo.getSourceToAxisDistance(
) * geo.getSourceToDetectorDistance() * np.pi / self._num_projections
else:
self._normalizer = self._manually_set_normalizer
self.is_configured = True
# TODO: property for _manually_set_normalizer
def _init_kernels(self):
if not self._module_backprojection:
with open(os.path.join(os.path.dirname(__file__), 'BackProjectionKernel.cu')) as f:
read_data = f.read()
self._module_backprojection = SourceModule(read_data, options=['-Wno-deprecated-gpu-targets'])
self._tex_backprojection = self._module_backprojection.get_texref(
'tex_sino')
self._kernel_backprojection = self._module_backprojection.get_function(
"backProjectionKernel")
self._kernel_backprojection_withvesselmask = self._module_backprojection.get_function(
"backProjectionKernelWithConstrainingVolume")
self._kernel_backprojection_multiplicative = self._module_backprojection.get_function(
"backprojectMultiplicative")
with open(os.path.join(os.path.dirname(__file__), 'ForwardProjectionKernel.cu')) as f:
read_data = f.read()
self._module_forwardprojection = SourceModule(read_data, options=['-Wno-deprecated-gpu-targets'])
self._kernel_forwardprojection = self._module_forwardprojection.get_function("forwardProjectionKernel")
self._tex_forwardprojection = self._module_forwardprojection.get_texref('gTex3D')
def _getOriginTransform(self):
currOrigin = _.SimpleVector.from_list(self._origin)
centeredOffset = _.SimpleVector.from_list(self._volumeSize)
voxelSpacing = _.SimpleVector.from_list(self._voxelSize)
centeredOffset.subtract(1.)
centeredOffset.multiplyElementWiseBy([voxelSpacing])
centeredOffset.divideBy(-2.)
return _.SimpleOperators.subtract(currOrigin, centeredOffset)
def forward_project_cuda_raybased(self,
vol,
sino_gpu,
use_maximum_intensity_projection=False,
additive=False,
**texture_kwargs):
self._check_config()
assert sino_gpu.ndim == 3
cu_array = None
if isinstance(vol, gpuarray.GPUArray) or (isinstance(vol, np.ndarray) and vol.ndim == 3):
cu_array = ndarray_to_float_tex(
self._tex_forwardprojection, vol, **texture_kwargs)
block = (32, 8, 1)
grid = (int(divup(sino_gpu.shape[2], block[0])),
int(divup(sino_gpu.shape[1], block[1])), 1)
for t in range(sino_gpu.shape[0]):
if isinstance(vol, list) or (isinstance(vol, np.ndarray) and vol.ndim == 4):
cu_array = ndarray_to_float_tex(
self._tex_forwardprojection, vol[t], **texture_kwargs)
assert vol[t].dtype == np.float32
elif isinstance(vol, collections.abc.Callable):
cu_array = ndarray_to_float_tex(
self._tex_forwardprojection, vol(t), **texture_kwargs)
assert vol(t).dtype == np.float32
elif isinstance(vol, gpuarray.GPUArray) or (isinstance(vol, np.ndarray) and vol.ndim == 3):
assert vol.dtype == np.float32
else:
raise TypeError('!')
assert sino_gpu.dtype == np.float32
self._kernel_forwardprojection(
sino_gpu[t],
np.int32(sino_gpu.shape[2]),
np.int32(sino_gpu.shape[1]),
np.float32(self.forward_projection_stepsize),
np.float32(self._voxelSize[0]),
np.float32(self._voxelSize[1]),
np.float32(self._voxelSize[2]),
np.float32(self._volumeEdgeMinPoint[0]),
np.float32(self._volumeEdgeMinPoint[1]),
np.float32(self._volumeEdgeMinPoint[2]),
np.float32(self._volumeEdgeMaxPoint[0]),
np.float32(self._volumeEdgeMaxPoint[1]),
np.float32(self._volumeEdgeMaxPoint[2]),
np.float32(self._srcPoint[3 * t + 0]),
np.float32(self._srcPoint[3 * t + 1]),
np.float32(self._srcPoint[3 * t + 2]),
self._inv_AR_matrix_gpu,
np.int32(t),
np.int32(use_maximum_intensity_projection),
np.int32(additive),
grid=grid, block=block
)
cu_array.free()
def forward_project_cuda_idx(self,
vol,
sino_gpu,
idx,
use_maximum_intensity_projection=False,
additive=False,
**texture_kwargs):
# self._check_config()
assert idx >= 0 and idx < self._num_projections, "Invalid projection index"
assert sino_gpu.ndim == 2
assert sino_gpu.size == sino_gpu.shape[1] * sino_gpu.shape[0]
assert sino_gpu.dtype == np.float32
block = (32, 8, 1)
grid = (int(divup(sino_gpu.shape[1], block[0])),
int(divup(sino_gpu.shape[0], block[1])), 1)
if isinstance(vol, list) or (isinstance(vol, np.ndarray) and vol.ndim == 4):
ndarray_to_float_tex(self._tex_forwardprojection, vol[idx], **texture_kwargs)
elif isinstance(vol, collections.Callable):
ndarray_to_float_tex(self._tex_forwardprojection, vol(idx), **texture_kwargs)
elif isinstance(vol, gpuarray.GPUArray) or (isinstance(vol, np.ndarray) and vol.ndim == 3):
ndarray_to_float_tex(self._tex_forwardprojection, vol, **texture_kwargs)
else:
raise TypeError('!')
self._kernel_forwardprojection(
sino_gpu,
np.int32(sino_gpu.shape[1]),
np.int32(sino_gpu.shape[0]),
np.float32(self.forward_projection_stepsize), # step size
np.float32(self._voxelSize[0]),
np.float32(self._voxelSize[1]),
np.float32(self._voxelSize[2]),
np.float32(self._volumeEdgeMinPoint[0]),
np.float32(self._volumeEdgeMinPoint[1]),
np.float32(self._volumeEdgeMinPoint[2]),
np.float32(self._volumeEdgeMaxPoint[0]),
np.float32(self._volumeEdgeMaxPoint[1]),
np.float32(self._volumeEdgeMaxPoint[2]),
np.float32(self._srcPoint[3 * idx + 0]),
np.float32(self._srcPoint[3 * idx + 1]),
np.float32(self._srcPoint[3 * idx + 2]),
self._inv_AR_matrix_gpu,
np.int32(idx),
np.int32(use_maximum_intensity_projection),
np.int32(additive),
grid=grid, block=block
)
def _computeCanonicalProjectionMatrix(self, projIdx):
geo = pyconrad.config.get_geometry()
proj = geo.getProjectionMatrices()[projIdx]
self._invVoxelScale = _.SimpleMatrix(3, 3)
self._invVoxelScale.setElementValue(0, 0, 1.0 / self._voxelSize[0])
self._invVoxelScale.setElementValue(1, 1, 1.0 / self._voxelSize[1])
self._invVoxelScale.setElementValue(2, 2, 1.0 / self._voxelSize[2])
invARmatrixMat = proj.getRTKinv()
invAR = _.SimpleOperators.multiplyMatrixProd(
self._invVoxelScale, invARmatrixMat)
counter = 3 * 3 * projIdx
for r in range(3):
for c in range(3):
self._invARmatrix[counter] = invAR.getElement(r, c)
counter += 1
originShift = self._getOriginTransform()
srcPtW = proj.computeCameraCenter().negated()
self._srcPoint[3 * projIdx + 0] = -(-0.5 * (self._volumeSize[0] - 1.0) + originShift.getElement(
0) * self._invVoxelScale.getElement(0, 0) + self._invVoxelScale.getElement(0, 0) * srcPtW.getElement(0))
self._srcPoint[3 * projIdx + 1] = -(-0.5 * (self._volumeSize[1] - 1.0) + originShift.getElement(
1) * self._invVoxelScale.getElement(1, 1) + self._invVoxelScale.getElement(1, 1) * srcPtW.getElement(1))
self._srcPoint[3 * projIdx + 2] = -(-0.5 * (self._volumeSize[2] - 1.0) + originShift.getElement(
2) * self._invVoxelScale.getElement(2, 2) + self._invVoxelScale.getElement(2, 2) * srcPtW.getElement(2))
def backProjectPixelDrivenCudaIdx(self,
sino_gpu: gpuarray.GPUArray,
vol_gpu: gpuarray.GPUArray,
projIdx,
constraining_vol=None,
multiplicative=False,
**texture_kwargs):
# self._check_config()
assert projIdx >= 0 and projIdx < self._num_projections, "Invalid projection index"
assert sino_gpu.ndim == 2
assert vol_gpu.shape == self._volshape
assert sino_gpu.dtype == np.float32
assert vol_gpu.dtype == np.float32
if constraining_vol:
assert isinstance(constraining_vol, gpuarray.GPUArray)
cu_array = ndarray_to_float_tex(self._tex_backprojection, sino_gpu, **texture_kwargs)
block = (32, 8, 1)
grid = (int(divup(vol_gpu.shape[2], block[0])),
int(divup(vol_gpu.shape[1], block[1])), 1)
if constraining_vol:
if multiplicative:
self._kernel_backprojection_multiplicative(vol_gpu.gpudata,
self._proj_mats_gpu,
constraining_vol,
np.int32(projIdx),
np.int32(
self._volshape[2]),
np.int32(
self._volshape[1]),
np.int32(
self._volshape[0]),
np.float32(
-self._origin[0]),
np.float32(
-self._origin[1]),
np.float32(
-self._origin[2]),
np.float32(
self._voxelSize[0]),
np.float32(
self._voxelSize[1]),
np.float32(
self._voxelSize[2]),
np.float32(
self._normalizer),
grid=grid, block=block
)
else:
self._kernel_backprojection_withvesselmask(vol_gpu.gpudata,
self._proj_mats_gpu,
constraining_vol,
np.int32(projIdx),
np.int32(
self._volshape[2]),
np.int32(
self._volshape[1]),
np.int32(
self._volshape[0]),
np.float32(
-self._origin[0]),
np.float32(
-self._origin[1]),
np.float32(
-self._origin[2]),
np.float32(
self._voxelSize[0]),
np.float32(
self._voxelSize[1]),
np.float32(
self._voxelSize[2]),
np.float32(
self._normalizer),
grid=grid, block=block
)
else:
self._kernel_backprojection(vol_gpu.gpudata,
self._proj_mats_gpu,
np.int32(projIdx),
np.int32(self._volshape[2]),
np.int32(self._volshape[1]),
np.int32(self._volshape[0]),
np.float32(-self._origin[0]),
np.float32(-self._origin[1]),
np.float32(-self._origin[2]),
np.float32(self._voxelSize[0]),
np.float32(self._voxelSize[1]),
np.float32(self._voxelSize[2]),
np.float32(self._normalizer),
grid=grid, block=block
)
cu_array.free()
def backProjectPixelDrivenCuda(self,
sino: np.ndarray,
vol=None,
multiplicative=False,
static_vol_gpu=None,
**texture_kwargs):
assert sino.dtype == np.float32
# self._check_config()
if not vol:
vol = np.zeros(self._volshape, np.float32)
if isinstance(vol, gpuarray.GPUArray):
vol_gpu = vol
assert vol_gpu.dtype == np.float32
else:
vol_gpu = cuda.mem_alloc(vol.nbytes)
if isinstance(vol, np.ndarray) and vol.ndim == 3:
cuda.memcpy_htod(vol_gpu, vol)
for t in range(self.start_idx, self.stop_idx):
if isinstance(vol, list) or vol.ndim == 4:
cuda.memcpy_htod(vol_gpu, vol[t])
cu_array = ndarray_to_float_tex(self._tex_backprojection, sino[t], **texture_kwargs)
block = (32, 8, 1)
grid = (int(divup(self._volshape[2], block[0])),
int(divup(self._volshape[1], block[1])), 1)
if multiplicative:
self._kernel_backprojection_multiplicative(vol_gpu,
self._proj_mats_gpu,
static_vol_gpu,
| np.int32(t) | numpy.int32 |
import numpy as np
import pytest
import aesara.tensor as aet
from aesara import config, shared
from aesara.compile.function import function
from aesara.compile.mode import Mode
from aesara.graph.basic import Constant
from aesara.graph.fg import FunctionGraph
from aesara.graph.opt import EquilibriumOptimizer
from aesara.graph.optdb import OptimizationQuery
from aesara.tensor.elemwise import DimShuffle
from aesara.tensor.random.basic import (
dirichlet,
multivariate_normal,
normal,
poisson,
uniform,
)
from aesara.tensor.random.op import RandomVariable
from aesara.tensor.random.opt import (
local_dimshuffle_rv_lift,
local_rv_size_lift,
local_subtensor_rv_lift,
)
from aesara.tensor.subtensor import AdvancedSubtensor, AdvancedSubtensor1, Subtensor
from aesara.tensor.type import iscalar, vector
no_mode = Mode("py", OptimizationQuery(include=[], exclude=[]))
def apply_local_opt_to_rv(opt, op_fn, dist_op, dist_params, size, rng):
dist_params_aet = []
for p in dist_params:
p_aet = aet.as_tensor(p).type()
p_aet.tag.test_value = p
dist_params_aet.append(p_aet)
size_aet = []
for s in size:
s_aet = iscalar()
s_aet.tag.test_value = s
size_aet.append(s_aet)
dist_st = op_fn(dist_op(*dist_params_aet, size=size_aet, rng=rng))
f_inputs = [
p for p in dist_params_aet + size_aet if not isinstance(p, (slice, Constant))
]
mode = Mode("py", EquilibriumOptimizer([opt], max_use_ratio=100))
f_opt = function(
f_inputs,
dist_st,
mode=mode,
)
(new_out,) = f_opt.maker.fgraph.outputs
return new_out, f_inputs, dist_st, f_opt
def test_inplace_optimization():
out = normal(0, 1)
out.owner.inputs[0].default_update = out.owner.outputs[0]
assert out.owner.op.inplace is False
f = function(
[],
out,
mode="FAST_RUN",
)
(new_out, new_rng) = f.maker.fgraph.outputs
assert new_out.type == out.type
assert isinstance(new_out.owner.op, type(out.owner.op))
assert new_out.owner.op.inplace is True
assert all(
np.array_equal(a.data, b.data)
for a, b in zip(new_out.owner.inputs[1:], out.owner.inputs[1:])
)
@config.change_flags(compute_test_value="raise")
@pytest.mark.parametrize(
"dist_op, dist_params, size",
[
(
normal,
[
np.array(1.0, dtype=config.floatX),
np.array(5.0, dtype=config.floatX),
],
[],
),
(
normal,
[
np.array([0.0, 1.0], dtype=config.floatX),
np.array(5.0, dtype=config.floatX),
],
[],
),
(
normal,
[
np.array([0.0, 1.0], dtype=config.floatX),
np.array(5.0, dtype=config.floatX),
],
[3, 2],
),
(
multivariate_normal,
[
np.array([[0], [10], [100]], dtype=config.floatX),
np.diag(np.array([1e-6], dtype=config.floatX)),
],
[2, 3],
),
(
dirichlet,
[np.array([[100, 1, 1], [1, 100, 1], [1, 1, 100]], dtype=config.floatX)],
[2, 3],
),
],
)
def test_local_rv_size_lift(dist_op, dist_params, size):
rng = shared(np.random.RandomState(1233532), borrow=False)
new_out, f_inputs, dist_st, f_opt = apply_local_opt_to_rv(
local_rv_size_lift,
lambda rv: rv,
dist_op,
dist_params,
size,
rng,
)
assert aet.get_vector_length(new_out.owner.inputs[1]) == 0
@pytest.mark.parametrize(
"ds_order, lifted, dist_op, dist_params, size, rtol",
[
(
("x",),
True,
normal,
(
np.array(-10.0, dtype=np.float64),
np.array(1e-6, dtype=np.float64),
),
(),
1e-7,
),
(
("x", "x", "x"),
True,
normal,
(
np.array(-10.0, dtype=np.float64),
np.array(1e-6, dtype=np.float64),
),
(),
1e-7,
),
(
(1, 0, 2),
True,
normal,
(
np.arange(2 * 2 * 2).reshape((2, 2, 2)).astype(config.floatX),
np.array(1e-6).astype(config.floatX),
),
(),
1e-3,
),
(
(0, 1, 2),
True,
normal,
(np.array(0).astype(config.floatX), np.array(1e-6).astype(config.floatX)),
(2, 1, 2),
1e-3,
),
(
(0, 2, 1),
True,
normal,
(np.array(0).astype(config.floatX), np.array(1e-6).astype(config.floatX)),
(2, 1, 2),
1e-3,
),
(
(1, 0, 2),
True,
normal,
(np.array(0).astype(config.floatX), np.array(1e-6).astype(config.floatX)),
(2, 1, 2),
1e-3,
),
(
(0, 2, 1),
True,
normal,
(
np.array([[-1, 20], [300, -4000]], dtype=config.floatX),
np.array([[1e-6, 2e-6]], dtype=config.floatX),
),
(3, 2, 2),
1e-3,
),
(
("x", 0, 2, 1, "x"),
True,
normal,
(
np.array([[-1, 20], [300, -4000]], dtype=config.floatX),
np.array([[1e-6, 2e-6]], dtype=config.floatX),
),
(3, 2, 2),
1e-3,
),
(
("x", 0, "x", 2, "x", 1, "x"),
True,
normal,
(
np.array([[-1, 20], [300, -4000]], dtype=config.floatX),
np.array([[1e-6, 2e-6]], dtype=config.floatX),
),
(3, 2, 2),
1e-3,
),
(
("x", 0, 2, 1, "x"),
True,
normal,
(
np.array([[-1, 20], [300, -4000]], dtype=config.floatX),
np.array([[1e-6, 2e-6]], dtype=config.floatX),
),
(3, 2, 2),
1e-3,
),
(
("x", 1, 0, 2, "x"),
False,
normal,
(
np.array([[-1, 20], [300, -4000]], dtype=config.floatX),
| np.array([[1e-6, 2e-6]], dtype=config.floatX) | numpy.array |
#
# lines.py
#
# purpose: Reproduce LineCurvature2D.m and LineNormals2D.m
# author: <NAME>
# e-mail: <EMAIL>
# web: http://ocefpaf.tiddlyspot.com/
# created: 17-Jul-2012
# modified: Mon 02 Mar 2015 10:07:06 AM BRT
#
# obs:
#
import numpy as np
def LineNormals2D(Vertices, Lines):
r"""This function calculates the normals, of the line points using the
neighbouring points of each contour point, and forward an backward
differences on the end points.
N = LineNormals2D(V, L)
inputs,
V : List of points/vertices 2 x M
(optional)
Lines : A N x 2 list of line pieces, by indices of the vertices
(if not set assume Lines=[1 2; 2 3 ; ... ; M-1 M])
outputs,
N : The normals of the Vertices 2 x M
Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> data = np.load('testdata.npz')
>>> Lines, Vertices = data['Lines'], data['Vertices']
>>> N = LineNormals2D(Vertices, Lines)
>>> fig, ax = plt.subplots(nrows=1, ncols=1)
>>> _ = ax.plot(np.c_[Vertices[:, 0], Vertices[:,0 ] + 10 * N[:, 0]].T,
... np.c_[Vertices[:, 1], Vertices[:, 1] + 10 * N[:, 1]].T)
Function based on LineNormals2D.m written by
D.Kroon University of Twente (August 2011)
"""
eps = np.spacing(1)
if isinstance(Lines, np.ndarray):
pass
elif not Lines:
Lines = np.c_[np.arange(1, Vertices.shape[0]),
np.arange(2, Vertices.shape[0] + 1)]
else:
print("Lines is passed but not recognized.")
# Calculate tangent vectors.
DT = Vertices[Lines[:, 0] - 1, :] - Vertices[Lines[:, 1] - 1, :]
# Make influence of tangent vector 1/Distance (Weighted Central
# Differences. Points which are closer give a more accurate estimate of
# the normal).
LL = np.sqrt(DT[:, 0] ** 2 + DT[:, 1] ** 2)
DT[:, 0] = DT[:, 0] / np.maximum(LL ** 2, eps)
DT[:, 1] = DT[:, 1] / np.maximum(LL ** 2, eps)
D1 = np.zeros_like(Vertices)
D2 = np.zeros_like(Vertices)
D1[Lines[:, 0] - 1, :] = DT
D2[Lines[:, 1] - 1, :] = DT
D = D1 + D2
# Normalize the normal.
LL = np.sqrt(D[:, 0] ** 2 + D[:, 1] ** 2)
N = np.zeros_like(D)
N[:, 0] = -D[:, 1] / LL
N[:, 1] = D[:, 0] / LL
return N
def LineCurvature2D(Vertices, Lines=None):
r"""This function calculates the curvature of a 2D line. It first fits
polygons to the points. Then calculates the analytical curvature from
the polygons.
k = LineCurvature2D(Vertices,Lines)
inputs,
Vertices : A M x 2 list of line points.
(optional)
Lines : A N x 2 list of line pieces, by indices of the vertices
(if not set assume Lines=[1 2; 2 3 ; ... ; M-1 M])
outputs,
k : M x 1 Curvature values
Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> data = np.load('testdata.npz', squeeze_me=True)
>>> Lines, Vertices = data['Lines'], data['Vertices']
>>> k = LineCurvature2D(Vertices, Lines)
>>> N = LineNormals2D(Vertices, Lines)
>>> k = k * 100
>>> fig, ax = plt.subplots(nrows=1, ncols=1)
>>> _ = ax.plot(np.c_[Vertices[:, 0], Vertices[:, 0] + k * N[:, 0]].T,
... np.c_[Vertices[:, 1], Vertices[:, 1] + k * N[:, 1]].T, 'g')
>>> _ = ax.plot(np.c_[Vertices[Lines[:, 0] - 1, 0],
... Vertices[Lines[:, 1] - 1, 0]].T,
... np.c_[Vertices[Lines[:, 0] - 1, 1],
... Vertices[Lines[:, 1] - 1, 1]].T, 'b')
>>> _ = ax.plot(Vertices[:, 0], Vertices[:, 1], 'r.')
Function based on LineCurvature2D.m written by
<NAME> of Twente (August 2011)
"""
# If no line-indices, assume a x[0] connected with x[1], x[2] with x[3].
if isinstance(Lines, np.ndarray):
pass
elif not Lines:
Lines = np.c_[np.arange(1, Vertices.shape[0]),
np.arange(2, Vertices.shape[0] + 1)]
else:
print("Lines is passed but not recognized.")
# Get left and right neighbor of each points.
Na = np.zeros(Vertices.shape[0], dtype=np.int)
Nb = np.zeros_like(Na)
# As int because we use it to index an array...
Na[Lines[:, 0] - 1] = Lines[:, 1]
Nb[Lines[:, 1] - 1] = Lines[:, 0]
# Check for end of line points, without a left or right neighbor.
checkNa = Na == 0
checkNb = Nb == 0
Naa, Nbb = Na, Nb
Naa[checkNa] = np.where(checkNa)[0]
Nbb[checkNb] = np.where(checkNb)[0]
# If no left neighbor use two right neighbors, and the same for right.
Na[checkNa] = Nbb[Nbb[checkNa]]
Nb[checkNb] = Naa[Naa[checkNb]]
# ... Also, I remove `1` to get python indexing correctly.
Na -= 1
Nb -= 1
# Correct for sampling differences.
Ta = -np.sqrt(np.sum((Vertices - Vertices[Na, :]) ** 2, axis=1))
Tb = np.sqrt(np.sum((Vertices - Vertices[Nb, :]) ** 2, axis=1))
# If no left neighbor use two right neighbors, and the same for right.
Ta[checkNa] = -Ta[checkNa]
Tb[checkNb] = -Tb[checkNb]
x = np.c_[Vertices[Na, 0], Vertices[:, 0], Vertices[Nb, 0]]
y = np.c_[Vertices[Na, 1], Vertices[:, 1], Vertices[Nb, 1]]
M = np.c_[np.ones_like(Tb),
-Ta,
Ta ** 2,
np.ones_like(Tb),
np.zeros_like(Tb),
np.zeros_like(Tb),
np.ones_like(Tb),
-Tb,
Tb ** 2]
invM = inverse3(M)
a = | np.zeros_like(x) | numpy.zeros_like |
# -*- coding: utf-8 -*-
import numpy as np
import math
# Import from relative path
try:
from .matrix import NUM_NODES, IDICT, BODY_NAMES
from . import construction as cons
# Import from absolute path
# These codes are for debugging
except ImportError:
from jos3.matrix import NUM_NODES, IDICT, BODY_NAMES
from jos3 import construction as cons
_BSAst = np.array([
0.110, 0.029, 0.175, 0.161, 0.221,
0.096, 0.063, 0.050, 0.096, 0.063, 0.050,
0.209, 0.112, 0.056, 0.209, 0.112, 0.056,])
def conv_coef(posture="standing", va=0.1, ta=28.8, tsk=34.0,):
"""
Calculate convective heat transfer coefficient (hc) [W/K.m2]
Parameters
----------
posture : str, optional
Select posture from standing, sitting or lying.
The default is "standing".
va : float or iter, optional
Air velocity [m/s]. If iter is input, its length should be 17.
The default is 0.1.
ta : float or iter, optional
Air temperature [oC]. If iter is input, its length should be 17.
The default is 28.8.
tsk : float or iter, optional
Skin temperature [oC]. If iter is input, its length should be 17.
The default is 34.0.
Returns
-------
hc : numpy.ndarray
Convective heat transfer coefficient (hc) [W/K.m2].
"""
# Natural convection
if posture.lower() == "standing":
# Ichihara et al., 1997, https://doi.org/10.3130/aija.62.45_5
hc_natural = np.array([
4.48, 4.48, 2.97, 2.91, 2.85,
3.61, 3.55, 3.67, 3.61, 3.55, 3.67,
2.80, 2.04, 2.04, 2.80, 2.04, 2.04,])
elif posture.lower() in ["sitting", "sedentary"]:
# Ichihara et al., 1997, https://doi.org/10.3130/aija.62.45_5
hc_natural = np.array([
4.75, 4.75, 3.12, 2.48, 1.84,
3.76, 3.62, 2.06, 3.76, 3.62, 2.06,
2.98, 2.98, 2.62, 2.98, 2.98, 2.62,])
elif posture.lower() in ["lying", "supine"]:
# Kurazumi et al., 2008, https://doi.org/10.20718/jjpa.13.1_17
# The values are applied under cold environment.
hc_a = np.array([
1.105, 1.105, 1.211, 1.211, 1.211,
0.913, 2.081, 2.178, 0.913, 2.081, 2.178,
0.945, 0.385, 0.200, 0.945, 0.385, 0.200,])
hc_b = np.array([
0.345, 0.345, 0.046, 0.046, 0.046,
0.373, 0.850, 0.297, 0.373, 0.850, 0.297,
0.447, 0.580, 0.966, 0.447, 0.580, 0.966,])
hc_natural = hc_a * (abs(ta - tsk) ** hc_b)
# Forced convection
# Ichihara et al., 1997, https://doi.org/10.3130/aija.62.45_5
hc_a = np.array([
15.0, 15.0, 11.0, 17.0, 13.0,
17.0, 17.0, 20.0, 17.0, 17.0, 20.0,
14.0, 15.8, 15.1, 14.0, 15.8, 15.1,])
hc_b = np.array([
0.62, 0.62, 0.67, 0.49, 0.60,
0.59, 0.61, 0.60, 0.59, 0.61, 0.60,
0.61, 0.74, 0.62, 0.61, 0.74, 0.62,])
hc_forced = hc_a * (va ** hc_b)
# Select natural or forced hc.
# If local va is under 0.2 m/s, the hc valuse is natural.
hc = np.where(va<0.2, hc_natural, hc_forced) # hc [W/K.m2)]
return hc
def rad_coef(posture="standing"):
"""
Calculate radiative heat transfer coefficient (hr) [W/K.m2]
Parameters
----------
posture : str, optional
Select posture from standing, sitting or lying.
The default is "standing".
Returns
-------
hc : numpy.ndarray
Radiative heat transfer coefficient (hr) [W/K.m2].
"""
if posture.lower() == "standing":
# Ichihara et al., 1997, https://doi.org/10.3130/aija.62.45_5
hr = np.array([
4.89, 4.89, 4.32, 4.09, 4.32,
4.55, 4.43, 4.21, 4.55, 4.43, 4.21,
4.77, 5.34, 6.14, 4.77, 5.34, 6.14,])
elif posture.lower() in ["sitting", "sedentary"]:
# Ichihara et al., 1997, https://doi.org/10.3130/aija.62.45_5
hr = np.array([
4.96, 4.96, 3.99, 4.64, 4.21,
4.96, 4.21, 4.74, 4.96, 4.21, 4.74,
4.10, 4.74, 6.36, 4.10, 4.74, 6.36,])
elif posture.lower() in ["lying", "supine"]:
# Kurazumi et al., 2008, https://doi.org/10.20718/jjpa.13.1_17
hr = np.array([
5.475, 5.475, 3.463, 3.463, 3.463,
4.249, 4.835, 4.119, 4.249, 4.835, 4.119,
4.440, 5.547, 6.085, 4.440, 5.547, 6.085,])
return hr
def fixed_hc(hc, va):
"""
Fixes hc values to fit tow-node-model's values.
"""
mean_hc = np.average(hc, weights=_BSAst)
mean_va = np.average(va, weights=_BSAst)
mean_hc_whole = max(3, 8.600001*(mean_va**0.53))
_fixed_hc = hc * mean_hc_whole/mean_hc
return _fixed_hc
def fixed_hr(hr):
"""
Fixes hr values to fit tow-node-model's values.
"""
mean_hr = np.average(hr, weights=_BSAst)
_fixed_hr = hr * 4.7/mean_hr
return _fixed_hr
def operative_temp(ta, tr, hc, hr):
to = (hc*ta + hr*tr) / (hc + hr)
return to
def clo_area_factor(clo):
fcl = np.where(clo<0.5, clo*0.2+1, clo*0.1+1.05)
return fcl
def dry_r(hc, hr, clo):
"""
Calculate total sensible thermal resistance.
Parameters
----------
hc : float or array
Convective heat transfer coefficient (hc) [W/K.m2].
hr : float or array
Radiative heat transfer coefficient (hr) [W/K.m2].
clo : float or array
Clothing insulation [clo].
Returns
-------
rt : float or array
Total sensible thermal resistance between skin and ambient.
"""
fcl = clo_area_factor(clo)
r_a = 1/(hc+hr)
r_cl = 0.155*clo
r_t = r_a/fcl + r_cl
return r_t
def wet_r(hc, clo, iclo=0.45, lewis_rate=16.5):
"""
Calculate total evaporative thermal resistance.
Parameters
----------
hc : float or array
Convective heat transfer coefficient (hc) [W/K.m2].
clo : float or array
Clothing insulation [clo].
iclo : float, or array, optional
Clothin vapor permeation efficiency [-]. The default is 0.45.
lewis_rate : float, optional
Lewis rate [K/kPa]. The default is 16.5.
Returns
-------
ret : float or array
Total evaporative thermal resistance.
"""
fcl = clo_area_factor(clo)
r_cl = 0.155 * clo
r_ea = 1 / (lewis_rate * hc)
r_ecl = r_cl / (lewis_rate * iclo)
r_et = r_ea / fcl + r_ecl
return r_et
def heat_resistances(
ta=np.ones(17)*28.8,
tr=np.ones(17)*28.8,
va=np.ones(17)*0.1,
tsk=np.ones(17)*34,
clo= | np.zeros(17) | numpy.zeros |
import pickle
import cv2
import skimage
import numpy as np
from shapely.geometry import Polygon
from concern.config import Configurable, State
def binary_search_smallest_width(poly):
if len(poly) < 3:
return 0
poly = Polygon(poly)
low = 0
high = 65536
while high - low > 0.1:
mid = (high + low) / 2
mid_poly = poly.buffer(-mid)
if mid_poly.geom_type == 'Polygon' and mid_poly.area > 0.1:
low = mid
else:
high = mid
height = (low + high) / 2
if height < 0.1:
return 0
else:
return height
def project_point_to_line(x, u, v, axis=0):
n = v - u
n = n / (np.linalg.norm(n, axis=axis, keepdims=True) + np.finfo(np.float32).eps)
p = u + n * np.sum((x - u) * n, axis=axis, keepdims=True)
return p
def project_point_to_segment(x, u, v, axis=0):
p = project_point_to_line(x, u, v, axis=axis)
outer = np.greater_equal(np.sum((u - p) * (v - p), axis=axis, keepdims=True), 0)
near_u = np.less_equal(
| np.linalg.norm(u - p, axis=axis, keepdims=True) | numpy.linalg.norm |
import h5py
import pandas as pd
import json
import cv2
import os, glob
from pylab import *
import numpy as np
import operator
from functools import reduce
from configparser import ConfigParser, MissingSectionHeaderError, NoOptionError
import errno
import simba.rw_dfs
#def importSLEAPbottomUP(inifile, dataFolder, currIDList):
data_folder = r'Z:\DeepLabCut\DLC_extract\Troubleshooting\Sleap_h5\import_folder'
configFile = str(r"Z:\DeepLabCut\DLC_extract\Troubleshooting\Sleap_h5\project_folder\project_config.ini")
config = ConfigParser()
try:
config.read(configFile)
except MissingSectionHeaderError:
print('ERROR: Not a valid project_config file. Please check the project_config.ini path.')
projectPath = config.get('General settings', 'project_path')
animalIDs = config.get('Multi animal IDs', 'id_list')
currIDList = animalIDs.split(",")
currIDList = [x.strip(' ') for x in currIDList]
filesFound = glob.glob(data_folder + '/*.analysis.h5')
videoFolder = os.path.join(projectPath, 'videos')
outputDfFolder = os.path.join(projectPath, 'csv', 'input_csv')
try:
wfileType = config.get('General settings', 'workflow_file_type')
except NoOptionError:
wfileType = 'csv'
animalsNo = len(currIDList)
bpNamesCSVPath = os.path.join(projectPath, 'logs', 'measures', 'pose_configs', 'bp_names', 'project_bp_names.csv')
poseEstimationSetting = config.get('create ensemble settings', 'pose_estimation_body_parts')
print('Converting sleap h5 into dataframes...')
csvPaths = []
for filename in filesFound:
video_save_name = os.path.basename(filename).replace('analysis.h5', wfileType)
savePath = os.path.join(outputDfFolder, video_save_name)
bpNames, orderVarList, OrderedBpList, MultiIndexCol, dfHeader, csvFilesFound, xy_heads, bp_cord_names, bpNameList, projBpNameList = [], [], [], [], [], [], [], [], [], []
print('Processing ' + str(os.path.basename(filename)) + '...')
hf = h5py.File(filename, 'r')
bp_name_list, track_list, = [], [],
for bp in hf.get('node_names'): bp_name_list.append(bp.decode('UTF-8'))
for track in hf.get('track_names'): track_list.append(track.decode('UTF-8'))
track_occupancy = hf.get('track_occupancy')
with track_occupancy.astype('int16'):
track_occupancy = track_occupancy[:]
tracks = hf.get('tracks')
with tracks.astype('int16'):
tracks = tracks[:]
frames = tracks.shape[3]
animal_df_list = []
for animals in range(len(track_list)):
animal_x_array, animal_y_array = np.transpose(tracks[animals][0]), np.transpose(tracks[animals][1])
animal_p_array = np.zeros(animal_x_array.shape)
animal_array = | np.ravel([animal_x_array, animal_y_array, animal_p_array], order="F") | numpy.ravel |
import mock
import numpy
from PIL import Image
from types import SimpleNamespace
import unittest
from machine_common_sense.mcs_action import MCS_Action
from machine_common_sense.mcs_goal import MCS_Goal
from machine_common_sense.mcs_object import MCS_Object
from machine_common_sense.mcs_pose import MCS_Pose
from machine_common_sense.mcs_return_status import MCS_Return_Status
from machine_common_sense.mcs_step_output import MCS_Step_Output
from .mock_mcs_controller_ai2thor import Mock_MCS_Controller_AI2THOR
class Test_MCS_Controller_AI2THOR(unittest.TestCase):
def setUp(self):
self.controller = Mock_MCS_Controller_AI2THOR()
self.controller.set_config({ 'metadata': '' })
def create_mock_scene_event(self, mock_scene_event_data):
# Wrap the dict in a SimpleNamespace object to permit property access with dotted notation since the actual
# variable is a class, not a dict.
return SimpleNamespace(**mock_scene_event_data)
def create_retrieve_object_list_scene_event(self):
return {
"events": [self.create_mock_scene_event({
"object_id_to_color": {
"testId1": (12, 34, 56),
"testId2": (98, 76, 54),
"testId3": (101, 102, 103)
}
})],
"metadata": {
"objects": [{
"colorsFromMaterials": ["c1"],
"direction": {
"x": 0,
"y": 0,
"z": 0
},
"distance": 0,
"distanceXZ": 0,
"isPickedUp": True,
"mass": 1,
"objectId": "testId1",
"position": {
"x": 1,
"y": 1,
"z": 2
},
"rotation": {
"x": 1.0,
"y": 2.0,
"z": 3.0
},
"salientMaterials": [],
"shape": "shape1",
"visibleInCamera": True
}, {
"colorsFromMaterials": ["c2", "c3"],
"direction": {
"x": 90,
"y": -30,
"z": 0
},
"distance": 1.5,
"distanceXZ": 1.1,
"isPickedUp": False,
"mass": 12.34,
"objectBounds": {
"objectBoundsCorners": ["p1", "p2", "p3", "p4", "p5", "p6", "p7", "p8"]
},
"objectId": "testId2",
"position": {
"x": 1,
"y": 2,
"z": 3
},
"rotation": {
"x": 1.0,
"y": 2.0,
"z": 3.0
},
"salientMaterials": ["Foobar", "Metal", "Plastic"],
"shape": "shape2",
"visibleInCamera": True
}, {
"colorsFromMaterials": [],
"direction": {
"x": -90,
"y": 180,
"z": 270
},
"distance": 2.5,
"distanceXZ": 2,
"isPickedUp": False,
"mass": 34.56,
"objectBounds": {
"objectBoundsCorners": ["pA", "pB", "pC", "pD", "pE", "pF", "pG", "pH"]
},
"objectId": "testId3",
"position": {
"x": -3,
"y": -2,
"z": -1
},
"rotation": {
"x": 11.0,
"y": 12.0,
"z": 13.0
},
"salientMaterials": ["Wood"],
"shape": "shape3",
"visibleInCamera": False
}]
}
}
def create_wrap_output_scene_event(self):
image_data = numpy.array([[0]], dtype=numpy.uint8)
depth_mask_data = numpy.array([[128]], dtype=numpy.uint8)
object_mask_data = numpy.array([[192]], dtype=numpy.uint8)
return {
"events": [self.create_mock_scene_event({
"depth_frame": depth_mask_data,
"frame": image_data,
"instance_segmentation_frame": object_mask_data,
"object_id_to_color": {
"testId": (12, 34, 56),
"testWallId": (101, 102, 103)
}
})],
"metadata": {
"agent": {
"cameraHorizon": 12.34,
"position": {
"x": 0.12,
"y": -0.23,
"z": 4.5
},
"rotation": {
"x": 1.111,
"y": 2.222,
"z": 3.333
}
},
"cameraPosition": {
"y": 0.1234
},
"clippingPlaneFar": 25,
"clippingPlaneNear": 0,
"fov": 42.5,
"lastActionStatus": "SUCCESSFUL",
"lastActionSuccess": True,
"objects": [{
"colorsFromMaterials": ["c1"],
"direction": {
"x": 90,
"y": -30,
"z": 0
},
"distance": 1.5,
"distanceXZ": 1.1,
"isPickedUp": False,
"mass": 12.34,
"objectBounds": {
"objectBoundsCorners": ["p1", "p2", "p3", "p4", "p5", "p6", "p7", "p8"]
},
"objectId": "testId",
"position": {
"x": 10,
"y": 11,
"z": 12
},
"rotation": {
"x": 1.0,
"y": 2.0,
"z": 3.0
},
"salientMaterials": ["Wood"],
"shape": "shape",
"visibleInCamera": True
}, {
"colorsFromMaterials": [],
"direction": {
"x": -90,
"y": 180,
"z": 270
},
"distance": 2.5,
"distanceXZ": 2.0,
"isPickedUp": False,
"mass": 34.56,
"objectBounds": {
"objectBoundsCorners": ["pA", "pB", "pC", "pD", "pE", "pF", "pG", "pH"]
},
"objectId": "testIdHidden",
"position": {
"x": -3,
"y": -2,
"z": -1
},
"rotation": {
"x": 11.0,
"y": 12.0,
"z": 13.0
},
"salientMaterials": ["Wood"],
"shape": "shapeHidden",
"visibleInCamera": False
}],
"structuralObjects": [{
"colorsFromMaterials": ["c2"],
"direction": {
"x": 180,
"y": -60,
"z": 0
},
"distance": 2.5,
"distanceXZ": 2.2,
"isPickedUp": False,
"mass": 56.78,
"objectBounds": {
"objectBoundsCorners": ["p11", "p12", "p13", "p14", "p15", "p16", "p17", "p18"]
},
"objectId": "testWallId",
"position": {
"x": 20,
"y": 21,
"z": 22
},
"rotation": {
"x": 4.0,
"y": 5.0,
"z": 6.0
},
"salientMaterials": ["Ceramic"],
"shape": "structure",
"visibleInCamera": True
}, {
"colorsFromMaterials": [],
"direction": {
"x": -180,
"y": 60,
"z": 90
},
"distance": 3.5,
"distanceXZ": 3.3,
"isPickedUp": False,
"mass": 78.90,
"objectBounds": {
"objectBoundsCorners": ["pAA", "pBB", "pCC", "pDD", "pEE", "pFF", "pGG", "pHH"]
},
"objectId": "testWallIdHidden",
"position": {
"x": 30,
"y": 31,
"z": 32
},
"rotation": {
"x": 14.0,
"y": 15.0,
"z": 16.0
},
"salientMaterials": ["Ceramic"],
"shape": "structureHidden",
"visibleInCamera": False
}]
}
}, image_data, depth_mask_data, object_mask_data
def test_end_scene(self):
# TODO When this function actually does anything
pass
def test_start_scene(self):
# TODO MCS-15
pass
def test_step(self):
# TODO MCS-15
pass
def test_restrict_goal_output_metadata(self):
goal = MCS_Goal(metadata={
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
})
actual = self.controller.restrict_goal_output_metadata(goal)
self.assertEqual(actual.metadata, {
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
})
def test_restrict_goal_output_metadata_full(self):
self.controller.set_config({ 'metadata': 'full' })
goal = MCS_Goal(metadata={
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
})
actual = self.controller.restrict_goal_output_metadata(goal)
self.assertEqual(actual.metadata, {
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
})
def test_restrict_goal_output_metadata_no_navigation(self):
self.controller.set_config({ 'metadata': 'no_navigation' })
goal = MCS_Goal(metadata={
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
})
actual = self.controller.restrict_goal_output_metadata(goal)
self.assertEqual(actual.metadata, {
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
})
def test_restrict_goal_output_metadata_no_vision(self):
self.controller.set_config({ 'metadata': 'no_vision' })
goal = MCS_Goal(metadata={
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
})
actual = self.controller.restrict_goal_output_metadata(goal)
self.assertEqual(actual.metadata, {
'target': { 'image': None },
'target_1': { 'image': None },
'target_2': { 'image': None }
})
def test_restrict_goal_output_metadata_none(self):
self.controller.set_config({ 'metadata': 'none' })
goal = MCS_Goal(metadata={
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
})
actual = self.controller.restrict_goal_output_metadata(goal)
self.assertEqual(actual.metadata, {
'target': { 'image': None },
'target_1': { 'image': None },
'target_2': { 'image': None }
})
def test_restrict_object_output_metadata(self):
test_object = MCS_Object(
color={ 'r': 1, 'g': 2, 'b': 3 },
dimensions={ 'x': 1, 'y': 2, 'z': 3 },
distance=12.34,
distance_in_steps=34.56,
distance_in_world=56.78,
position={ 'x': 4, 'y': 5, 'z': 6 },
rotation={ 'x': 7, 'y': 8, 'z': 9 },
shape='sofa',
texture_color_list=['c1', 'c2']
)
actual = self.controller.restrict_object_output_metadata(test_object)
self.assertEqual(actual.color, { 'r': 1, 'g': 2, 'b': 3 })
self.assertEqual(actual.dimensions, { 'x': 1, 'y': 2, 'z': 3 })
self.assertEqual(actual.distance, 12.34)
self.assertEqual(actual.distance_in_steps, 34.56)
self.assertEqual(actual.distance_in_world, 56.78)
self.assertEqual(actual.position, { 'x': 4, 'y': 5, 'z': 6 })
self.assertEqual(actual.rotation, { 'x': 7, 'y': 8, 'z': 9 })
self.assertEqual(actual.shape, 'sofa')
self.assertEqual(actual.texture_color_list, ['c1', 'c2'])
def test_restrict_object_output_metadata_full(self):
self.controller.set_config({ 'metadata': 'full' })
test_object = MCS_Object(
color={ 'r': 1, 'g': 2, 'b': 3 },
dimensions={ 'x': 1, 'y': 2, 'z': 3 },
distance=12.34,
distance_in_steps=34.56,
distance_in_world=56.78,
position={ 'x': 4, 'y': 5, 'z': 6 },
rotation={ 'x': 7, 'y': 8, 'z': 9 },
shape='sofa',
texture_color_list=['c1', 'c2']
)
actual = self.controller.restrict_object_output_metadata(test_object)
self.assertEqual(actual.color, { 'r': 1, 'g': 2, 'b': 3 })
self.assertEqual(actual.dimensions, { 'x': 1, 'y': 2, 'z': 3 })
self.assertEqual(actual.distance, 12.34)
self.assertEqual(actual.distance_in_steps, 34.56)
self.assertEqual(actual.distance_in_world, 56.78)
self.assertEqual(actual.position, { 'x': 4, 'y': 5, 'z': 6 })
self.assertEqual(actual.rotation, { 'x': 7, 'y': 8, 'z': 9 })
self.assertEqual(actual.shape, 'sofa')
self.assertEqual(actual.texture_color_list, ['c1', 'c2'])
def test_restrict_object_output_metadata_no_navigation(self):
self.controller.set_config({ 'metadata': 'no_navigation' })
test_object = MCS_Object(
color={ 'r': 1, 'g': 2, 'b': 3 },
dimensions={ 'x': 1, 'y': 2, 'z': 3 },
distance=12.34,
distance_in_steps=34.56,
distance_in_world=56.78,
position={ 'x': 4, 'y': 5, 'z': 6 },
rotation={ 'x': 7, 'y': 8, 'z': 9 },
shape='sofa',
texture_color_list=['c1', 'c2']
)
actual = self.controller.restrict_object_output_metadata(test_object)
self.assertEqual(actual.color, { 'r': 1, 'g': 2, 'b': 3 })
self.assertEqual(actual.dimensions, { 'x': 1, 'y': 2, 'z': 3 })
self.assertEqual(actual.distance, 12.34)
self.assertEqual(actual.distance_in_steps, 34.56)
self.assertEqual(actual.distance_in_world, 56.78)
self.assertEqual(actual.position, None)
self.assertEqual(actual.rotation, None)
self.assertEqual(actual.shape, 'sofa')
self.assertEqual(actual.texture_color_list, ['c1', 'c2'])
def test_restrict_object_output_metadata_no_vision(self):
self.controller.set_config({ 'metadata': 'no_vision' })
test_object = MCS_Object(
color={ 'r': 1, 'g': 2, 'b': 3 },
dimensions={ 'x': 1, 'y': 2, 'z': 3 },
distance=12.34,
distance_in_steps=34.56,
distance_in_world=56.78,
position={ 'x': 4, 'y': 5, 'z': 6 },
rotation={ 'x': 7, 'y': 8, 'z': 9 },
shape='sofa',
texture_color_list=['c1', 'c2']
)
actual = self.controller.restrict_object_output_metadata(test_object)
self.assertEqual(actual.color, None)
self.assertEqual(actual.dimensions, None)
self.assertEqual(actual.distance, None)
self.assertEqual(actual.distance_in_steps, None)
self.assertEqual(actual.distance_in_world, None)
self.assertEqual(actual.position, { 'x': 4, 'y': 5, 'z': 6 })
self.assertEqual(actual.rotation, { 'x': 7, 'y': 8, 'z': 9 })
self.assertEqual(actual.shape, None)
self.assertEqual(actual.texture_color_list, None)
def test_restrict_object_output_metadata_none(self):
self.controller.set_config({ 'metadata': 'none' })
test_object = MCS_Object(
color={ 'r': 1, 'g': 2, 'b': 3 },
dimensions={ 'x': 1, 'y': 2, 'z': 3 },
distance=12.34,
distance_in_steps=34.56,
distance_in_world=56.78,
position={ 'x': 4, 'y': 5, 'z': 6 },
rotation={ 'x': 7, 'y': 8, 'z': 9 },
shape='sofa',
texture_color_list=['c1', 'c2']
)
actual = self.controller.restrict_object_output_metadata(test_object)
self.assertEqual(actual.color, None)
self.assertEqual(actual.dimensions, None)
self.assertEqual(actual.distance, None)
self.assertEqual(actual.distance_in_steps, None)
self.assertEqual(actual.distance_in_world, None)
self.assertEqual(actual.position, None)
self.assertEqual(actual.rotation, None)
self.assertEqual(actual.shape, None)
self.assertEqual(actual.texture_color_list, None)
def test_restrict_step_output_metadata(self):
step = MCS_Step_Output(
camera_aspect_ratio=(1, 2),
camera_clipping_planes=(3, 4),
camera_field_of_view=5,
camera_height=6,
depth_mask_list=[7],
object_mask_list=[8],
position={ 'x': 4, 'y': 5, 'z': 6 },
rotation={ 'x': 7, 'y': 8, 'z': 9 }
)
actual = self.controller.restrict_step_output_metadata(step)
self.assertEqual(actual.camera_aspect_ratio, (1, 2))
self.assertEqual(actual.camera_clipping_planes, (3, 4))
self.assertEqual(actual.camera_field_of_view, 5)
self.assertEqual(actual.camera_height, 6)
self.assertEqual(actual.depth_mask_list, [7])
self.assertEqual(actual.object_mask_list, [8])
self.assertEqual(actual.position, { 'x': 4, 'y': 5, 'z': 6 })
self.assertEqual(actual.rotation, { 'x': 7, 'y': 8, 'z': 9 })
def test_restrict_step_output_metadata_full(self):
self.controller.set_config({ 'metadata': 'full' })
step = MCS_Step_Output(
camera_aspect_ratio=(1, 2),
camera_clipping_planes=(3, 4),
camera_field_of_view=5,
camera_height=6,
depth_mask_list=[7],
object_mask_list=[8],
position={ 'x': 4, 'y': 5, 'z': 6 },
rotation={ 'x': 7, 'y': 8, 'z': 9 }
)
actual = self.controller.restrict_step_output_metadata(step)
self.assertEqual(actual.camera_aspect_ratio, (1, 2))
self.assertEqual(actual.camera_clipping_planes, (3, 4))
self.assertEqual(actual.camera_field_of_view, 5)
self.assertEqual(actual.camera_height, 6)
self.assertEqual(actual.depth_mask_list, [7])
self.assertEqual(actual.object_mask_list, [8])
self.assertEqual(actual.position, { 'x': 4, 'y': 5, 'z': 6 })
self.assertEqual(actual.rotation, { 'x': 7, 'y': 8, 'z': 9 })
def test_restrict_step_output_metadata_no_navigation(self):
self.controller.set_config({ 'metadata': 'no_navigation' })
step = MCS_Step_Output(
camera_aspect_ratio=(1, 2),
camera_clipping_planes=(3, 4),
camera_field_of_view=5,
camera_height=6,
depth_mask_list=[7],
object_mask_list=[8],
position={ 'x': 4, 'y': 5, 'z': 6 },
rotation={ 'x': 7, 'y': 8, 'z': 9 }
)
actual = self.controller.restrict_step_output_metadata(step)
self.assertEqual(actual.camera_aspect_ratio, (1, 2))
self.assertEqual(actual.camera_clipping_planes, (3, 4))
self.assertEqual(actual.camera_field_of_view, 5)
self.assertEqual(actual.camera_height, 6)
self.assertEqual(actual.depth_mask_list, [7])
self.assertEqual(actual.object_mask_list, [8])
self.assertEqual(actual.position, None)
self.assertEqual(actual.rotation, None)
def test_restrict_step_output_metadata_no_vision(self):
self.controller.set_config({ 'metadata': 'no_vision' })
step = MCS_Step_Output(
camera_aspect_ratio=(1, 2),
camera_clipping_planes=(3, 4),
camera_field_of_view=5,
camera_height=6,
depth_mask_list=[7],
object_mask_list=[8],
position={ 'x': 4, 'y': 5, 'z': 6 },
rotation={ 'x': 7, 'y': 8, 'z': 9 }
)
actual = self.controller.restrict_step_output_metadata(step)
self.assertEqual(actual.camera_aspect_ratio, None)
self.assertEqual(actual.camera_clipping_planes, None)
self.assertEqual(actual.camera_field_of_view, None)
self.assertEqual(actual.camera_height, None)
self.assertEqual(actual.depth_mask_list, [])
self.assertEqual(actual.object_mask_list, [])
self.assertEqual(actual.position, { 'x': 4, 'y': 5, 'z': 6 })
self.assertEqual(actual.rotation, { 'x': 7, 'y': 8, 'z': 9 })
def test_restrict_step_output_metadata_none(self):
self.controller.set_config({ 'metadata': 'none' })
step = MCS_Step_Output(
camera_aspect_ratio=(1, 2),
camera_clipping_planes=(3, 4),
camera_field_of_view=5,
camera_height=6,
depth_mask_list=[7],
object_mask_list=[8],
position={ 'x': 4, 'y': 5, 'z': 6 },
rotation={ 'x': 7, 'y': 8, 'z': 9 }
)
actual = self.controller.restrict_step_output_metadata(step)
self.assertEqual(actual.camera_aspect_ratio, None)
self.assertEqual(actual.camera_clipping_planes, None)
self.assertEqual(actual.camera_field_of_view, None)
self.assertEqual(actual.camera_height, None)
self.assertEqual(actual.depth_mask_list, [])
self.assertEqual(actual.object_mask_list, [])
self.assertEqual(actual.position, None)
self.assertEqual(actual.rotation, None)
def test_retrieve_action_list(self):
self.assertEqual(self.controller.retrieve_action_list(MCS_Goal(), 0), self.controller.ACTION_LIST)
self.assertEqual(self.controller.retrieve_action_list(MCS_Goal(action_list=[]), 0), \
self.controller.ACTION_LIST)
self.assertEqual(self.controller.retrieve_action_list(MCS_Goal(action_list=[[]]), 0), \
self.controller.ACTION_LIST)
self.assertEqual(self.controller.retrieve_action_list(MCS_Goal(action_list=[['MoveAhead',\
'RotateLook,rotation=180']]), 0), ['MoveAhead', 'RotateLook,rotation=180'])
self.assertEqual(self.controller.retrieve_action_list(MCS_Goal(action_list=[['MoveAhead',\
'RotateLook,rotation=180']]), 1), self.controller.ACTION_LIST)
self.assertEqual(self.controller.retrieve_action_list(MCS_Goal(action_list=[['MoveAhead',\
'RotateLook,rotation=180'], []]), 1), self.controller.ACTION_LIST)
self.assertEqual(self.controller.retrieve_action_list(MCS_Goal(action_list=[[],['MoveAhead',\
'RotateLook,rotation=180']]), 0), self.controller.ACTION_LIST)
self.assertEqual(self.controller.retrieve_action_list(MCS_Goal(action_list=[[],['MoveAhead',\
'RotateLook,rotation=180']]), 1), ['MoveAhead', 'RotateLook,rotation=180'])
def test_retrieve_goal(self):
goal_1 = self.controller.retrieve_goal({})
self.assertEqual(goal_1.action_list, None)
self.assertEqual(goal_1.info_list, [])
self.assertEqual(goal_1.last_step, None)
self.assertEqual(goal_1.task_list, [])
self.assertEqual(goal_1.type_list, [])
self.assertEqual(goal_1.metadata, {})
goal_2 = self.controller.retrieve_goal({
"goal": {
}
})
self.assertEqual(goal_2.action_list, None)
self.assertEqual(goal_2.info_list, [])
self.assertEqual(goal_2.last_step, None)
self.assertEqual(goal_2.task_list, [])
self.assertEqual(goal_2.type_list, [])
self.assertEqual(goal_2.metadata, {})
goal_3 = self.controller.retrieve_goal({
"goal": {
"action_list": [["action1"], [], ["action2", "action3", "action4"]],
"info_list": ["info1", "info2", 12.34],
"last_step": 10,
"task_list": ["task1", "task2"],
"type_list": ["type1", "type2"],
"metadata": {
"key": "value"
}
}
})
self.assertEqual(goal_3.action_list, [["action1"], [], ["action2", "action3", "action4"]])
self.assertEqual(goal_3.info_list, ["info1", "info2", 12.34])
self.assertEqual(goal_3.last_step, 10)
self.assertEqual(goal_3.task_list, ["task1", "task2"])
self.assertEqual(goal_3.type_list, ["type1", "type2"])
self.assertEqual(goal_3.metadata, {
"key": "value"
})
def test_retrieve_goal_with_config_metadata(self):
self.controller.set_config({ 'metadata': 'full' })
actual = self.controller.retrieve_goal({
'goal': {
'metadata': {
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
}
}
})
self.assertEqual(actual.metadata, {
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
})
self.controller.set_config({ 'metadata': 'no_navigation' })
actual = self.controller.retrieve_goal({
'goal': {
'metadata': {
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
}
}
})
self.assertEqual(actual.metadata, {
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
})
self.controller.set_config({ 'metadata': 'no_vision' })
actual = self.controller.retrieve_goal({
'goal': {
'metadata': {
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
}
}
})
self.assertEqual(actual.metadata, {
'target': { 'image': None },
'target_1': { 'image': None },
'target_2': { 'image': None }
})
self.controller.set_config({ 'metadata': 'none' })
actual = self.controller.retrieve_goal({
'goal': {
'metadata': {
'target': { 'image': [0] },
'target_1': { 'image': [1] },
'target_2': { 'image': [2] }
}
}
})
self.assertEqual(actual.metadata, {
'target': { 'image': None },
'target_1': { 'image': None },
'target_2': { 'image': None }
})
def test_retrieve_head_tilt(self):
mock_scene_event_data = {
"metadata": {
"agent": {
"cameraHorizon": 12.34
}
}
}
actual = self.controller.retrieve_head_tilt(self.create_mock_scene_event(mock_scene_event_data))
self.assertEqual(actual, 12.34)
mock_scene_event_data = {
"metadata": {
"agent": {
"cameraHorizon": -56.78
}
}
}
actual = self.controller.retrieve_head_tilt(self.create_mock_scene_event(mock_scene_event_data))
self.assertEqual(actual, -56.78)
def test_retrieve_object_list(self):
mock_scene_event_data = self.create_retrieve_object_list_scene_event()
actual = self.controller.retrieve_object_list(self.create_mock_scene_event(mock_scene_event_data))
self.assertEqual(len(actual), 2)
self.assertEqual(actual[0].uuid, "testId1")
self.assertEqual(actual[0].color, {
"r": 12,
"g": 34,
"b": 56
})
self.assertEqual(actual[0].dimensions, {})
self.assertEqual(actual[0].direction, {
"x": 0,
"y": 0,
"z": 0
})
self.assertEqual(actual[0].distance, 0)
self.assertEqual(actual[0].distance_in_steps, 0)
self.assertEqual(actual[0].distance_in_world, 0)
self.assertEqual(actual[0].held, True)
self.assertEqual(actual[0].mass, 1)
self.assertEqual(actual[0].material_list, [])
self.assertEqual(actual[0].position, { "x": 1, "y": 1, "z": 2 })
self.assertEqual(actual[0].rotation, 2.0)
self.assertEqual(actual[0].shape, 'shape1')
self.assertEqual(actual[0].texture_color_list, ['c1'])
self.assertEqual(actual[0].visible, True)
self.assertEqual(actual[1].uuid, "testId2")
self.assertEqual(actual[1].color, {
"r": 98,
"g": 76,
"b": 54
})
self.assertEqual(actual[1].dimensions, ["p1", "p2", "p3", "p4", "p5", "p6", "p7", "p8"])
self.assertEqual(actual[1].direction, {
"x": 90,
"y": -30,
"z": 0
})
self.assertEqual(actual[1].distance, 2.2)
self.assertEqual(actual[1].distance_in_steps, 2.2)
self.assertEqual(actual[1].distance_in_world, 1.5)
self.assertEqual(actual[1].held, False)
self.assertEqual(actual[1].mass, 12.34)
self.assertEqual(actual[1].material_list, ["METAL", "PLASTIC"])
self.assertEqual(actual[1].position, { "x": 1, "y": 2, "z": 3 })
self.assertEqual(actual[1].rotation, 2)
self.assertEqual(actual[1].shape, 'shape2')
self.assertEqual(actual[1].texture_color_list, ['c2', 'c3'])
self.assertEqual(actual[1].visible, True)
def test_retrieve_object_list_with_config_metadata_full(self):
self.controller.set_config({ 'metadata': 'full' })
mock_scene_event_data = self.create_retrieve_object_list_scene_event()
actual = self.controller.retrieve_object_list(self.create_mock_scene_event(mock_scene_event_data))
self.assertEqual(len(actual), 3)
self.assertEqual(actual[0].uuid, "testId1")
self.assertEqual(actual[0].color, {
"r": 12,
"g": 34,
"b": 56
})
self.assertEqual(actual[0].dimensions, {})
self.assertEqual(actual[0].direction, {
"x": 0,
"y": 0,
"z": 0
})
self.assertEqual(actual[0].distance, 0)
self.assertEqual(actual[0].distance_in_steps, 0)
self.assertEqual(actual[0].distance_in_world, 0)
self.assertEqual(actual[0].held, True)
self.assertEqual(actual[0].mass, 1)
self.assertEqual(actual[0].material_list, [])
self.assertEqual(actual[0].position, { "x": 1, "y": 1, "z": 2 })
self.assertEqual(actual[0].rotation, 2.0)
self.assertEqual(actual[0].shape, 'shape1')
self.assertEqual(actual[0].texture_color_list, ['c1'])
self.assertEqual(actual[0].visible, True)
self.assertEqual(actual[1].uuid, "testId2")
self.assertEqual(actual[1].color, {
"r": 98,
"g": 76,
"b": 54
})
self.assertEqual(actual[1].dimensions, ["p1", "p2", "p3", "p4", "p5", "p6", "p7", "p8"])
self.assertEqual(actual[1].direction, {
"x": 90,
"y": -30,
"z": 0
})
self.assertEqual(actual[1].distance, 2.2)
self.assertEqual(actual[1].distance_in_steps, 2.2)
self.assertEqual(actual[1].distance_in_world, 1.5)
self.assertEqual(actual[1].held, False)
self.assertEqual(actual[1].mass, 12.34)
self.assertEqual(actual[1].material_list, ["METAL", "PLASTIC"])
self.assertEqual(actual[1].position, { "x": 1, "y": 2, "z": 3 })
self.assertEqual(actual[1].rotation, 2)
self.assertEqual(actual[1].shape, 'shape2')
self.assertEqual(actual[1].texture_color_list, ['c2', 'c3'])
self.assertEqual(actual[1].visible, True)
self.assertEqual(actual[2].uuid, "testId3")
self.assertEqual(actual[2].color, {
"r": 101,
"g": 102,
"b": 103
})
self.assertEqual(actual[2].dimensions, ["pA", "pB", "pC", "pD", "pE", "pF", "pG", "pH"])
self.assertEqual(actual[2].direction, {
"x": -90,
"y": 180,
"z": 270
})
self.assertEqual(actual[2].distance, 4)
self.assertEqual(actual[2].distance_in_steps, 4)
self.assertEqual(actual[2].distance_in_world, 2.5)
self.assertEqual(actual[2].held, False)
self.assertEqual(actual[2].mass, 34.56)
self.assertEqual(actual[2].material_list, ["WOOD"])
self.assertEqual(actual[2].position, { "x": -3, "y": -2, "z": -1 })
self.assertEqual(actual[2].rotation, 12)
self.assertEqual(actual[2].shape, 'shape3')
self.assertEqual(actual[2].texture_color_list, [])
self.assertEqual(actual[2].visible, False)
def test_retrieve_object_list_with_config_metadata_no_navigation(self):
self.controller.set_config({ 'metadata': 'no_navigation' })
mock_scene_event_data = self.create_retrieve_object_list_scene_event()
actual = self.controller.retrieve_object_list(self.create_mock_scene_event(mock_scene_event_data))
self.assertEqual(len(actual), 2)
self.assertEqual(actual[0].uuid, "testId1")
self.assertEqual(actual[0].color, {
"r": 12,
"g": 34,
"b": 56
})
self.assertEqual(actual[0].dimensions, {})
self.assertEqual(actual[0].direction, {
"x": 0,
"y": 0,
"z": 0
})
self.assertEqual(actual[0].distance, 0)
self.assertEqual(actual[0].distance_in_steps, 0)
self.assertEqual(actual[0].distance_in_world, 0)
self.assertEqual(actual[0].held, True)
self.assertEqual(actual[0].mass, 1)
self.assertEqual(actual[0].material_list, [])
self.assertEqual(actual[0].position, None)
self.assertEqual(actual[0].rotation, None)
self.assertEqual(actual[0].shape, 'shape1')
self.assertEqual(actual[0].texture_color_list, ['c1'])
self.assertEqual(actual[0].visible, True)
self.assertEqual(actual[1].uuid, "testId2")
self.assertEqual(actual[1].color, {
"r": 98,
"g": 76,
"b": 54
})
self.assertEqual(actual[1].dimensions, ["p1", "p2", "p3", "p4", "p5", "p6", "p7", "p8"])
self.assertEqual(actual[1].direction, {
"x": 90,
"y": -30,
"z": 0
})
self.assertEqual(actual[1].distance, 2.2)
self.assertEqual(actual[1].distance_in_steps, 2.2)
self.assertEqual(actual[1].distance_in_world, 1.5)
self.assertEqual(actual[1].held, False)
self.assertEqual(actual[1].mass, 12.34)
self.assertEqual(actual[1].material_list, ["METAL", "PLASTIC"])
self.assertEqual(actual[1].position, None)
self.assertEqual(actual[1].rotation, None)
self.assertEqual(actual[1].shape, 'shape2')
self.assertEqual(actual[1].texture_color_list, ['c2', 'c3'])
self.assertEqual(actual[1].visible, True)
def test_retrieve_object_list_with_config_metadata_no_vision(self):
self.controller.set_config({ 'metadata': 'no_vision' })
mock_scene_event_data = self.create_retrieve_object_list_scene_event()
actual = self.controller.retrieve_object_list(self.create_mock_scene_event(mock_scene_event_data))
self.assertEqual(len(actual), 2)
self.assertEqual(actual[0].uuid, "testId1")
self.assertEqual(actual[0].color, None)
self.assertEqual(actual[0].dimensions, None)
self.assertEqual(actual[0].direction, None)
self.assertEqual(actual[0].distance, None)
self.assertEqual(actual[0].distance_in_steps, None)
self.assertEqual(actual[0].distance_in_world, None)
self.assertEqual(actual[0].held, True)
self.assertEqual(actual[0].mass, 1)
self.assertEqual(actual[0].material_list, [])
self.assertEqual(actual[0].position, { "x": 1, "y": 1, "z": 2 })
self.assertEqual(actual[0].rotation, 2.0)
self.assertEqual(actual[0].shape, None)
self.assertEqual(actual[0].texture_color_list, None)
self.assertEqual(actual[0].visible, True)
self.assertEqual(actual[1].uuid, "testId2")
self.assertEqual(actual[1].color, None)
self.assertEqual(actual[1].dimensions, None)
self.assertEqual(actual[1].direction, None)
self.assertEqual(actual[1].distance, None)
self.assertEqual(actual[1].distance_in_steps, None)
self.assertEqual(actual[1].distance_in_world, None)
self.assertEqual(actual[1].held, False)
self.assertEqual(actual[1].mass, 12.34)
self.assertEqual(actual[1].material_list, ["METAL", "PLASTIC"])
self.assertEqual(actual[1].position, { "x": 1, "y": 2, "z": 3 })
self.assertEqual(actual[1].rotation, 2)
self.assertEqual(actual[1].shape, None)
self.assertEqual(actual[1].texture_color_list, None)
self.assertEqual(actual[1].visible, True)
def test_retrieve_object_list_with_config_metadata_none(self):
self.controller.set_config({ 'metadata': 'none' })
mock_scene_event_data = self.create_retrieve_object_list_scene_event()
actual = self.controller.retrieve_object_list(self.create_mock_scene_event(mock_scene_event_data))
self.assertEqual(len(actual), 2)
self.assertEqual(actual[0].uuid, "testId1")
self.assertEqual(actual[0].color, None)
self.assertEqual(actual[0].dimensions, None)
self.assertEqual(actual[0].direction, None)
self.assertEqual(actual[0].distance, None)
self.assertEqual(actual[0].distance_in_steps, None)
self.assertEqual(actual[0].distance_in_world, None)
self.assertEqual(actual[0].held, True)
self.assertEqual(actual[0].mass, 1)
self.assertEqual(actual[0].material_list, [])
self.assertEqual(actual[0].position, None)
self.assertEqual(actual[0].rotation, None)
self.assertEqual(actual[0].shape, None)
self.assertEqual(actual[0].texture_color_list, None)
self.assertEqual(actual[0].visible, True)
self.assertEqual(actual[1].uuid, "testId2")
self.assertEqual(actual[1].color, None)
self.assertEqual(actual[1].dimensions, None)
self.assertEqual(actual[1].direction, None)
self.assertEqual(actual[1].distance, None)
self.assertEqual(actual[1].distance_in_steps, None)
self.assertEqual(actual[1].distance_in_world, None)
self.assertEqual(actual[1].held, False)
self.assertEqual(actual[1].mass, 12.34)
self.assertEqual(actual[1].material_list, ["METAL", "PLASTIC"])
self.assertEqual(actual[1].position, None)
self.assertEqual(actual[1].rotation, None)
self.assertEqual(actual[1].shape, None)
self.assertEqual(actual[1].texture_color_list, None)
self.assertEqual(actual[1].visible, True)
def test_retrieve_pose(self):
# TODO MCS-18
pass
def test_retrieve_return_status(self):
mock_scene_event_data = {
"metadata": {
"lastActionStatus": "SUCCESSFUL"
}
}
actual = self.controller.retrieve_return_status(self.create_mock_scene_event(mock_scene_event_data))
self.assertEqual(actual, MCS_Return_Status.SUCCESSFUL.name)
mock_scene_event_data = {
"metadata": {
"lastActionStatus": "FAILED"
}
}
actual = self.controller.retrieve_return_status(self.create_mock_scene_event(mock_scene_event_data))
self.assertEqual(actual, MCS_Return_Status.FAILED.name)
mock_scene_event_data = {
"metadata": {
"lastActionStatus": "INVALID_STATUS"
}
}
actual = self.controller.retrieve_return_status(self.create_mock_scene_event(mock_scene_event_data))
self.assertEqual(actual, MCS_Return_Status.UNDEFINED.name)
mock_scene_event_data = {
"metadata": {
"lastActionStatus": None
}
}
actual = self.controller.retrieve_return_status(self.create_mock_scene_event(mock_scene_event_data))
self.assertEqual(actual, MCS_Return_Status.UNDEFINED.name)
def test_save_images(self):
image_data = numpy.array([[0]], dtype=numpy.uint8)
depth_mask_data = numpy.array([[128]], dtype=numpy.uint8)
object_mask_data = numpy.array([[192]], dtype=numpy.uint8)
mock_scene_event_data = {
"events": [self.create_mock_scene_event({
"depth_frame": depth_mask_data,
"frame": image_data,
"instance_segmentation_frame": object_mask_data
})]
}
image_list, depth_mask_list, object_mask_list = self.controller.save_images(self.create_mock_scene_event(
mock_scene_event_data))
self.assertEqual(len(image_list), 1)
self.assertEqual(len(depth_mask_list), 1)
self.assertEqual(len(object_mask_list), 1)
self.assertEqual(numpy.array(image_list[0]), image_data)
self.assertEqual(numpy.array(depth_mask_list[0]), depth_mask_data)
self.assertEqual(numpy.array(object_mask_list[0]), object_mask_data)
def test_save_images_with_multiple_images(self):
image_data_1 = numpy.array([[64]], dtype=numpy.uint8)
depth_mask_data_1 = numpy.array([[128]], dtype=numpy.uint8)
object_mask_data_1 = numpy.array([[192]], dtype=numpy.uint8)
image_data_2 = numpy.array([[32]], dtype=numpy.uint8)
depth_mask_data_2 = numpy.array([[96]], dtype=numpy.uint8)
object_mask_data_2 = numpy.array([[160]], dtype=numpy.uint8)
mock_scene_event_data = {
"events": [self.create_mock_scene_event({
"depth_frame": depth_mask_data_1,
"frame": image_data_1,
"instance_segmentation_frame": object_mask_data_1
}), self.create_mock_scene_event({
"depth_frame": depth_mask_data_2,
"frame": image_data_2,
"instance_segmentation_frame": object_mask_data_2
})]
}
image_list, depth_mask_list, object_mask_list = self.controller.save_images(self.create_mock_scene_event(
mock_scene_event_data))
self.assertEqual(len(image_list), 2)
self.assertEqual(len(depth_mask_list), 2)
self.assertEqual(len(object_mask_list), 2)
self.assertEqual(numpy.array(image_list[0]), image_data_1)
self.assertEqual(numpy.array(depth_mask_list[0]), depth_mask_data_1)
self.assertEqual(numpy.array(object_mask_list[0]), object_mask_data_1)
self.assertEqual(numpy.array(image_list[1]), image_data_2)
self.assertEqual( | numpy.array(depth_mask_list[1]) | numpy.array |
import pandas as pd
import numpy as np
import pickle
from .utils import *
def predNextDays(optmod_name, opt_mod, var_name, pred_days):
pred = (opt_mod[optmod_name]['mod_data'][var_name])[opt_mod[optmod_name]['i_start'] + opt_mod[optmod_name]['period'] -1 :opt_mod[optmod_name]['i_start'] + opt_mod[optmod_name]['period']+pred_days]
print("Mod: %s \t Next days: %s: \t %s" %(optmod_name, var_name, str([int(x) for x in pred])))
print("Mod: %s \t Variation: %s: \t %s" %(optmod_name, var_name, str([int(x) for x in (pred[1:len(pred)] - pred[0:len(pred)-1])])))
class ModelStats:
def __init__(self, model, act_data, pred_days = 10):
self.model = model
self.act_data = act_data
self.data = pd.DataFrame(self.calcData())
self.data.set_index("date", inplace=True)
def printKpi(self, date, kpi_name, title, num_format = 'd', bperc = False):
var_uff = "uff_" + kpi_name
var_mod = "mod_" + kpi_name
if "uff_" + kpi_name in self.data.columns.tolist():
#print(("%30s: %7" + num_format + " vs %7" + num_format + " (%5" + num_format + " vs %5" + num_format + "), errore: %" + num_format + "") %(
print(("%30s: %7s vs %7s (%5s vs %5s), errore: %s") %(
title,
format_number(self.data[var_uff][np.datetime64(date, 'D')], bperc = bperc),
format_number(self.data[var_mod][np.datetime64(date, 'D')], bperc = bperc),
format_number(self.data[var_uff][np.datetime64(date, 'D')] - self.data[var_uff][np.datetime64(date, 'D') - np.timedelta64(1, 'D')], bperc = bperc),
format_number(self.data[var_mod][np.datetime64(date, 'D')] - self.data[var_mod][np.datetime64(date, 'D') - np.timedelta64(1, 'D')], bperc = bperc),
format_number(self.data[var_uff][np.datetime64(date, 'D')] - self.data[var_mod][np.datetime64(date, 'D')], bperc = bperc)
))
else:
#print(("%30s: %7" + num_format + " (%5" + num_format + ")") %(
print(("%30s: %7s (%5s)") %(
title,
format_number(self.data[var_mod][np.datetime64(date, 'D')], bperc = bperc),
format_number(self.data[var_mod][np.datetime64(date, 'D')] - self.data[var_mod][np.datetime64(date, 'D') - np.timedelta64(1, 'D')], bperc = bperc)
))
def printKpis(self, date):
self.printKpi(date, 'Igc_cum', "Tot Infected")
self.printKpi(date, 'Igc', "Currently Infected")
self.printKpi(date, 'Igci_t', "Currently in Int. Care")
self.printKpi(date, 'Gc_cum', "Tot Recovered")
self.printKpi(date, 'M_cum', "Tot Dead")
print()
self.printKpi(date, 'Igc_cum_pinc', "% Increase, Infected", num_format=".3f", bperc = True)
self.printKpi(date, 'ratio_Gc_Igc', "% Mortality Rate", num_format=".3f", bperc = True)
self.printKpi(date, 'ratio_M_Igc', "% Known Recovery Rate", num_format=".3f", bperc = True)
print()
self.printKpi(date, 'ratio_Gccum_Igccum', "% Recovered / Tot", num_format=".3f", bperc = True)
self.printKpi(date, 'ratio_Mcum_Igccum', "% Dead / Tot", num_format=".3f", bperc = True)
self.printKpi(date, 'ratio_Igci_Igc', "% Intensive Care", num_format=".3f", bperc = True)
self.printKpi(date, 'ratio_Igcn_Igc', "% Non Intensive Care", num_format=".3f", bperc = True)
self.printKpi(date, 'ratio_I_Igc', "% Total Infected / Known Infected", num_format=".3f", bperc = True)
self.printKpi(date, 'R0_t', "R0", num_format=".3f")
print()
print()
print("*** 7 days ahead predictions ***")
self.printPredict(date, 'Igc_cum', "Tot Infettati", pred_step = 7, bperc = False)
print()
self.printPredict(date, 'Igc', "Attualmente Infetti", pred_step = 7, bperc = False)
print()
self.printPredict(date, 'Igci_t', "Attualmente in Intensiva", pred_step = 7, bperc = False)
print()
self.printPredict(date, 'Gc_cum', "Tot Guariti", pred_step = 7, bperc = False)
print()
self.printPredict(date, 'M_cum', "Tot Morti", pred_step = 7, bperc = False)
def printPredict(self, curr_date, kpi_name, title, pred_step = 7, bperc = False):
var_mod = "mod_" + kpi_name
data = self.data[var_mod][ | np.datetime64(curr_date, 'D') | numpy.datetime64 |
import ctypes
import numpy as np
import pytest
from psyneulink.core import llvm as pnlvm
from llvmlite import ir
DIM_X = 1000
DIM_Y = 2000
u = np.random.rand(DIM_X, DIM_Y)
v = np.random.rand(DIM_X, DIM_Y)
vector = np.random.rand(DIM_X)
trans_vector = | np.random.rand(DIM_Y) | numpy.random.rand |
import numpy as np
import h5py
import json
sys.path.append('F:\Linux')
import illustris_python as il
import matplotlib.pyplot as plt
def Flatness(MassTensor):
#c / a = (M3)**0.5 / (M1)**0.5
return | np.sqrt(MassTensor[0]) | numpy.sqrt |
import pandas as pd
import numpy as np
from causality.estimation.parametric import (DifferenceInDifferences,
PropensityScoreMatching,
InverseProbabilityWeightedLS)
from tests.unit import TestAPI
class TestDID(TestAPI):
def setUp(self):
SIZE = 2000
assignment = | np.random.binomial(1,0.5, size=SIZE) | numpy.random.binomial |
"""
Filename: visualization.py
Purpose: Set of go-to plotting functions
Author: <NAME>
Date created: 28.11.2018
Possible problems:
1.
"""
import os
import numpy as np
from tractor.galaxy import ExpGalaxy
from tractor import EllipseE
from tractor.galaxy import ExpGalaxy
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm, SymLogNorm
from matplotlib.patches import Ellipse
from matplotlib.patches import Rectangle
from skimage.segmentation import find_boundaries
from astropy.visualization import hist
from scipy import stats
import config as conf
import matplotlib.cm as cm
import random
from time import time
from astropy.io import fits
import logging
logger = logging.getLogger('farmer.visualization')
# Random discrete color generator
colors = cm.rainbow(np.linspace(0, 1, 1000))
cidx = np.arange(0, 1000)
random.shuffle(cidx)
colors = colors[cidx]
def plot_background(brick, idx, band=''):
fig, ax = plt.subplots(figsize=(20,20))
vmin, vmax = brick.background_images[idx].min(), brick.background_images[idx].max()
vmin = -vmax
img = ax.imshow(brick.background_images[idx], cmap='RdGy', norm=SymLogNorm(linthresh=0.03))
# plt.colorbar(img, ax=ax)
out_path = os.path.join(conf.PLOT_DIR, f'B{brick.brick_id}_{band}_background.pdf')
ax.axis('off')
ax.margins(0,0)
fig.savefig(out_path, dpi = 300, overwrite=True, pad_inches=0.0)
plt.close()
logger.info(f'Saving figure: {out_path}')
def plot_mask(brick, idx, band=''):
fig, ax = plt.subplots(figsize=(20,20))
img = ax.imshow(brick.masks[idx])
out_path = os.path.join(conf.PLOT_DIR, f'B{brick.brick_id}_{band}_mask.pdf')
ax.axis('off')
ax.margins(0,0)
fig.savefig(out_path, dpi = 300, overwrite=True, pad_inches=0.0)
plt.close()
logger.info(f'Saving figure: {out_path}')
def plot_brick(brick, idx, band=''):
fig, ax = plt.subplots(figsize=(20,20))
backlevel, noisesigma = brick.backgrounds[idx]
vmin, vmax = np.max([backlevel + noisesigma, 1E-5]), brick.images[idx].max()
# vmin, vmax = brick.images[idx].min(), brick.images[idx].max()
if vmin > vmax:
logger.warning(f'{band} brick not plotted!')
return
vmin = -vmax
norm = SymLogNorm(linthresh=0.03)
img = ax.imshow(brick.images[idx], cmap='RdGy', origin='lower', norm=norm)
# plt.colorbar(img, ax=ax)
out_path = os.path.join(conf.PLOT_DIR, f'B{brick.brick_id}_{band}_brick.pdf')
ax.axis('off')
ax.margins(0,0)
fig.savefig(out_path, dpi = 300, overwrite=True, pad_inches=0.0)
plt.close()
logger.info(f'Saving figure: {out_path}')
def plot_blob(myblob, myfblob):
fig, ax = plt.subplots(ncols=4, nrows=1+myfblob.n_bands, figsize=(5 + 5*myfblob.n_bands, 10), sharex=True, sharey=True)
back = myblob.backgrounds[0]
mean, rms = back[0], back[1]
noise = np.random.normal(mean, rms, size=myfblob.dims)
tr = myblob.solution_tractor
norm = LogNorm(np.max([mean + rms, 1E-5]), myblob.images.max(), clip='True')
img_opt = dict(cmap='Greys', norm=norm)
# img_opt = dict(cmap='RdGy', vmin=-5*rms, vmax=5*rms)
mmask = myblob.masks[0].copy()
mmask[mmask==1] = np.nan
ax[0, 0].imshow(myblob.images[0], **img_opt)
ax[0, 0].imshow(mmask, alpha=0.5, cmap='Greys')
ax[0, 1].imshow(myblob.solution_model_images[0] + noise, **img_opt)
ax[0, 2].imshow(myblob.images[0] - myblob.solution_model_images[0], cmap='RdGy', vmin=-5*rms, vmax=5*rms)
ax[0, 3].imshow(myblob.solution_chi_images[0], cmap='RdGy', vmin = -7, vmax = 7)
ax[0, 0].set_ylabel(f'Detection ({myblob.bands[0]})')
ax[0, 0].set_title('Data')
ax[0, 1].set_title('Model')
ax[0, 2].set_title('Data - Model')
ax[0, 3].set_title('$\chi$-map')
band = myblob.bands[0]
for j, src in enumerate(myblob.solution_catalog):
try:
mtype = src.name
except:
mtype = 'PointSource'
flux = src.getBrightness().getFlux(band)
chisq = myblob.solved_chisq[j]
topt = dict(color=colors[j], transform = ax[0, 3].transAxes)
ystart = 0.99 - j * 0.4
ax[0, 3].text(1.05, ystart - 0.1, f'{j}) {mtype}', **topt)
ax[0, 3].text(1.05, ystart - 0.2, f' F({band}) = {flux:4.4f}', **topt)
ax[0, 3].text(1.05, ystart - 0.3, f' $\chi^{2}$ = {chisq:4.4f}', **topt)
objects = myblob.bcatalog[j]
e = Ellipse(xy=(objects['x'], objects['y']),
width=6*objects['a'],
height=6*objects['b'],
angle=objects['theta'] * 180. / np.pi)
e.set_facecolor('none')
e.set_edgecolor('red')
ax[0, 0].add_artist(e)
try:
for i in np.arange(myfblob.n_bands):
back = myfblob.backgrounds[i]
mean, rms = back[0], back[1]
noise = np.random.normal(mean, rms, size=myfblob.dims)
tr = myfblob.solution_tractor
# norm = LogNorm(np.max([mean + rms, 1E-5]), myblob.images.max(), clip='True')
# img_opt = dict(cmap='Greys', norm=norm)
img_opt = dict(cmap='RdGy', vmin=-5*rms, vmax=5*rms)
ax[i+1, 0].imshow(myfblob.images[i], **img_opt)
ax[i+1, 1].imshow(myfblob.solution_model_images[i] + noise, **img_opt)
ax[i+1, 2].imshow(myfblob.images[i] - myfblob.solution_model_images[i], cmap='RdGy', vmin=-5*rms, vmax=5*rms)
ax[i+1, 3].imshow(myfblob.solution_chi_images[i], cmap='RdGy', vmin = -7, vmax = 7)
ax[i+1, 0].set_ylabel(myfblob.bands[i])
band = myfblob.bands[i]
for j, src in enumerate(myfblob.solution_catalog):
try:
mtype = src.name
except:
mtype = 'PointSource'
flux = src.getBrightness().getFlux(band)
chisq = myfblob.solution_chisq[j, i]
Nres = myfblob.n_residual_sources[i]
topt = dict(color=colors[j], transform = ax[i+1, 3].transAxes)
ystart = 0.99 - j * 0.4
ax[i+1, 3].text(1.05, ystart - 0.1, f'{j}) {mtype}', **topt)
ax[i+1, 3].text(1.05, ystart - 0.2, f' F({band}) = {flux:4.4f}', **topt)
ax[i+1, 3].text(1.05, ystart - 0.3, f' $\chi^{2}$ = {chisq:4.4f}', **topt)
if Nres > 0:
ax[i+1, 3].text(1.05, ystart - 0.4, f'{Nres} residual sources found!', **topt)
res_x = myfblob.residual_catalog[i]['x']
res_y = myfblob.residual_catalog[i]['y']
for x, y in zip(res_x, res_y):
ax[i+1, 3].scatter(x, y, marker='+', color='r')
for s, src in enumerate(myfblob.solution_catalog):
x, y = src.pos
color = colors[s]
for i in np.arange(1 + myfblob.n_bands):
for j in np.arange(4):
ax[i,j].plot([x, x], [y - 10, y - 5], c=color)
ax[i,j].plot([x - 10, x - 5], [y, y], c=color)
except:
logger.warning('Could not plot multiwavelength diagnostic figures')
[[ax[i,j].set(xlim=(0,myfblob.dims[1]), ylim=(0,myfblob.dims[0])) for i in np.arange(myfblob.n_bands+1)] for j in np.arange(4)]
#fig.suptitle(f'Solution for {blob_id}')
fig.subplots_adjust(wspace=0.01, hspace=0, right=0.8)
if myblob._is_itemblob:
sid = myblob.bcatalog['source_id'][0]
fig.savefig(os.path.join(conf.PLOT_DIR, f'{myblob.brick_id}_B{myblob.blob_id}_S{sid}.pdf'))
else:
fig.savefig(os.path.join(conf.PLOT_DIR, f'{myblob.brick_id}_B{myblob.blob_id}.pdf'))
plt.close()
def plot_srcprofile(blob, src, sid, bands=None):
if bands is None:
band = conf.MODELING_NICKNAME
nickname = conf.MODELING_NICKNAME
bidx = [0,]
bands = [band,]
outpath = os.path.join(conf.PLOT_DIR, f'T{blob.brick_id}_B{blob.blob_id}_S{sid}_{conf.MODELING_NICKNAME}_srcprofile.pdf')
elif (len(bands) == 1) & (bands[0] == conf.MODELING_NICKNAME):
band = conf.MODELING_NICKNAME
nickname = conf.MODELING_NICKNAME
bidx = [0,]
bands = [band,]
outpath = os.path.join(conf.PLOT_DIR, f'T{blob.brick_id}_B{blob.blob_id}_S{sid}_{conf.MODELING_NICKNAME}_srcprofile.pdf')
else:
bidx = [blob._band2idx(b, bands=blob.bands) for b in bands]
if bands[0].startswith(conf.MODELING_NICKNAME):
nickname = conf.MODELING_NICKNAME
else:
nickname = conf.MULTIBAND_NICKNAME
if len(bands) > 1:
outpath = os.path.join(conf.PLOT_DIR, f'T{blob.brick_id}_B{blob.blob_id}_S{sid}_{nickname}_srcprofile.pdf')
else:
outpath = os.path.join(conf.PLOT_DIR, f'T{blob.brick_id}_B{blob.blob_id}_S{sid}_{bands[0]}_srcprofile.pdf')
import matplotlib.backends.backend_pdf
pdf = matplotlib.backends.backend_pdf.PdfPages(outpath)
for idx, band in zip(bidx, bands):
if band == conf.MODELING_NICKNAME:
zpt = conf.MODELING_ZPT
rband = conf.MODELING_NICKNAME
elif band.startswith(conf.MODELING_NICKNAME):
band_name = band[len(conf.MODELING_NICKNAME)+1:]
# zpt = conf.MULTIBAND_ZPT[blob._band2idx(band_name)]
if band_name == conf.MODELING_NICKNAME:
zpt = conf.MODELING_ZPT
rband = band
else:
zpt = conf.MULTIBAND_ZPT[blob._band2idx(band_name)]
rband = conf.MODELING_NICKNAME + '_' + band_name
else:
zpt = conf.MULTIBAND_ZPT[blob._band2idx(band)]
rband = conf.MODELING_NICKNAME + '_' + band
# information
bid = blob.blob_id
bsrc = blob.bcatalog[blob.bcatalog['source_id'] == sid]
ra, dec = bsrc['RA'][0], bsrc['DEC'][0]
if nickname == conf.MODELING_NICKNAME:
xp0, yp0 = bsrc['x_orig'][0] - blob.subvector[1], bsrc['y_orig'][0] - blob.subvector[0]
else:
xp0, yp0 = bsrc['x_orig'][0] - blob.subvector[1] - blob.mosaic_origin[1] + conf.BRICK_BUFFER, bsrc['y_orig'][0] - blob.subvector[0] - blob.mosaic_origin[0] + conf.BRICK_BUFFER
xp, yp = src.pos[0], src.pos[1]
xps, yps = xp, yp
flux, flux_err = bsrc[f'FLUX_{band}'][0], bsrc[f'FLUXERR_{band}'][0]
mag, mag_err = bsrc[f'MAG_{band}'][0], bsrc[f'MAGERR_{band}'][0]
n_blob = bsrc['N_BLOB'][0]
chi2 = bsrc[f'CHISQ_{band}'][0]
snr = bsrc[f'SNR_{band}'][0]
is_resolved = False
if src.name not in ('PointSource', 'SimpleGalaxy'):
is_resolved = True
col = np.array(bsrc.colnames)[np.array([tcoln.startswith('REFF') for tcoln in bsrc.colnames])][0]
rband = col[len('REFF_'):]
reff, reff_err = np.exp(bsrc[f'REFF_{rband}'][0])*conf.PIXEL_SCALE, np.exp(bsrc[f'REFF_{rband}'][0])*bsrc[f'REFF_ERR_{rband}'][0]*2.303*conf.PIXEL_SCALE
ab, ab_err = bsrc[f'AB_{rband}'][0], bsrc[f'AB_ERR_{rband}'][0]
if ab == -99.0:
ab = -99
ab_err = -99
theta, theta_err = bsrc[f'THETA_{rband}'][0], bsrc[f'THETA_ERR_{rband}'][0]
if 'Sersic' in src.name:
nre, nre_err = bsrc[f'N_{rband}'][0], bsrc[f'N_ERR_{rband}'][0]
# images
img = blob.images[idx]
wgt = blob.weights[idx]
err = 1. / np.sqrt(wgt)
mask = blob.masks[idx]
seg = blob.segmap.copy()
seg[blob.segmap != sid] = 0
mod = blob.solution_model_images[idx]
chi = blob.solution_tractor.getChiImage(idx)
chi[blob.segmap != sid] = 0
res = img - mod
rms = np.median(blob.background_rms_images[idx])
xpix, ypix = | np.nonzero(seg) | numpy.nonzero |
"""
FluctuatingBackground.py
Author: <NAME>
Affiliation: UCLA
Created on: Mon Oct 10 14:29:54 PDT 2016
Description:
"""
import numpy as np
from math import factorial
from ..physics import Cosmology
from ..util import ParameterFile
from ..util.Stats import bin_c2e
from scipy.special import erfinv
from scipy.optimize import fsolve
from scipy.interpolate import interp1d
from scipy.integrate import quad, simps
from ..physics.Hydrogen import Hydrogen
from ..physics.HaloModel import HaloModel
from ..util.Math import LinearNDInterpolator
from ..populations.Composite import CompositePopulation
from ..physics.CrossSections import PhotoIonizationCrossSection
from ..physics.Constants import g_per_msun, cm_per_mpc, dnu, s_per_yr, c, \
s_per_myr, erg_per_ev, k_B, m_p, dnu, g_per_msun
root2 = np.sqrt(2.)
four_pi = 4. * np.pi
class Fluctuations(object): # pragma: no cover
def __init__(self, grid=None, **kwargs):
"""
Initialize a FluctuatingBackground object.
Creates an object capable of modeling fields that fluctuate spatially.
"""
self._kwargs = kwargs.copy()
self.pf = ParameterFile(**kwargs)
# Some useful physics modules
if grid is not None:
self.grid = grid
self.cosm = grid.cosm
else:
self.grid = None
self.cosm = Cosmology()
self._done = {}
@property
def zeta(self):
if not hasattr(self, '_zeta'):
raise AttributeError('Must set zeta by hand!')
return self._zeta
@zeta.setter
def zeta(self, value):
self._zeta = value
@property
def zeta_X(self):
if not hasattr(self, '_zeta_X'):
raise AttributeError('Must set zeta_X by hand!')
return self._zeta_X
@zeta_X.setter
def zeta_X(self, value):
self._zeta_X = value
@property
def hydr(self):
if not hasattr(self, '_hydr'):
if self.grid is None:
self._hydr = Hydrogen(**self.pf)
else:
self._hydr = self.grid.hydr
return self._hydr
@property
def xset(self):
if not hasattr(self, '_xset'):
xset_pars = \
{
'xset_window': 'tophat-real',
'xset_barrier': 'constant',
'xset_pdf': 'gaussian',
}
xset = ares.physics.ExcursionSet(**xset_pars)
xset.tab_M = pop.halos.tab_M
xset.tab_sigma = pop.halos.tab_sigma
xset.tab_ps = pop.halos.tab_ps_lin
xset.tab_z = pop.halos.tab_z
xset.tab_k = pop.halos.tab_k_lin
xset.tab_growth = pop.halos.tab_growth
self._xset = xset
return self._xset
def _overlap_region(self, dr, R1, R2):
"""
Volume of intersection between two spheres of radii R1 < R2.
"""
Vo = np.pi * (R2 + R1 - dr)**2 \
* (dr**2 + 2. * dr * R1 - 3. * R1**2 \
+ 2. * dr * R2 + 6. * R1 * R2 - 3. * R2**2) / 12. / dr
if type(Vo) == np.ndarray:
# Small-scale vs. large Scale
SS = dr <= R2 - R1
LS = dr >= R1 + R2
Vo[LS == 1] = 0.0
if type(R1) == np.ndarray:
Vo[SS == 1] = 4. * np.pi * R1[SS == 1]**3 / 3.
else:
Vo[SS == 1] = 4. * np.pi * R1**3 / 3.
return Vo
def IV(self, dr, R1, R2):
"""
Just a vectorized version of the overlap calculation.
"""
return self._overlap_region(dr, R1, R2)
def intersectional_volumes(self, dr, R1, R2, R3):
IV = self.IV
V11 = IV(dr, R1, R1)
zeros = np.zeros_like(V11)
if np.all(R2 == 0):
return V11, zeros, zeros, zeros, zeros, zeros
V12 = IV(dr, R1, R2)
V22 = IV(dr, R2, R2)
if np.all(R3 == 0):
return V11, V12, V22, zeros, zeros, zeros
V13 = IV(dr, R1, R3)
V23 = IV(dr, R2, R3)
V33 = IV(dr, R3, R3)
return V11, V12, V22, V13, V23, V33
def overlap_volumes(self, dr, R1, R2):
"""
Overlap volumes, i.e., volumes in which a source affects two points
in different ways. For example, V11 is the volume in which a source
ionizes both points (at separation `dr`), V12 is the volume in which
a source ionizes one point and heats the other, and so on.
In this order: V11, V12, V13, V22, V23, V33
"""
IV = self.IV
V1 = 4. * np.pi * R1**3 / 3.
if self.pf['ps_temp_model'] == 1:
V2 = 4. * np.pi * (R2**3 - R1**3) / 3.
else:
V2 = 4. * np.pi * R2**3 / 3.
Vt = 4. * np.pi * R2**3 / 3.
V11 = IV(dr, R1, R1)
if self.pf['ps_include_temp'] and self.pf['ps_temp_model'] == 2:
V12 = V1
else:
V12 = 2 * IV(dr, R1, R2) - IV(dr, R1, R1)
V22 = IV(dr, R2, R2)
if self.pf['ps_temp_model'] == 1:
V22 += -2. * IV(dr, R1, R2) + IV(dr, R1, R1)
if self.pf['ps_include_temp'] and self.pf['ps_temp_model'] == 1:
V1n = V1 - IV(dr, R1, R2)
elif self.pf['ps_include_temp'] and self.pf['ps_temp_model'] == 2:
V1n = V1
else:
V1n = V1 - V11
V2n = V2 - IV(dr, R2, R2)
if self.pf['ps_temp_model'] == 1:
V2n += IV(dr, R1, R2)
# 'anything' to one point, 'nothing' to other.
# Without temperature fluctuations, same as V1n
if self.pf['ps_include_temp']:
Van = Vt - IV(dr, R2, R2)
else:
Van = V1n
return V11, V12, V22, V1n, V2n, Van
def exclusion_volumes(self, dr, R1, R2, R3):
"""
Volume in which a single source only affects one
"""
pass
@property
def heating_ongoing(self):
if not hasattr(self, '_heating_ongoing'):
self._heating_ongoing = True
return self._heating_ongoing
@heating_ongoing.setter
def heating_ongoing(self, value):
self._heating_ongoing = value
def BubbleShellFillingFactor(self, z, R_s=None):
"""
"""
# Hard exit.
if not self.pf['ps_include_temp']:
return 0.0
Qi = self.MeanIonizedFraction(z)
if self.pf['ps_temp_model'] == 1:
R_i, M_b, dndm_b = self.BubbleSizeDistribution(z)
if Qi == 1:
return 0.0
if type(R_s) is np.ndarray:
nz = R_i > 0
const_rsize = np.allclose(np.diff(R_s[nz==1] / R_i[nz==1]), 0.0)
if const_rsize:
fvol = (R_s[0] / R_i[0])**3 - 1.
Qh = Qi * fvol
else:
V = 4. * np.pi * (R_s**3 - R_i**3) / 3.
Mmin = self.Mmin(z) * self.zeta
Qh = self.get_prob(z, M_b, dndm_b, Mmin, V,
exp=False, ep=0.0, Mmax=None)
#raise NotImplemented("No support for absolute scaling of hot bubbles yet.")
if (Qh > (1. - Qi) * 1.): #or Qh > 0.5: #or Qi > 0.5:
self.heating_ongoing = 0
Qh = np.minimum(Qh, 1. - Qi)
return Qh
else:
# This will get called if temperature fluctuations are off
return 0.0
elif self.pf['ps_temp_model'] == 2:
Mmin = self.Mmin(z) * self.zeta_X
R_i, M_b, dndm_b = self.BubbleSizeDistribution(z, ion=False)
V = 4. * np.pi * R_i**3 / 3.
Qh = self.get_prob(z, M_b, dndm_b, Mmin, V,
exp=False, ep=0.0, Mmax=None)
#Qh = self.BubbleFillingFactor(z, ion=False)
#print('Qh', Qh)
return np.minimum(Qh, 1. - Qi)
else:
raise NotImplemented('Uncrecognized option for BSD.')
#return min(Qh, 1.), min(Qc, 1.)
@property
def bsd_model(self):
return self.pf['bubble_size_dist'].lower()
def MeanIonizedFraction(self, z, ion=True):
Mmin = self.Mmin(z)
logM = np.log10(Mmin)
if ion:
if not self.pf['ps_include_ion']:
return 0.0
zeta = self.zeta
return np.minimum(1.0, zeta * self.halos.fcoll_2d(z, logM))
else:
if not self.pf['ps_include_temp']:
return 0.0
zeta = self.zeta_X
# Assume that each heated region contains the same volume
# of fully-ionized material.
Qi = self.MeanIonizedFraction(z, ion=True)
Qh = zeta * self.halos.fcoll_2d(z, logM) - Qi
return np.minimum(1.0 - Qi, Qh)
def delta_shell(self, z):
"""
Relative density != relative over-density.
"""
if not self.pf['ps_include_temp']:
return 0.0
if self.pf['ps_temp_model'] == 2:
return self.delta_bubble_vol_weighted(z, ion=False)
delta_i_bar = self.delta_bubble_vol_weighted(z)
rdens = self.pf["bubble_shell_rdens_zone_0"]
return rdens * (1. + delta_i_bar) - 1.
def BulkDensity(self, z, R_s):
Qi = self.MeanIonizedFraction(z)
#Qh = self.BubbleShellFillingFactor(z, R_s)
Qh = self.MeanIonizedFraction(z, ion=False)
delta_i_bar = self.delta_bubble_vol_weighted(z)
delta_h_bar = self.delta_shell(z)
if self.pf['ps_igm_model'] == 2:
delta_hal_bar = self.mean_halo_overdensity(z)
Qhal = self.Qhal(z, Mmax=self.Mmin(z))
else:
Qhal = 0.0
delta_hal_bar = 0.0
return -(delta_i_bar * Qi + delta_h_bar * Qh + delta_hal_bar * Qhal) \
/ (1. - Qi - Qh - Qhal)
def BubbleFillingFactor(self, z, ion=True, rescale=True):
"""
Fraction of volume filled by bubbles.
This is never actually used, but for reference, the mean ionized
fraction would be 1 - exp(-this). What we actually do is re-normalize
the bubble size distribution to guarantee Q = zeta * fcoll. See
MeanIonizedFraction and BubbleSizeDistribution for more details.
"""
if ion:
zeta = self.zeta
else:
zeta = self.zeta_X
if self.bsd_model is None:
R_i = self.pf['bubble_size']
V_i = 4. * np.pi * R_i**3 / 3.
ni = self.BubbleDensity(z)
Qi = 1. - np.exp(-ni * V_i)
elif self.bsd_model in ['fzh04', 'hmf']:
# Smallest bubble is one around smallest halo.
# Don't actually need its mass, just need index to correctly
# truncate integral.
Mmin = self.Mmin(z) * zeta
# M_b should just be self.m? No.
R_i, M_b, dndm_b = self.BubbleSizeDistribution(z, ion=ion,
rescale=rescale)
V_i = 4. * np.pi * R_i**3 / 3.
iM = np.argmin(np.abs(Mmin - M_b))
Qi = np.trapz(dndm_b[iM:] * M_b[iM:] * V_i[iM:], x=np.log(M_b[iM:]))
# This means reionization is over.
if self.bsd_model == 'fzh04':
if self._B0(z, zeta) <= 0:
return 1.
else:
raise NotImplemented('Uncrecognized option for BSD.')
return min(Qi, 1.)
# Grab heated phase to enforce BC
#Rs = self.BubbleShellRadius(z, R_i)
#Vsh = 4. * np.pi * (Rs - R_i)**3 / 3.
#Qh = np.trapz(dndm * Vsh * M_b, x=np.log(M_b))
#if lya and self.pf['bubble_pod_size_func'] in [None, 'const', 'linear']:
# Rc = self.BubblePodRadius(z, R_i, zeta, zeta_lya)
# Vc = 4. * np.pi * (Rc - R_i)**3 / 3.
#
# if self.pf['powspec_rescale_Qlya']:
# # This isn't actually correct since we care about fluxes
# # not number of photons, but fine for now.
# Qc = min(zeta_lya * self.halos.fcoll_2d(z, np.log10(self.Mmin(z))), 1)
# else:
# Qc = np.trapz(dndlnm[iM:] * Vc[iM:], x=np.log(M_b[iM:]))
#
# return min(Qc, 1.)
#
#elif lya and self.pf['bubble_pod_size_func'] == 'fzh04':
# return self.BubbleFillingFactor(z, zeta_lya, None, lya=False)
#else:
@property
def tab_Mmin(self):
if not hasattr(self, '_tab_Mmin'):
raise AttributeError('Must set Mmin by hand (right now)')
return self._tab_Mmin
@tab_Mmin.setter
def tab_Mmin(self, value):
if type(value) is not np.ndarray:
value = np.ones_like(self.halos.tab_z) * value
else:
assert value.size == self.halos.tab_z.size
self._tab_Mmin = value
def Mmin(self, z):
return np.interp(z, self.halos.tab_z, self.tab_Mmin)
def mean_halo_bias(self, z):
bias = self.halos.Bias(z)
M_h = self.halos.tab_M
iz_h = np.argmin(np.abs(z - self.halos.tab_z))
iM_h = np.argmin(np.abs(self.Mmin(z) - M_h))
dndm_h = self.halos.tab_dndm[iz_h]
return 1.0
#return simps(M_h * dndm_h * bias, x=np.log(M_h)) \
# / simps(M_h * dndm_h, x=np.log(M_h))
def tab_bubble_bias(self, zeta):
if not hasattr(self, '_tab_bubble_bias'):
func = lambda z: self._fzh04_eq22(z, zeta)
self._tab_bubble_bias = np.array(map(func, self.halos.tab_z_ps))
return self._tab_bubble_bias
def _fzh04_eq22(self, z, ion=True):
if ion:
zeta = self.zeta
else:
zeta = self.zeta_X
iz = np.argmin(np.abs(z - self.halos.tab_z))
s = self.sigma
S = s**2
#return 1. + ((self.LinearBarrier(z, zeta, zeta) / S - (1. / self._B0(z, zeta))) \
# / self._growth_factor(z))
return 1. + (self._B0(z, zeta)**2 / S / self._B(z, zeta, zeta))
def bubble_bias(self, z, ion=True):
"""
Eq. 9.24 in Loeb & Furlanetto (2013) or Eq. 22 in FZH04.
"""
return self._fzh04_eq22(z, ion)
#iz = np.argmin(np.abs(z - self.halos.tab_z_ps))
#
#x, y = self.halos.tab_z_ps, self.tab_bubble_bias(zeta)[iz]
#
#
#
#m = (y[-1] - y[-2]) / (x[-1] - x[-2])
#
#return m * z + y[-1]
#iz = np.argmin(np.abs(z - self.halos.tab_z))
#s = self.sigma
#S = s**2
#
##return 1. + ((self.LinearBarrier(z, zeta, zeta) / S - (1. / self._B0(z, zeta))) \
## / self._growth_factor(z))
#
#fzh04 = 1. + (self._B0(z, zeta)**2 / S / self._B(z, zeta, zeta))
#
#return fzh04
def mean_bubble_bias(self, z, ion=True):
"""
"""
R, M_b, dndm_b = self.BubbleSizeDistribution(z, ion=ion)
#if ('h' in term) or ('c' in term) and self.pf['powspec_temp_method'] == 'shell':
# R_s, Rc = self.BubbleShellRadius(z, R_i)
# R = R_s
#else:
if ion:
zeta = self.zeta
else:
zeta = self.zeta_X
V = 4. * np.pi * R**3 / 3.
Mmin = self.Mmin(z) * zeta
iM = np.argmin(np.abs(Mmin - self.m))
bHII = self.bubble_bias(z, ion)
#tmp = dndm[iM:]
#print(z, len(tmp[np.isnan(tmp)]), len(bHII[np.isnan(bHII)]))
#imax = int(min(np.argwhere(np.isnan(R_i))))
if ion and self.pf['ps_include_ion']:
Qi = self.MeanIonizedFraction(z)
elif ion and not self.pf['ps_include_ion']:
raise NotImplemented('help')
elif (not ion) and self.pf['ps_include_temp']:
Qi = self.MeanIonizedFraction(z, ion=False)
elif ion and self.pf['ps_include_temp']:
Qi = self.MeanIonizedFraction(z, ion=False)
else:
raise NotImplemented('help')
return np.trapz(dndm_b[iM:] * V[iM:] * bHII[iM:] * M_b[iM:],
x=np.log(M_b[iM:])) / Qi
#def delta_bubble_mass_weighted(self, z, zeta):
# if self._B0(z, zeta) <= 0:
# return 0.
#
# R_i, M_b, dndm_b = self.BubbleSizeDistribution(z, zeta)
# V_i = 4. * np.pi * R_i**3 / 3.
#
# Mmin = self.Mmin(z) * zeta
# iM = np.argmin(np.abs(Mmin - self.m))
# B = self._B(z, zeta)
# rho0 = self.cosm.mean_density0
#
# dm_ddel = rho0 * V_i
#
# return simps(B[iM:] * dndm_b[iM:] * M_b[iM:], x=np.log(M_b[iM:]))
def delta_bubble_vol_weighted(self, z, ion=True):
if not self.pf['ps_include_ion']:
return 0.0
if not self.pf['ps_include_xcorr_ion_rho']:
return 0.0
if ion:
zeta = self.zeta
else:
zeta = self.zeta_X
if self._B0(z, zeta) <= 0:
return 0.
R_i, M_b, dndm_b = self.BubbleSizeDistribution(z, ion=ion)
V_i = 4. * np.pi * R_i**3 / 3.
Mmin = self.Mmin(z) * zeta
iM = np.argmin(np.abs(Mmin - self.m))
B = self._B(z, ion=ion)
return np.trapz(B[iM:] * dndm_b[iM:] * V_i[iM:] * M_b[iM:],
x=np.log(M_b[iM:]))
#def mean_bubble_overdensity(self, z, zeta):
# if self._B0(z, zeta) <= 0:
# return 0.
#
# R_i, M_b, dndm_b = self.BubbleSizeDistribution(z, zeta)
# V_i = 4. * np.pi * R_i**3 / 3.
#
# Mmin = self.Mmin(z) * zeta
# iM = np.argmin(np.abs(Mmin - self.m))
# B = self._B(z, zeta)
# rho0 = self.cosm.mean_density0
#
# dm_ddel = rho0 * V_i
#
# return simps(B[iM:] * dndm_b[iM:] * M_b[iM:], x=np.log(M_b[iM:]))
def mean_halo_abundance(self, z, Mmin=False):
M_h = self.halos.tab_M
iz_h = np.argmin(np.abs(z - self.halos.tab_z))
if Mmin:
iM_h = np.argmin(np.abs(self.Mmin(z) - M_h))
else:
iM_h = 0
dndm_h = self.halos.tab_dndm[iz_h]
return np.trapz(M_h * dndm_h, x=np.log(M_h))
def spline_cf_mm(self, z):
if not hasattr(self, '_spline_cf_mm_'):
self._spline_cf_mm_ = {}
if z not in self._spline_cf_mm_:
iz = np.argmin(np.abs(z - self.halos.tab_z_ps))
self._spline_cf_mm_[z] = interp1d(np.log(self.halos.tab_R),
self.halos.tab_cf_mm[iz], kind='cubic', bounds_error=False,
fill_value=0.0)
return self._spline_cf_mm_[z]
def excess_probability(self, z, R, ion=True):
"""
This is the excess probability that a point is ionized given that
we already know another point (at distance r) is ionized.
"""
# Function of bubble mass (bubble size)
bHII = self.bubble_bias(z, ion)
bbar = self.mean_bubble_bias(z, ion)
if R < self.halos.tab_R.min():
print("R too small")
if R > self.halos.tab_R.max():
print("R too big")
xi_dd = self.spline_cf_mm(z)(np.log(R))
#if term == 'ii':
return bHII * bbar * xi_dd
#elif term == 'id':
# return bHII * bbar * xi_dd
#else:
# raise NotImplemented('help!')
def _K(self, zeta):
return erfinv(1. - (1. / zeta))
def _growth_factor(self, z):
return np.interp(z, self.halos.tab_z, self.halos.tab_growth,
left=np.inf, right=np.inf)
def _delta_c(self, z):
return self.cosm.delta_c0 / self._growth_factor(z)
def _B0(self, z, ion=True):
if ion:
zeta = self.zeta
else:
zeta = self.zeta_X
iz = np.argmin(np.abs(z - self.halos.tab_z))
s = self.sigma
# Variance on scale of smallest collapsed object
sigma_min = self.sigma_min(z)
return self._delta_c(z) - root2 * self._K(zeta) * sigma_min
def _B1(self, z, ion=True):
if ion:
zeta = self.zeta
else:
zeta = self.zeta_X
iz = np.argmin(np.abs(z - self.halos.tab_z))
s = self.sigma #* self.halos.growth_factor[iz]
sigma_min = self.sigma_min(z)
return self._K(zeta) / np.sqrt(2. * sigma_min**2)
def _B(self, z, ion=True, zeta_min=None):
return self.LinearBarrier(z, ion, zeta_min=zeta_min)
def LinearBarrier(self, z, ion=True, zeta_min=None):
if ion:
zeta = self.zeta
else:
zeta = self.zeta_X
iz = np.argmin(np.abs(z - self.halos.tab_z))
s = self.sigma #/ self.halos.growth_factor[iz]
if zeta_min is None:
zeta_min = zeta
return self._B0(z, ion) + self._B1(z, ion) * s**2
def Barrier(self, z, ion=True, zeta_min=None):
"""
Full barrier.
"""
if ion:
zeta = self.zeta
else:
zeta = self.zeta_X
if zeta_min is None:
zeta_min = zeta
#iz = np.argmin(np.abs(z - self.halos.tab_z))
#D = self.halos.growth_factor[iz]
sigma_min = self.sigma_min(z)
#Mmin = self.Mmin(z)
#sigma_min = np.interp(Mmin, self.halos.M, self.halos.sigma_0)
delta = self._delta_c(z)
return delta - np.sqrt(2.) * self._K(zeta) \
* np.sqrt(sigma_min**2 - self.sigma**2)
#return self.cosm.delta_c0 - np.sqrt(2.) * self._K(zeta) \
# * np.sqrt(sigma_min**2 - s**2)
def sigma_min(self, z):
Mmin = self.Mmin(z)
return np.interp(Mmin, self.halos.tab_M, self.halos.tab_sigma)
#def BubblePodSizeDistribution(self, z, zeta):
# if self.pf['powspec_lya_method'] == 1:
# # Need to modify zeta and critical threshold
# Rc, Mc, dndm = self.BubbleSizeDistribution(z, zeta)
# return Rc, Mc, dndm
# else:
# raise NotImplemented('help please')
@property
def m(self):
"""
Mass array used for bubbles.
"""
if not hasattr(self, '_m'):
self._m = 10**np.arange(5, 18.1, 0.1)
return self._m
@property
def sigma(self):
if not hasattr(self, '_sigma'):
self._sigma = np.interp(self.m, self.halos.tab_M, self.halos.tab_sigma)
# Crude but chill it's temporary
bigm = self.m > self.halos.tab_M.max()
if np.any(bigm):
print("WARNING: Extrapolating sigma to higher masses.")
slope = np.diff(np.log10(self.halos.tab_sigma[-2:])) \
/ np.diff(np.log10(self.halos.tab_M[-2:]))
self._sigma[bigm == 1] = self.halos.tab_sigma[-1] \
* (self.m[bigm == 1] / self.halos.tab_M.max())**slope
return self._sigma
@property
def dlns_dlnm(self):
if not hasattr(self, '_dlns_dlnm'):
self._dlns_dlnm = np.interp(self.m, self.halos.tab_M, self.halos.tab_dlnsdlnm)
bigm = self.m > self.halos.tab_M.max()
if np.any(bigm):
print("WARNING: Extrapolating dlns_dlnm to higher masses.")
slope = np.diff(np.log10(np.abs(self.halos.tab_dlnsdlnm[-2:]))) \
/ np.diff(np.log10(self.halos.tab_M[-2:]))
self._dlns_dlnm[bigm == 1] = self.halos.tab_dlnsdlnm[-1] \
* (self.m[bigm == 1] / self.halos.tab_M.max())**slope
return self._dlns_dlnm
def BubbleSizeDistribution(self, z, ion=True, rescale=True):
"""
Compute the ionized bubble size distribution.
Parameters
----------
z: int, float
Redshift of interest.
zeta : int, float, np.ndarray
Ionizing efficiency.
Returns
-------
Tuple containing (in order) the bubble radii, masses, and the
differential bubble size distribution. Each is an array of length
self.halos.tab_M, i.e., with elements corresponding to the masses
used to compute the variance of the density field.
"""
if ion:
zeta = self.zeta
else:
zeta = self.zeta_X
if ion and not self.pf['ps_include_ion']:
R_i = M_b = dndm = np.zeros_like(self.m)
return R_i, M_b, dndm
if (not ion) and not self.pf['ps_include_temp']:
R_i = M_b = dndm = np.zeros_like(self.m)
return R_i, M_b, dndm
reionization_over = False
# Comoving matter density
rho0_m = self.cosm.mean_density0
rho0_b = rho0_m * self.cosm.fbaryon
# Mean (over-)density of bubble material
delta_B = self._B(z, ion)
if self.bsd_model is None:
if self.pf['bubble_density'] is not None:
R_i = self.pf['bubble_size']
M_b = (4. * np.pi * Rb**3 / 3.) * rho0_m
dndm = self.pf['bubble_density']
else:
raise NotImplementedError('help')
elif self.bsd_model == 'hmf':
M_b = self.halos.tab_M * zeta
# Assumes bubble material is at cosmic mean density
R_i = (3. * M_b / rho0_b / 4. / np.pi)**(1./3.)
iz = np.argmin(np.abs(z - self.halos.tab_z))
dndm = self.halos.tab_dndm[iz].copy()
elif self.bsd_model == 'fzh04':
# Just use array of halo mass as array of ionized region masses.
# Arbitrary at this point, just need an array of masses.
# Plus, this way, the sigma's from the HMF are OK.
M_b = self.m
# Radius of ionized regions as function of delta (mass)
R_i = (3. * M_b / rho0_m / (1. + delta_B) / 4. / np.pi)**(1./3.)
V_i = four_pi * R_i**3 / 3.
# This is Eq. 9.38 from Steve's book.
# The factors of 2, S, and M_b are from using dlns instead of
# dS (where S=s^2)
dndm = rho0_m * self.pcross(z, ion) * 2 * np.abs(self.dlns_dlnm) \
* self.sigma**2 / M_b**2
# Reionization is over!
# Only use barrier condition if we haven't asked to rescale
# or supplied Q ourselves.
if self._B0(z, ion) <= 0:
reionization_over = True
dndm = np.zeros_like(dndm)
#elif Q is not None:
# if Q == 1:
# reionization_over = True
# dndm = np.zeros_like(dndm)
else:
raise NotImplementedError('Unrecognized option: %s' % self.pf['bubble_size_dist'])
# This is a trick to guarantee that the integral over the bubble
# size distribution yields the mean ionized fraction.
if (not reionization_over) and rescale:
Mmin = self.Mmin(z) * zeta
iM = np.argmin(np.abs(M_b - Mmin))
Qi = np.trapz(dndm[iM:] * V_i[iM:] * M_b[iM:], x=np.log(M_b[iM:]))
xibar = self.MeanIonizedFraction(z, ion=ion)
dndm *= -np.log(1. - xibar) / Qi
return R_i, M_b, dndm
def pcross(self, z, ion=True):
"""
Up-crossing probability.
"""
if ion:
zeta = self.zeta
else:
zeta = self.zeta_X
S = self.sigma**2
Mmin = self.Mmin(z) #* zeta # doesn't matter for zeta=const
if type(zeta) == np.ndarray:
raise NotImplemented('this is wrong.')
zeta_min = np.interp(Mmin, self.m, zeta)
else:
zeta_min = zeta
zeros = np.zeros_like(self.sigma)
B0 = self._B0(z, ion)
B1 = self._B1(z, ion)
Bl = self.LinearBarrier(z, ion=ion, zeta_min=zeta_min)
p = (B0 / np.sqrt(2. * np.pi * S**3)) * np.exp(-0.5 * Bl**2 / S)
#p = (B0 / np.sqrt(2. * np.pi * S**3)) \
# * np.exp(-0.5 * B0**2 / S) * np.exp(-B0 * B1) * np.exp(-0.5 * B1**2 / S)
return p#np.maximum(p, zeros)
@property
def halos(self):
if not hasattr(self, '_halos'):
self._halos = HaloModel(**self.pf)
return self._halos
@property
def Emin_X(self):
if not hasattr(self, '_Emin_X'):
xrpop = None
for i, pop in enumerate(self.pops):
if not pop.is_src_heat_fl:
continue
if xrpop is not None:
raise AttributeError('help! can only handle 1 X-ray pop right now')
xrpop = pop
self._Emin_X = pop.src.Emin
return self._Emin_X
def get_Nion(self, z, R_i):
return 4. * np.pi * (R_i * cm_per_mpc / (1. + z))**3 \
* self.cosm.nH(z) / 3.
def _cache_jp(self, z, term):
if not hasattr(self, '_cache_jp_'):
self._cache_jp_ = {}
if z not in self._cache_jp_:
self._cache_jp_[z] = {}
if term not in self._cache_jp_[z]:
return None
else:
#print("Loaded P_{} at z={} from cache.".format(term, z))
return self._cache_jp_[z][term]
def _cache_cf(self, z, term):
if not hasattr(self, '_cache_cf_'):
self._cache_cf_ = {}
if z not in self._cache_cf_:
self._cache_cf_[z] = {}
if term not in self._cache_cf_[z]:
return None
else:
#print("Loaded cf_{} at z={} from cache.".format(term, z))
return self._cache_cf_[z][term]
def _cache_ps(self, z, term):
if not hasattr(self, '_cache_ps_'):
self._cache_ps_ = {}
if z not in self._cache_ps_:
self._cache_ps_[z] = {}
if term not in self._cache_ps_[z]:
return None
else:
return self._cache_ps_[z][term]
@property
def is_Rs_const(self):
if not hasattr(self, '_is_Rs_const'):
self._is_Rs_const = True
return self._is_Rs_const
@is_Rs_const.setter
def is_Rs_const(self, value):
self._is_Rs_const = value
def _cache_Vo(self, z):
if not hasattr(self, '_cache_Vo_'):
self._cache_Vo_ = {}
if z in self._cache_Vo_:
return self._cache_Vo_[z]
#if self.is_Rs_const and len(self._cache_Vo_.keys()) > 0:
# return self._cache_Vo_[self._cache_Vo_.keys()[0]]
return None
def _cache_IV(self, z):
if not hasattr(self, '_cache_IV_'):
self._cache_IV_ = {}
if z in self._cache_IV_:
return self._cache_IV_[z]
#if self.is_Rs_const and len(self._cache_IV_.keys()) > 0:
# return self._cache_IV_[self._cache_IV_.keys()[0]]
return None
def _cache_p(self, z, term):
if not hasattr(self, '_cache_p_'):
self._cache_p_ = {}
if z not in self._cache_p_:
self._cache_p_[z] = {}
if term not in self._cache_p_[z]:
return None
else:
return self._cache_p_[z][term]
def mean_halo_overdensity(self, z):
# Mean density of halos (mass is arbitrary)
rho_h = self.halos.MeanDensity(1e8, z) * cm_per_mpc**3 / g_per_msun
return rho_h / self.cosm.mean_density0 - 1.
def Qhal(self, z, Mmin=None, Mmax=None):
"""
This may not be quite right, since we just integrate over the mass
range we have....
"""
M_h = self.halos.tab_M
iz_h = np.argmin(np.abs(z - self.halos.tab_z))
dndm_h = self.halos.tab_dndm[iz_h]
# Volume of halos (within virial radii)
Rvir = self.halos.VirialRadius(M_h, z) / 1e3 # Convert to Mpc
Vvir = 4. * np.pi * Rvir**3 / 3.
if Mmin is not None:
imin = np.argmin(np.abs(M_h - Mmin))
else:
imin = 0
if Mmax is not None:
imax = np.argmin(np.abs(M_h - Mmax))
else:
imax = None
integ = dndm_h * Vvir * M_h
Q_hal = 1. - np.exp(-np.trapz(integ[imin:imax],
x=np.log(M_h[imin:imax])))
return Q_hal
#return self.get_prob(z, M_h, dndm_h, Mmin, Vvir, exp=False, ep=0.0,
# Mmax=Mmax)
def ExpectationValue1pt(self, z, term='i', R_s=None, R3=None,
Th=500.0, Ts=None, Tk=None, Ja=None):
"""
Compute the probability that a point is something.
These are the one point terms in brackets, e.g., <x>, <x delta>, etc.
Note that use of the asterisk is to imply that both quatities
are in the same set of brackets. Maybe a better way to handle this
notationally...
"""
##
# Check cache for match
##
cached_result = self._cache_p(z, term)
if cached_result is not None:
return cached_result
Qi = self.MeanIonizedFraction(z)
Qh = self.MeanIonizedFraction(z, ion=False)
if self.pf['ps_igm_model'] == 2:
Qhal = self.Qhal(z, Mmax=self.Mmin(z))
del_hal = self.mean_halo_overdensity(z)
else:
Qhal = 0.0
del_hal = 0.0
Qb = 1. - Qi - Qh - Qhal
Tcmb = self.cosm.TCMB(z)
del_i = self.delta_bubble_vol_weighted(z)
del_h = self.delta_shell(z)
del_b = self.BulkDensity(z, R_s)
ch = self.TempToContrast(z, Th=Th, Tk=Tk, Ts=Ts, Ja=Ja)
if Ts is not None:
cb = Tcmb / Ts
else:
cb = 0.0
##
# Otherwise, get to it.
##
if term == 'b':
val = 1. - Qi - Qh - Qhal
elif term == 'i':
val = Qi
elif term == 'n':
val = 1. - Qi
elif term == 'h':
assert R_s is not None
val = Qh
elif term in ['m', 'd']:
val = 0.0
elif term in ['n*d', 'i*d']:
# <xd> = <(1-x_i)d> = <d> - <x_i d> = - <x_i d>
if self.pf['ps_include_xcorr_ion_rho']:
if term == 'i*d':
val = Qi * del_i
else:
val = -Qi * del_i
else:
val = 0.0
elif term == 'pc':
# <psi * c> = <x (1 + d) c>
# = <(1 - i) (1 + d) c> = <(1 + d) c> - <i (1 + d) c>
# ...
# = <c> + <cd>
avg_c = Qh * ch + Qb * cb
if self.pf['ps_include_xcorr_hot_rho']:
val = avg_c \
+ Qh * ch * del_h \
+ Qb * cb * del_b
else:
val = avg_c
elif term in ['ppc', 'ppcc']:
avg_psi = self.ExpectationValue1pt(z, term='psi',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
avg_c = self.ExpectationValue1pt(z, term='c',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
if term == 'ppc':
val = avg_psi**2 * avg_c
else:
val = avg_psi**2 * avg_c**2
#cc = Qh**2 * ch**2 \
# + 2 * Qh * Qb * ch * cb \
# + Qb**2 * cb**2
#ccd = Qh**2 * ch**2 * delta_h_bar \
# + Qh * Qb * ch * cb * delta_h_bar \
# + Qh * Qb * ch * cb * delta_b_bar \
# + Qb**2 * cb**2 * delta_b_bar
elif term == 'c*d':
if self.pf['ps_include_xcorr_hot_rho']:
val = Qh * ch * del_h + Qb * cb * del_b
else:
val = 0.0
elif term.strip() == 'i*h':
val = 0.0
elif term.strip() == 'n*h':
# <xh> = <h> - <x_i h> = <h>
val = Qh
elif term.strip() == 'i*c':
val = 0.0
elif term == 'c':
val = ch * Qh + cb * Qb
elif term.strip() == 'n*c':
# <xc> = <c> - <x_i c>
val = ch * Qh
elif term == 'psi':
# <psi> = <x (1 + d)> = <x> + <xd> = 1 - <x_i> + <d> - <x_i d>
# = 1 - <x_i> - <x_i d>
#avg_xd = self.ExpectationValue1pt(z, zeta, term='n*d',
# R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#avg_x = self.ExpectationValue1pt(z, zeta, term='n',
# R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#
#val = avg_x + avg_xd
avg_id = self.ExpectationValue1pt(z, term='i*d',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
avg_i = self.ExpectationValue1pt(z, term='i',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
val = 1. - avg_i - avg_id
elif term == 'phi':
# <phi> = <psi * (1 - c)> = <psi> - <psi * c>
# <psi * c> = <x * c> + <x * c * d>
# = <c> - <x_i c> + <cd> - <x_i c * d>
avg_psi = self.ExpectationValue1pt(z, term='psi',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
avg_psi_c = self.ExpectationValue1pt(z, term='pc',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
val = avg_psi - avg_psi_c
# <phi> = <psi * (1 + c)> = <psi> + <psi * c>
#
# <psi * c> = <x * c> + <x * c * d>
# = <c> - <x_i c> + <cd> - <x_i c * d>
#avg_xcd = self.ExpectationValue1pt(z, zeta, term='n*d*c',
# R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#
## Equivalent to <c> in binary field model.
#ch = self.TempToContrast(z, Th=Th, Tk=Tk, Ts=Ts, Ja=Ja)
#ci = self.BubbleContrast(z, Th=Th, Tk=Tk, Ts=Ts, Ja=Ja)
#avg_c = self.ExpectationValue1pt(z, zeta, term='c',
# R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#avg_cd = self.ExpectationValue1pt(z, zeta, term='c*d',
# R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#avg_id = self.ExpectationValue1pt(z, zeta, term='i*d',
# R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#
#avg_psi = self.ExpectationValue1pt(z, zeta, term='psi',
# R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#avg_psi_c = avg_c - ci * Qi + avg_cd - avg_id * ci
#
## Tagged on these last two terms if c=1 (ionized regions)
#val = avg_psi + avg_psi_c
elif term == '21':
# dTb = T0 * (1 + d21) = T0 * xHI * (1 + d) = T0 * psi
# so d21 = psi - 1
if self.pf['ps_include_temp']:
avg_phi = self.ExpectationValue1pt(z, term='phi',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
val = avg_phi - 1.
else:
avg_psi = self.ExpectationValue1pt(z, term='psi',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
val = avg_psi - 1.
elif term == 'o':
# <omega>^2 = <psi * c>^2 - 2 <psi> <psi * c>
avg_psi = self.ExpectationValue1pt(z, term='psi',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
avg_psi_c = self.ExpectationValue1pt(z, term='pc',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
# <omega>^2 = <psi c>^2 - 2 <psi c> <psi>
val = np.sqrt(avg_psi_c**2 - 2. * avg_psi_c * avg_psi)
elif term == 'oo':
avg_psi = self.ExpectationValue1pt(z, term='psi',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
avg_psi_c = self.ExpectationValue1pt(z, term='pc',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
# <omega>^2 = <psi c>^2 - 2 <psi c> <psi>
val = avg_psi_c**2 - 2. * avg_psi_c * avg_psi
else:
raise ValueError('Don\' know how to handle <{}>'.format(term))
self._cache_p_[z][term] = val
return val
@property
def _getting_basics(self):
if not hasattr(self, '_getting_basics_'):
self._getting_basics_ = False
return self._getting_basics_
def get_basics(self, z, R, R_s, Th, Ts, Tk, Ja):
self._getting_basics_ = True
basics = {}
for term in ['ii', 'ih', 'ib', 'hh', 'hb', 'bb']:
cache = self._cache_jp(z, term)
if self.pf['ps_include_temp'] and self.pf['ps_temp_model'] == 2:
Qi = self.MeanIonizedFraction(z)
Qh = self.MeanIonizedFraction(z, ion=False)
if term == 'ih':
P = Qi * Qh * np.ones_like(R)
P1 = P2 = np.zeros_like(R)
basics[term] = P, P1, P2
continue
elif term == 'ib':
P = Qi * (1. - Qi - Qh) * np.ones_like(R)
P1 = P2 = np.zeros_like(R)
basics[term] = P, P1, P2
continue
elif term == 'hb':
P = Qh * (1. - Qi - Qh) * np.ones_like(R)
P1 = P2 = np.zeros_like(R)
basics[term] = P, P1, P2
continue
#elif term == 'bb':
# P = (1. - Qi - Qh)**2 * np.ones_like(R)
# P1 = P2 = np.zeros_like(R)
# basics[term] = P, P1, P2
# continue
if cache is None and term != 'bb':
P, P1, P2 = self.ExpectationValue2pt(z,
R=R, term=term, R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
elif cache is None and term == 'bb':
P = 1. - (basics['ii'][0] + 2 * basics['ib'][0]
+ 2 * basics['ih'][0] + basics['hh'][0] + 2 * basics['hb'][0])
P1 = P2 = np.zeros_like(P)
self._cache_jp_[z][term] = R, P, np.zeros_like(P), np.zeros_like(P)
else:
P, P1, P2 = cache[1:]
basics[term] = P, P1, P2
self._getting_basics_ = False
return basics
def ExpectationValue2pt(self, z, R, term='ii', R_s=None, R3=None,
Th=500.0, Ts=None, Tk=None, Ja=None, k=None):
"""
Essentially a wrapper around JointProbability that scales
terms like <cc'>, <xc'>, etc., from their component probabilities
<hh'>, <ih'>, etc.
Parameters
----------
z : int, float
zeta : int, float
Ionization efficiency
R : np.ndarray
Array of scales to consider.
term : str
Returns
-------
Tuple: total, one-source, two-source contributions to joint probability.
"""
##
# Check cache for match
##
#cached_result = self._cache_jp(z, term)
#
#if cached_result is not None:
# _R, _jp, _jp1, _jp2 = cached_result
#
# if _R.size == R.size:
# if np.allclose(_R, R):
# return cached_result[1:]
#
# print("interpolating jp_{}".format(ii))
# return np.interp(R, _R, _jp), np.interp(R, _R, _jp1), np.interp(R, _R, _jp2)
# Remember, we scaled the BSD so that these two things are equal
# by construction.
xibar = Q = Qi = self.MeanIonizedFraction(z)
# Call this early so that heating_ongoing is set before anything
# else can happen.
#Qh = self.BubbleShellFillingFactor(z, R_s=R_s)
Qh = self.MeanIonizedFraction(z, ion=False)
delta_i_bar = self.delta_bubble_vol_weighted(z)
delta_h_bar = self.delta_shell(z)
delta_b_bar = self.BulkDensity(z, R_s)
Tcmb = self.cosm.TCMB(z)
ch = self.TempToContrast(z, Th=Th, Tk=Tk, Ts=Ts, Ja=Ja)
if Ts is None:
cb = 0.0
else:
cb = Tcmb / Ts
Rones = np.ones_like(R)
Rzeros = np.zeros_like(R)
# If reionization is over, don't waste our time!
if xibar == 1:
return np.ones(R.size), Rzeros, Rzeros
iz = np.argmin(np.abs(z - self.halos.tab_z_ps))
iz_hmf = np.argmin(np.abs(z - self.halos.tab_z))
# Grab the matter power spectrum
if R.size == self.halos.tab_R.size:
if np.allclose(R, self.halos.tab_R):
xi_dd = self.halos.tab_cf_mm[iz]
else:
xi_dd = self.spline_cf_mm(z)(np.log(R))
else:
xi_dd = self.spline_cf_mm(z)(np.log(R))
# Some stuff we need
R_i, M_b, dndm_b = self.BubbleSizeDistribution(z)
V_i = 4. * np.pi * R_i**3 / 3.
if self.pf['ps_include_temp']:
if self.pf['ps_temp_model'] == 1:
V_h = 4. * np.pi * (R_s**3 - R_i**3) / 3.
V_ioh = 4. * np.pi * R_s**3 / 3.
dndm_s = dndm_b
M_s = M_b
zeta_X = 0.0
elif self.pf['ps_temp_model'] == 2:
zeta_X = self.zeta_X
R_s, M_s, dndm_s = self.BubbleSizeDistribution(z, ion=False)
V_h = 4. * np.pi * R_s**3 / 3.
V_ioh = 4. * np.pi * R_s**3 / 3.
else:
raise NotImplemented('help')
else:
zeta_X = 0
if R_s is None:
R_s = np.zeros_like(R_i)
V_h = np.zeros_like(R_i)
V_ioh = V_i
zeta_X = 0.0
if R3 is None:
R3 = np.zeros_like(R_i)
##
# Before we begin: anything we're turning off?
##
if not self.pf['ps_include_ion']:
if term == 'ii':
self._cache_jp_[z][term] = R, Qi**2 * Rones, Rzeros, Rzeros
return Qi**2 * Rones, Rzeros, Rzeros
elif term in ['id']:
self._cache_jp_[z][term] = R, Rzeros, Rzeros, Rzeros
return Rzeros, Rzeros, Rzeros
elif term == 'idd':
ev2pt = Qi * xi_dd
self._cache_jp_[z][term] = R, ev2pt, Rzeros, Rzeros
return ev2pt, Rzeros, Rzeros #
elif term == 'iidd':
ev2pt = Qi**2 * xi_dd
self._cache_jp_[z][term] = R, ev2pt, Rzeros, Rzeros
return ev2pt, Rzeros, Rzeros
#elif 'i' in term:
# #self._cache_jp_[z][term] = R, Rzeros, Rzeros, Rzeros
# return Rzeros, Rzeros, Rzeros
# also iid, iidd
if not self.pf['ps_include_temp']:
if ('c' in term) or ('h' in term):
return Rzeros, Rzeros, Rzeros
##
# Handy
##
if not self._getting_basics:
basics = self.get_basics(z, R, R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
if term in basics:
return basics[term]
_P_ii, _P_ii_1, _P_ii_2 = basics['ii']
_P_hh, _P_hh_1, _P_hh_2 = basics['hh']
_P_bb, _P_bb_1, _P_bb_2 = basics['bb']
_P_ih, _P_ih_1, _P_ih_2 = basics['ih']
_P_ib, _P_ib_1, _P_ib_2 = basics['ib']
_P_hb, _P_hb_1, _P_hb_2 = basics['hb']
##
# Check for derived quantities like psi, phi
##
if term == 'psi':
# <psi psi'> = <x (1 + d) x' (1 + d')> = <xx'(1+d)(1+d')>
# = <xx'(1 + d + d' + dd')>
# = <xx'> + 2<xx'd> + <xx'dd'>
#xx, xx1, xx2 = self.ExpectationValue2pt(z, zeta, R=R, term='nn',
# R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#
#xxd, xxd1, xxd2 = self.ExpectationValue2pt(z, zeta, R=R, term='nnd',
# R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#
#xxdd, xxdd1, xxdd2 = self.ExpectationValue2pt(z, zeta, R=R,
# term='xxdd', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#
#ev2pt = xx + 2. * xxd + xxdd
#
ev2pt_1 = Rzeros
ev2pt_2 = Rzeros
# All in terms of ionized fraction perturbation.
dd, dd1, dd2 = self.ExpectationValue2pt(z, R=R, term='dd',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
ii, ii1, ii2 = self.ExpectationValue2pt(z, R=R, term='ii',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
di, di1, di2 = self.ExpectationValue2pt(z, R=R, term='id',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
iidd, on, tw = self.ExpectationValue2pt(z, R=R, term='iidd',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
idd, on, tw = self.ExpectationValue2pt(z, R=R, term='idd',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
iid, on, tw = self.ExpectationValue2pt(z, R=R, term='iid',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
ev_id_1 = self.ExpectationValue1pt(z, term='i*d',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
ev2pt = dd + ii - 2. * di + iidd - 2. * (idd - iid) \
+ 1. - 2 * Qi - 2 * ev_id_1
#self._cache_jp_[z][term] = R, ev2pt, ev2pt_1, ev2pt_2
return ev2pt, ev2pt_1, ev2pt_2
elif term == 'phi':
ev_psi, ev_psi1, ev_psi2 = self.ExpectationValue2pt(z, R,
term='psi', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
ev_oo, ev_oo1, ev_oo2 = self.ExpectationValue2pt(z, R,
term='oo', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
return ev_psi + ev_oo, ev_psi1 + ev_oo1, ev_psi2 + ev_oo2
elif term == '21':
# dTb = T0 * (1 + d21) = T0 * psi
# d21 = psi - 1
# <d21 d21'> = <(psi - 1)(psi' - 1)>
# = <psi psi'> - 2 <psi> + 1
if self.pf['ps_include_temp']:
# New formalism
# <phi phi'> = <psi psi'> + 2 <psi psi' c> + <psi psi' c c'>
ev_phi, ev_phi1, ev_phi2 = self.ExpectationValue2pt(z, R,
term='phi', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
avg_phi = self.ExpectationValue1pt(z, term='phi',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
ev21 = ev_phi + 1. - 2. * avg_phi
else:
ev_psi, ev_psi1, ev_psi2 = self.ExpectationValue2pt(z, R,
term='psi', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
avg_psi = self.ExpectationValue1pt(z, term='psi',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
ev21 = ev_psi + 1. - 2. * avg_psi
#raise NotImplemented('still working!')
#Phi, junk1, junk2 = self.ExpectationValue2pt(z, zeta, R, term='Phi',
# R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja, k=k)
#
#ev_psi, ev_psi1, ev_psi2 = self.ExpectationValue2pt(z, zeta, R,
# term='psi', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#ev2pt = ev_psi + Phi
#
#self._cache_jp_[z][term] = R, ev2pt, Rzeros, Rzeros
return ev21, Rzeros, Rzeros
elif term == 'oo':
# New formalism
# <phi phi'> = <psi psi'> - 2 <psi psi' c> + <psi psi' c c'>
# = <psi psi'> + <o o'>
ppc, _p1, _p2 = self.ExpectationValue2pt(z, R=R, term='ppc',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
ppcc, _p1, _p2 = self.ExpectationValue2pt(z, R=R, term='ppcc',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
ev2pt = ppcc - 2 * ppc
return ev2pt, Rzeros, Rzeros
#elif term == 'bb':
# ev_ii, one, two = self.ExpectationValue2pt(z, zeta, R,
# term='ii', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
# ev_ib, one, two = self.ExpectationValue2pt(z, zeta, R,
# term='ib', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#
# if self.pf['ps_include_temp']:
# ev_ih, one, two = self.ExpectationValue2pt(z, zeta, R,
# term='ih', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
# ev_hh, one, two = self.ExpectationValue2pt(z, zeta, R,
# term='hh', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
# ev_hb, one, two = self.ExpectationValue2pt(z, zeta, R,
# term='hb', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
# else:
# ev_ih = ev_hh = ev_hb = 0.0
#
# #return (1. - Qi - Qh)**2 * Rones, Rzeros, Rzeros
#
# ev_bb = 1. - (ev_ii + 2 * ev_ib + 2 * ev_ih + ev_hh + 2 * ev_hb)
#
# self._cache_jp_[z][term] = R, ev_bb, Rzeros, Rzeros
#
# return ev_bb, Rzeros, Rzeros
# <psi psi' c> = <cdd'> - 2 <cdi'> - 2 <ci'dd>
elif term == 'ppc':
avg_c = self.ExpectationValue1pt(z, term='c',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
avg_cd = self.ExpectationValue1pt(z, term='c*d',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
cd, _j1, _j2 = self.ExpectationValue2pt(z, R=R, term='cd',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
ci, _j1, _j2 = self.ExpectationValue2pt(z, R=R, term='ic',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
cdd, _j1, _j2 = self.ExpectationValue2pt(z, R=R, term='cdd',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
cdip, _j1, _j2 = self.ExpectationValue2pt(z, R=R, term='cdip',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
cddip, _j1, _j2 = self.ExpectationValue2pt(z, R=R, term='cddip',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
cdpip, _j1, _j2 = self.ExpectationValue2pt(z, R=R, term='cdpip',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
ppc = avg_c + cd - ci - cdpip + avg_cd + cdd - cdip - cddip
return ppc, Rzeros, Rzeros
elif term == 'ppcc':
ccdd, _j1, _j2 = self.ExpectationValue2pt(z, R=R, term='ccdd',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
cc, _j1, _j2 = self.ExpectationValue2pt(z, R=R, term='cc',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
ccd, _j1, _j2 = self.ExpectationValue2pt(z, R=R, term='ccd',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
return cc + 2 * ccd + ccdd, Rzeros, Rzeros
elif term in ['mm', 'dd']:
# Equivalent to correlation function since <d> = 0
return self.spline_cf_mm(z)(np.log(R)), np.zeros_like(R), np.zeros_like(R)
#elif term == 'dd':
# dd = _P_ii * delta_i_bar**2 \
# + _P_hh * delta_h_bar**2 \
# + _P_bb * delta_b_bar**2 \
# + 2 * _P_ih * delta_i_bar * delta_h_bar \
# + 2 * _P_ib * delta_i_bar * delta_b_bar \
# + 2 * _P_hb * delta_h_bar * delta_b_bar
#
# return dd, Rzeros, Rzeros
##
# For 3-zone IGM, can compute everything from permutations of
# i, h, and b.
##
if self.pf['ps_igm_model'] == 1 and not self._getting_basics:
return self.ThreeZoneModel(z, R=R, term=term,
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
##
# On to things we must be more careful with.
##
# Minimum bubble size
Mmin = self.Mmin(z) * self.zeta
iM = np.argmin(np.abs(M_b - Mmin))
# Only need overlap volumes once per redshift
all_OV_z = self._cache_Vo(z)
if all_OV_z is None:
all_OV_z = np.zeros((len(R), 6, len(R_i)))
for i, sep in enumerate(R):
all_OV_z[i,:,:] = \
np.array(self.overlap_volumes(sep, R_i, R_s))
self._cache_Vo_[z] = all_OV_z.copy()
#print("Generated z={} overlap_volumes".format(z))
#else:
# print("Read in z={} overlap_volumes".format(z))
all_IV_z = self._cache_IV(z)
if all_IV_z is None:
all_IV_z = np.zeros((len(R), 6, len(R_i)))
for i, sep in enumerate(R):
all_IV_z[i,:,:] = \
np.array(self.intersectional_volumes(sep, R_i, R_s, R3))
self._cache_IV_[z] = all_IV_z.copy()
Mmin_b = self.Mmin(z) * self.zeta
Mmin_h = self.Mmin(z)
Mmin_s = self.Mmin(z) * zeta_X
if term in ['hh', 'ih', 'ib', 'hb'] and self.pf['ps_temp_model'] == 1 \
and self.pf['ps_include_temp']:
Qh_int = self.get_prob(z, M_s, dndm_s, Mmin, V_h,
exp=False, ep=0.0, Mmax=None)
f_h = -np.log(1. - Qh) / Qh_int
else:
f_h = 1.
#dR = np.diff(10**bin_c2e(np.log(R)))#np.concatenate((np.diff(R), [np.diff(R)[-1]]))
#dR = 10**np.arange(np.log(R).min(), np.log(R).max() + 2 * dlogR, dlogR)
# Loop over scales
P1 = np.zeros(R.size)
P2 = np.zeros(R.size)
PT = np.zeros(R.size)
for i, sep in enumerate(R):
##
# Note: each element of this loop we're constructing an array
# over bubble mass, which we then integrate over to get a total
# probability. The shape of every quantity should be `self.m`.
##
# Yields: V11, V12, V22, V1n, V2n, Van
# Remember: these radii arrays depend on redshift (through delta_B)
all_V = all_OV_z[i]
all_IV = all_IV_z[i]
# For two-halo terms, need bias of sources.
if self.pf['ps_include_bias']:
# Should modify for temp_model==2
if self.pf['ps_include_temp']:
if self.pf['ps_temp_model'] == 2 and 'h' in term:
_ion = False
else:
_ion = True
else:
_ion = True
ep = self.excess_probability(z, sep, ion=_ion)
else:
ep = np.zeros_like(self.m)
##
# For each zone, figure out volume of region where a
# single source can ionize/heat/couple both points, as well
# as the region where a single source is not enough (Vss_ne)
##
if term == 'ii':
Vo = all_V[0]
# Subtract off more volume if heating is ON.
#if self.pf['ps_include_temp']:
# #Vne1 = Vne2 = V_i - self.IV(sep, R_i, R_s)
# Vne1 = Vne2 = V_i - all_IV[1]
#else:
# You might think: hey! If temperature fluctuations are on,
# we need to make sure the second point isn't *heated* by
# the first point. This gets into issues of overlap. By not
# introducing this correction (commented out above), we're
# saying "yes, the second point can still lie in the heated
# region of the first (ionized) point, but that point itself
# may actually be ionized, since the way we construct regions
# doesn't know that a heated region may actually live in the
# ionized region of another bubble." That is, a heated point
# can be ionized but an ionized pt can't later be designated
# a hot point.
Vne1 = Vne2 = V_i - Vo
_P1 = self.get_prob(z, M_b, dndm_b, Mmin_b, Vo, True)
_P2_1 = self.get_prob(z, M_b, dndm_b, Mmin_b, Vne1, True)
_P2_2 = self.get_prob(z, M_b, dndm_b, Mmin_b, Vne2, True, ep)
_P2 = (1. - _P1) * _P2_1 * _P2_2
if self.pf['ps_volfix'] and Qi > 0.5:
P1[i] = _P1
P2[i] = (1. - P1[i]) * _P2_1**2
else:
P1[i] = _P1
P2[i] = _P2
# Probability that one point is ionized, other in "bulk IGM"
elif term == 'ib':
Vo_iN = all_V[3] # region in which a source ionized one point
# and does nothing to the other.
# Probability that a single source does something to
# each point. If no temp fluctuations, same as _Pis
P1_iN = self.get_prob(z, M_b, dndm_b, Mmin_b, all_V[3], True)
# "probability of an ionized pt 2 given ionized pt 1"
Pigi = self.get_prob(z, M_b, dndm_b, Mmin_b, V_i-all_V[0], True, ep)
if self.pf['ps_include_temp']:
if self.pf['ps_temp_model'] == 1:
Vne2 = V_ioh - all_IV[2] - (V_i - all_IV[1])
# "probability of a heated pt 2 given ionized pt 1"
Phgi = self.get_prob(z, M_b, dndm_b * f_h, Mmin_b, Vne2, True, ep)
P2[i] = P1_iN * (1. - Pigi - Phgi)
else:
P2[i] = Qi * (1. - Qi - Qh)
else:
P2[i] = P1_iN * (1. - Pigi)
elif term == 'hb':
#if self.pf['ps_temp_model'] == 2:
# print('Ignoring hb term for now...')
# continue
#else:
# pass
if self.pf['ps_temp_model'] == 2:
P1_hN = self.get_prob(z, M_s, dndm_s, Mmin_s, all_V[4], True)
# Given that the first point is heated, what is the probability
# that the second pt is heated or ionized by a different source?
# We want the complement of that.
# Volume in which I heat but don't ionize (or heat) the other pt,
# i.e., same as the two-source term for <hh'>
#Vne2 = Vh - self.IV(sep, R_i, R_s)
Vne2 = V_ioh - all_IV[2] - (V_i - all_IV[1])
# Volume in which single source ioniz
V2ii = V_i - all_V[0]
Phgh = self.get_prob(z, M_b, dndm_b * f_h, Mmin_b, Vne2, True, ep)
Pigh = self.get_prob(z, M_b, dndm_b, Mmin_b, V2ii, True, ep)
#P1[i] = P1_hN
#ih2 = _P_ih_2[i]
#hh2 = _P_hh_2[i]
P2[i] = P1_hN * (1. - Phgh - Pigh)
else:
# Probability that single source can heat one pt but
# does nothing to the other.
P1_hN = self.get_prob(z, M_b, dndm_b * f_h, Mmin_b, all_V[4], True)
# Given that the first point is heated, what is the probability
# that the second pt is heated or ionized by a different source?
# We want the complement of that.
# Volume in which I heat but don't ionize (or heat) the other pt,
# i.e., same as the two-source term for <hh'>
#Vne2 = Vh - self.IV(sep, R_i, R_s)
Vne2 = V_ioh - all_IV[2] - (V_i - all_IV[1])
# Volume in which single source ioniz
V2ii = V_i - all_V[0]
Phgh = self.get_prob(z, M_b, dndm_b * f_h, Mmin_b, Vne2, True, ep)
Pigh = self.get_prob(z, M_b, dndm_b, Mmin_b, V2ii, True, ep)
#P1[i] = P1_hN
#ih2 = _P_ih_2[i]
#hh2 = _P_hh_2[i]
P2[i] = P1_hN * (1. - Phgh - Pigh)
elif term == 'hh':
# Excursion set approach for temperature.
if self.pf['ps_temp_model'] == 2:
Vo = all_V[2]
Vne1 = Vne2 = V_h - Vo
_P1 = self.get_prob(z, M_s, dndm_s, Mmin_s, Vo, True)
_P2_1 = self.get_prob(z, M_s, dndm_s, Mmin_s, Vne1, True)
_P2_2 = self.get_prob(z, M_s, dndm_s, Mmin_s, Vne2, True, ep)
#_P2_1 -= Qi
#_P2_1 -= Qi
_P2 = (1. - _P1) * _P2_1 * _P2_2
#if self.pf['ps_volfix'] and Qi > 0.5:
# P1[i] = _P1
# P2[i] = (1. - P1[i]) * _P2_1**2
#
#else:
P1[i] = _P1
P2[i] = _P2
else:
#Vii = all_V[0]
#_integrand1 = dndm * Vii
#
#_exp_int1 = np.exp(-simps(_integrand1[iM:] * M_b[iM:],
# x=np.log(M_b[iM:])))
#_P1_ii = (1. - _exp_int1)
# Region in which two points are heated by the same source
Vo = all_V[2]
# Subtract off region of the intersection HH volume
# in which source 1 would do *anything* to point 2.
#Vss_ne_1 = Vh - (Vo - self.IV(sep, R_i, R_s) + all_V[0])
#Vne1 = Vne2 = Vh - Vo
# For ionization, this is just Vi - Vo
#Vne1 = V2 - all_IV[2] - (V1 - all_IV[1])
Vne1 = V_ioh - all_IV[2] - (V_i - all_IV[1])
#Vne1 = V2 - self.IV(sep, R_s, R_s) - (V1 - self.IV(sep, R_i, R_s))
Vne2 = Vne1
# Shouldn't max(Vo) = Vh?
#_P1, _P2 = self.get_prob(z, zeta, Vo, Vne1, Vne2, corr, term)
_P1 = self.get_prob(z, M_b, dndm_b * f_h, Mmin_b, Vo, True)
_P2_1 = self.get_prob(z, M_b, dndm_b * f_h, Mmin_b, Vne1, True)
_P2_2 = self.get_prob(z, M_b, dndm_b * f_h, Mmin_b, Vne2, True, ep)
# kludge! to account for Qh = 1 - Qi at late times.
# Integrals above will always get over-estimated for hot
# regions.
#_P2_1 = min(Qh, _P2_1)
#_P2_2 = min(Qh, _P2_2)
_P2 = (1. - _P1) * _P2_1 * _P2_2
# The BSD is normalized so that its integral will recover
# zeta * fcoll.
# Start chugging along on two-bubble term
if np.any(Vne1 < 1e-12):
N = sum(Vne1 < 1e-12)
print('z={}, R={}: Vss_ne_1 (hh) < 0 {} / {} times'.format(z, sep, N, len(R_s)))
#print(Vne1[Vne1 < 1e-12])
print(np.all(V_ioh > V_i), np.all(V_ioh > all_IV[2]), all_IV[2][-1], all_IV[1][-1])
# Must correct for the fact that Qi+Qh<=1
if self.heating_ongoing:
P1[i] = _P1
P2[i] = _P2
else:
P1[i] = _P1 * (1. - Qh - Qi)
P2[i] = Qh**2
elif term == 'ih':
if self.pf['ps_temp_model'] == 2:
continue
if not self.pf['ps_include_xcorr_ion_hot']:
P1[i] = 0.0
P2[i] = Qh * Qi
continue
#Vo_sh_r1, Vo_sh_r2, Vo_sh_r3 = \
# self.overlap_region_shell(sep, R_i, R_s)
#Vo = 2. * Vo_sh_r2 - Vo_sh_r3
Vo = all_V[1]
#V1 = 4. * np.pi * R_i**3 / 3.
#V2 = 4. * np.pi * R_s**3 / 3.
#Vh = 4. * np.pi * (R_s**3 - R_i**3) / 3.
# Volume in which I ionize but don't heat (or ionize) the other pt.
Vne1 = V_i - all_IV[1]
# Volume in which I heat but don't ionize (or heat) the other pt,
# i.e., same as the two-source term for <hh'>
#Vne2 = Vh - self.IV(sep, R_i, R_s)
Vne2 = V_ioh - all_IV[2] - (V_i - all_IV[1])
#Vne2 = V2 - self.IV(sep, R_s, R_s) - (V1 - self.IV(sep, R_i, R_s))
if np.any(Vne2 < 0):
N = sum(Vne2 < 0)
print('R={}: Vss_ne_2 (ih) < 0 {} / {} times'.format(sep, N, len(R_s)))
#_P1, _P2 = self.get_prob(z, zeta, Vo, Vne1, Vne2, corr, term)
_P1 = self.get_prob(z, M_b, dndm_b * f_h, Mmin_b, Vo, True)
_P2_1 = self.get_prob(z, M_b, dndm_b, Mmin_b, Vne1, True)
_P2_2 = self.get_prob(z, M_b, dndm_b * f_h, Mmin_b, Vne2, True, ep)
# Kludge!
#_P2_1 = min(_P2_2, Qi)
#_P2_2 = min(_P2_2, Qh)
_P2 = (1. - _P1) * _P2_1 * _P2_2
#
#P2[i] = min(_P2, Qh * Qi)
if self.heating_ongoing:
P1[i] = _P1
P2[i] = _P2
else:
P1[i] = _P1 * (1. - Qh - Qi)
P2[i] = Qh * Qi
##
# Density stuff from here down
##
if term.count('d') == 0:
continue
if not (self.pf['ps_include_xcorr_ion_rho'] \
or self.pf['ps_include_xcorr_hot_rho']):
# These terms will remain zero
#if term.count('d') > 0:
continue
##
# First, grab a bunch of stuff we'll need.
##
# Ionization auto-correlations
#Pii, Pii_1, Pii_2 = \
# self.ExpectationValue2pt(z, zeta, R, term='ii',
# R_s=R_s, R3=R3, Th=Th, Ts=Ts)
Vo = all_V[0]
Vne1 = V_i - Vo
Vo_hh = all_V[2]
# These are functions of mass
Vsh_sph = 4. * np.pi * R_s**3 / 3.
Vsh = 4. * np.pi * (R_s**3 - R_i**3) / 3.
# Mean bubble density
#B = self._B(z, zeta)
#rho0 = self.cosm.mean_density0
#delta = M_b / V_i / rho0 - 1.
M_h = self.halos.tab_M
iM_h = np.argmin(np.abs(self.Mmin(z) - M_h))
dndm_h = self.halos.tab_dndm[iz_hmf]
fcoll_h = self.halos.tab_fcoll[iz_hmf,iM_h]
# Luminous halos, i.e., Mh > Mmin
Q_lhal = self.Qhal(z, Mmin=Mmin)
# Dark halos, i.e., those outside bubbles
Q_dhal = self.Qhal(z, Mmax=Mmin)
# All halos
Q_hal = self.Qhal(z)
# Since integration must be perfect
Q_dhal = Q_hal - Q_lhal
R_hal = self.halos.VirialRadius(M_h, z) / 1e3 # Convert to Mpc
V_hal = four_pi * R_hal**3 / 3.
# Bias of bubbles and halos
##
db = self._B(z, ion=True)
bh = self.halos.Bias(z)
bb = self.bubble_bias(z, ion=True)
xi_dd_r = xi_dd[i]#self.spline_cf_mm(z)(np.log(sep))
bh_bar = self.mean_halo_bias(z)
bb_bar = self.mean_bubble_bias(z, ion=True)
ep_bh = bh * bb_bar * xi_dd_r
exc = bh_bar * bb_bar * xi_dd_r
# Mean density of halos (mass is arbitrary)
delta_hal_bar = self.mean_halo_overdensity(z)
nhal_avg = self.mean_halo_abundance(z)
# <d> = 0 = <d_i> * Qi + <d_hal> * Q_hal + <d_nohal> * Q_nh
# Problem is Q_hal and Q_i are not mutually exclusive.
# Actually: they are inclusive! At least above Mmin.
delta_nothal_bar = -delta_hal_bar * Q_hal / (1. - Q_hal)
avg_c = self.ExpectationValue1pt(z, term='c',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
#dnh = -dh_avg * fcoll_h / (1. - fcoll_h)
#_P1_ii = self.get_prob(z, M_b, dndm_b, Mmin_b, Vo, True)
#delta_i_bar = self.mean_bubble_overdensity(z, zeta)
if term == 'id':
##
# Analog of one source or one bubble term is P_in, i.e.,
# probability that points are in the same bubble.
# The "two bubble term" is instead P_out, i.e., the
# probability that points are *not* in the same bubble.
# In the latter case, the density can be anything, while
# in the former it will be the mean bubble density.
##
# Actually think about halos
# <x_i d'> = \int d' f(d; x_i=1) f(x_i=1) f(d'; d) dd'
# Crux is f(d'; d): could be 3-d integral in general.
# Loop over bubble density.
#ixd_inner = np.zeros(self.m.size)
#for k, d1 in enumerate(db):
#
# # Excess probability of halo with mass mh
# # given bubble nearby
# exc = 0.0#bh * bb[k] * xi_dd_r
#
# #Ph = np.minimum(Ph, 1.)
#
# # <d> = fcoll_V * dh + Qi * di + rest
# #Pn = 1. - Ph
# #if sep < R_i[k]:
# # dn = d1
# #else:
# #dn = delta_n_bar
#
# # How to guarantee that <x_i d'> -> 0 on L.S.?
# # Is the key formalizing whether we're at the
# # center of the bubble or not?
# integ = dndm_h * V_h * (1. + exc)
#
# # Don't truncate at Mmin! Don't need star-forming
# # galaxy, just need mass.
# ixd_inner[k] = np.trapz(integ * M_h, x=np.log(M_h))
#_integrand = dndm_h * (M_h / rho_bar) * bh
#fcorr = 1. - np.trapz(_integrand * M_h, x=np.log(M_h))
# Just halos *outside* bubbles
hal = np.trapz(dndm_h[:iM_h] * V_hal[:iM_h] * (1. + ep_bh[:iM_h]) * M_h[:iM_h],
x=np.log(M_h[:iM_h]))
bub = np.trapz(dndm_b[iM:] * V_i[iM:] * self.m[iM:],
x=np.log(self.m[iM:]))
P_ihal = (1. - np.exp(-bub)) * (1. - np.exp(-hal))
#P2[i] = P_ihal * delta_hal_bar + _P_ib[i] * delta_b_bar
P1[i] = _P_ii_1[i] * delta_i_bar
P2[i] = _P_ii_2[i] * delta_i_bar + _P_ib[i] * delta_b_bar \
+ P_ihal * delta_hal_bar
#P2[i] = Phal * dh_avg + np.exp(-hal) * dnih_avg
#P2[i] += np.exp(-hal) * dnih_avg * Qi
#P2[i] += _P_in[i] * delta_n_bar
elif term in ['cd', 'cdip']:
continue
elif term == 'idd':
hal = np.trapz(dndm_h[:iM_h] * V_hal[:iM_h] * (1. + ep_bh[:iM_h]) * M_h[:iM_h],
x=np.log(M_h[:iM_h]))
bub = np.trapz(dndm_b[iM:] * V_i[iM:] * self.m[iM:],
x=np.log(self.m[iM:]))
P_ihal = (1. - np.exp(-bub)) * (1. - np.exp(-hal))
#P2[i] = P_ihal * delta_hal_bar + _P_ib[i] * delta_b_bar
P1[i] = _P_ii_1[i] * delta_i_bar**2
P2[i] = _P_ii_2[i] * delta_i_bar**2 \
+ _P_ib[i] * delta_b_bar * delta_i_bar\
+ P_ihal * delta_hal_bar * delta_i_bar
#exc = bh_bar * bb_bar * xi_dd_r
#
#hal = np.trapz(dndm_h * V_hal * (1. + exc) * M_h,
# x=np.log(M_h))
#bub = np.trapz(dndm_b[iM:] * V_i[iM:] * self.m[iM:],
# x=np.log(self.m[iM:]))
#
#P2[i] = ((1. - np.exp(-hal)) * delta_hal_bar
# + np.exp(-hal) * delta_nothal_bar) \
# * (1. - np.exp(-bub)) * delta_i_bar
#_P1 = _P_ii_1[i] * delta_i_bar**2
#
##_P2 = _P_ii_2[i] * delta_i_bar**2 \
## + Qi * (1. - _P_ii_1[i]) * delta_i_bar * delta_n_bar \
## - Qi**2 * delta_i_bar**2
##
#P1[i] = _P1
#
##P2[i] = Qi * xi_dd[i] # There's gonna be a bias here
##P2[i] = _P_ii_2[i] * delta_i_bar**2 - Qi**2 * delta_i_bar**2
#
##continue
#
#idd_ii = np.zeros(self.m.size)
#idd_in = np.zeros(self.m.size)
#
## Convert from dm to dd
##dmdd = np.diff(self.m) / np.diff(db)
##dmdd = np.concatenate(([0], dmdd))
#
## Should be able to speed this up
#
#for k, d1 in enumerate(db):
#
#
# exc = bb[k] * bb * xi_dd_r
#
# grand = db[k] * dndm_b[k] * V_i[k] \
# * db * dndm_b * V_i \
# * (1. + exc)
#
# idd_ii[k] = np.trapz(grand[iM:] * self.m[iM:],
# x=np.log(self.m[iM:]))
#
# #exc_in = bb[k] * bh * xi_dd_r
# #
# #grand_in = db[k] * dndm_b[k] * V_i[k] #\
# # #* dh * dndm_h * Vvir \
# # #* (1. + exc_in)
# #
# #idd_in[k] = np.trapz(grand_in[iM_h:] * M_h[iM_h:],
# # x=np.log(M_h[iM_h:]))
#
##idd_in = np.trapz(db[iM:] * dndm_b[iM:] * V_i[iM:] * delta_n_bar * self.m[iM:],
## x=np.log(self.m[iM:]))
#
#
#P2[i] = _P_ii_2[i] \
# * np.trapz(idd_ii[iM:] * self.m[iM:],
# x=np.log(self.m[iM:]))
#
## Another term for <x_i x'> possibility. Doesn't really
## fall into the one bubble two bubble language, so just
## sticking it in P2.
## Assumes neutral phase is at cosmic mean neutral density
## Could generalize...
#P2[i] += _P_ib[i] * delta_i_bar * delta_b_bar
#
## We're neglecting overdensities by just using the
## mean neutral density
#
#continue
elif term == 'iid':
# This is like the 'id' term except the second point
# has to be ionized.
P2[i] = _P_ii[i] * delta_i_bar
elif term == 'iidd':
P2[i] = _P_ii[i] * delta_i_bar**2
continue
# Might have to actually do a double integral here.
iidd_2 = np.zeros(self.m.size)
# Convert from dm to dd
#dmdd = np.diff(self.m) / np.diff(db)
#dmdd = np.concatenate(([0], dmdd))
# Should be able to speed this up
for k, d1 in enumerate(db):
exc = bb[k] * bb * xi_dd_r
grand = db[k] * dndm_b[k] * V_i[k] \
* db * dndm_b * V_i \
* (1. + exc)
iidd_2[k] = np.trapz(grand[iM:] * self.m[iM:],
x=np.log(self.m[iM:]))
P2[i] = _P_ii_2[i] \
* np.trapz(iidd_2[iM:] * self.m[iM:],
x=np.log(self.m[iM:]))
#elif term == 'cd':
#
# if self.pf['ps_include_xcorr_hot_rho'] == 0:
# break
# elif self.pf['ps_include_xcorr_hot_rho'] == 1:
# hal = np.trapz(dndm_h * V_hal * (1. + exc) * M_h,
# x=np.log(M_h))
# hot = np.trapz(dndm_b[iM:] * V_h[iM:] * self.m[iM:],
# x=np.log(self.m[iM:]))
# P2[i] = ((1. - np.exp(-hal)) * dh_avg + np.exp(-hal) * dnih_avg) \
# * (1. - np.exp(-hot)) * avg_c
# elif self.pf['ps_include_xcorr_hot_rho'] == 2:
# P2[i] = _P_hh[i] * delta_h_bar + _P_hb[i] * delta_b_bar
# else:
# raise NotImplemented('help')
#
#elif term == 'ccd':
#
#
# _P1 = _P_hh_1[i] * delta_i_bar
# #B = self._B(z, zeta)
# #_P1 = delta_i_bar \
# # * self.get_prob(z, M_b, dndm_b, Mmin_b, Vo, True) \
#
#
# _P2 = _P_hh_2[i] * delta_i_bar
#
# #_P2 = (1. - _P_ii_1[i]) * delta_i_bar \
# # * self.get_prob(z, M_b, dndm_b, Mmin_b, Vne1, True) \
# # * self.get_prob(z, M_b, dndm_b, Mmin_b, Vne1, True, ep)
# # #* self.get_prob(z, M_h, dndm_h, Mmi\n_h, Vvir, False, ep_bb)
#
# P1[i] = _P1
# P2[i] = _P2
#
elif term == 'cdd':
raise NotImplemented('help')
hal = np.trapz(dndm_h * V_hal * (1. + exc) * M_h,
x=np.log(M_h))
hot = np.trapz(dndm_b[iM:] * Vsh[iM:] * self.m[iM:],
x=np.log(self.m[iM:]))
hoi = np.trapz(dndm_b[iM:] * Vsh_sph[iM:] * self.m[iM:],
x=np.log(self.m[iM:])) # 'hot or ionized'
# One point in shell, other point in halo
# One point ionized, other point in halo
# Q. Halos exist only in ionized regions?
elif term == 'ccdd':
raise NotImplemented('help')
# Add in bulk IGM correction.
# Add routines for calculating 'ib' and 'hb'?
P2[i] = _P_hh[i] * delta_h_bar**2 \
+ _P_bb[i] * delta_h_bar**2 \
+ _P_hb[i] * delta_h_bar * delta_b_bar
continue
# Might have to actually do a double integral here.
iidd_2 = np.zeros(self.m.size)
# Convert from dm to dd
#dmdd = np.diff(self.m) / np.diff(db)
#dmdd = np.concatenate(([0], dmdd))
# Should be able to speed this up
for k, d1 in enumerate(db):
exc = bb[k] * bb * xi_dd_r
grand = db[k] * dndm_b[k] * V_i[k] \
* db * dndm_b * V_i \
* (1. + exc)
iidd_2[k] = np.trapz(grand[iM:] * self.m[iM:],
x=np.log(self.m[iM:]))
P2[i] = _P_ii_2[i] \
* np.trapz(iidd_2[iM:] * self.m[iM:],
x=np.log(self.m[iM:]))
else:
raise NotImplementedError('No method found for term=\'{}\''.format(term))
##
# SUM UP
##
PT = P1 + P2
if term in ['ii', 'hh', 'ih', 'ib', 'hb', 'bb']:
if term not in self._cache_jp_[z]:
self._cache_jp_[z][term] = R, PT, P1, P2
return PT, P1, P2
def ThreeZoneModel(self, z, R, term='ii', R_s=None, R3=None,
Th=500.0, Ts=None, Tk=None, Ja=None, k=None):
"""
Model in which IGM partitioned into three phases: ionized, hot, bulk.
.. note :: If ps_include_temp==False, this is just a two-zone model
since there is no heated phase in this limit.
"""
if not self._getting_basics:
basics = self.get_basics(z, R, R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
if term in basics:
return basics[term]
_P_ii, _P_ii_1, _P_ii_2 = basics['ii']
_P_hh, _P_hh_1, _P_hh_2 = basics['hh']
_P_bb, _P_bb_1, _P_bb_2 = basics['bb']
_P_ih, _P_ih_1, _P_ih_2 = basics['ih']
_P_ib, _P_ib_1, _P_ib_2 = basics['ib']
_P_hb, _P_hb_1, _P_hb_2 = basics['hb']
Rones = np.zeros_like(R)
Rzeros = np.zeros_like(R)
delta_i_bar = self.delta_bubble_vol_weighted(z, ion=True)
delta_h_bar = self.delta_shell(z)
delta_b_bar = self.BulkDensity(z, R_s)
Qi = self.MeanIonizedFraction(z)
Qh = self.MeanIonizedFraction(z, ion=False)
Tcmb = self.cosm.TCMB(z)
ci = 0.0
ch = self.TempToContrast(z, Th=Th, Tk=Tk, Ts=Ts, Ja=Ja)
if Ts is None:
cb = 0.0
else:
cb = Tcmb / Ts
##
# On to derived quantities
##
if term == 'cc':
result = Rzeros.copy()
if self.pf['ps_include_temp']:
result += _P_hh * ch**2 + 2 * _P_hb * ch * cb + _P_bb * cb**2
if self.pf['ps_include_lya']:
xa = self.hydr.RadiativeCouplingCoefficient(z, Ja, Tk)
if xa < self.pf['ps_lya_cut']:
ev_aa, ev_aa1, ev_aa2 = \
self.ExpectationValue2pt(z, R, term='aa',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, k=k, Ja=Ja)
Tcmb = self.cosm.TCMB(z)
result += ev_aa / (1. + xa)**2
return result, Rzeros, Rzeros
elif term == 'ic':
if not self.pf['ps_include_xcorr_ion_hot']:
return (Qi**2 * ci + Qh * Qi * ch) * Rones, Rzeros, Rzeros
ev = _P_ih * ch + _P_ib * cb
return ev, Rzeros, Rzeros
elif term == 'icc':
ch = self.TempToContrast(z, Th=Th, Tk=Tk, Ts=Ts, Ja=Ja)
ci = self.BubbleContrast(z, Th=Th, Tk=Tk, Ts=Ts, Ja=Ja)
ev_ii, ev_ii1, ev_ii2 = self.ExpectationValue2pt(z, R=R,
term='ii', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
ev_ih, ev_ih1, ev_ih2 = self.ExpectationValue2pt(z, R=R,
term='ih', R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
return ev_ii * ci**2 + ev_ih * ch * ci, Rzeros, Rzeros
elif term == 'iidd':
if self.pf['ps_use_wick']:
ev_ii, one_pt, two_pt = self.ExpectationValue2pt(z, R,
term='ii')
ev_dd, one_pt, two_pt = self.ExpectationValue2pt(z, R,
term='dd')
ev_id, one_pt, two_pt = self.ExpectationValue2pt(z, R,
term='id')
#if self.pf['ps_include_ion']:
avg_id = self.ExpectationValue1pt(z, term='i*d')
idt, id1, id2 = \
self.ExpectationValue2pt(z, R, term='id')
return ev_ii * ev_dd + ev_id**2 + avg_id**2, Rzeros, Rzeros
else:
return _P_ii * delta_i_bar**2, Rzeros, Rzeros
elif term == 'id':
P = _P_ii * delta_i_bar \
+ _P_ih * delta_h_bar \
+ _P_ib * delta_b_bar
return P, Rzeros, Rzeros
elif term == 'iid':
return _P_ii * delta_i_bar, Rzeros, Rzeros
elif term == 'idd':
P = _P_ii * delta_i_bar**2 \
+ _P_ih * delta_i_bar * delta_h_bar \
+ _P_ib * delta_i_bar * delta_b_bar
return P, Rzeros, Rzeros
elif term == 'cd':
if not self.pf['ps_include_xcorr_hot_rho']:
return Rzeros, Rzeros, Rzeros
ev = _P_ih * ch * delta_i_bar \
+ _P_ib * cb * delta_i_bar \
+ _P_hh * ch * delta_h_bar \
+ _P_hb * ch * delta_b_bar \
+ _P_hb * cb * delta_h_bar \
+ _P_bb * cb * delta_b_bar
return ev, Rzeros, Rzeros
elif term == 'ccdd' and self.pf['ps_use_wick']:
ev_cc, one_pt, two_pt = self.ExpectationValue2pt(z, R,
term='cc')
ev_dd, one_pt, two_pt = self.ExpectationValue2pt(z, R,
term='dd')
ev_cd, one_pt, two_pt = self.ExpectationValue2pt(z, R,
term='cd')
#if self.pf['ps_include_ion']:
avg_cd = self.ExpectationValue1pt(z, term='c*d')
cdt, cd1, cd2 = \
self.ExpectationValue2pt(z, R, term='cd')
return ev_cc * ev_dd + ev_cd**2 + avg_cd**2, Rzeros, Rzeros
elif term == 'aa':
aa = self.CorrelationFunction(z, R, term='aa',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja, k=k)
return aa, Rzeros, Rzeros
##
# BUNCHA TEMPERATURE-DENSITY STUFF BELOW
##
elif term == 'ccd':
ev = _P_hh * ch**2 * delta_h_bar \
+ _P_hb * ch * cb * delta_h_bar \
+ _P_hb * ch * cb * delta_b_bar \
+ _P_bb * cb**2 * delta_b_bar
return ev, Rzeros, Rzeros
elif term == 'cdd':
ev = _P_ih * ch * delta_i_bar * delta_h_bar \
+ _P_ib * cb * delta_i_bar * delta_b_bar \
+ _P_hh * ch * delta_h_bar**2 \
+ _P_hb * ch * delta_h_bar * delta_b_bar \
+ _P_hb * cb * delta_h_bar * delta_b_bar \
+ _P_bb * cb * delta_b_bar**2
return ev, Rzeros, Rzeros
# <c d x_i'>
elif term == 'cdip':
ev = _P_ih * delta_h_bar * ch + _P_ib * delta_b_bar * cb
return ev, Rzeros, Rzeros
# <c d d' x_i'>
elif term == 'cddip':
ev = _P_ih * delta_i_bar * delta_h_bar * ch \
+ _P_ib * delta_i_bar * delta_b_bar * cb
return ev, Rzeros, Rzeros
elif term == 'cdpip':
ev = _P_ih * delta_i_bar * ch \
+ _P_ib * delta_i_bar * cb
return ev, Rzeros, Rzeros
# Wick's theorem approach above
elif term == 'ccdd':
ev = _P_hh * delta_h_bar**2 * ch**2 \
+ 2 * _P_hb * delta_h_bar * ch * delta_b_bar * cb \
+ _P_bb * delta_b_bar**2 * cb**2
return ev, Rzeros, Rzeros
else:
raise NotImplementedError('No model for term={} in ThreeZoneModel.'.format(term))
def get_prob(self, z, M, dndm, Mmin, V, exp=True, ep=0.0, Mmax=None):
"""
Basically do an integral over some distribution function.
"""
# Set lower integration limit
iM = np.argmin(np.abs(M - Mmin))
if Mmax is not None:
iM2 = np.argmin(np.abs(M - Mmax)) + 1
else:
iM2 = None
# One-source term
integrand = dndm * V * (1. + ep)
integr = np.trapz(integrand[iM:iM2] * M[iM:iM2], x=np.log(M[iM:iM2]))
# Exponentiate?
if exp:
exp_int = np.exp(-integr)
P = 1. - exp_int
else:
P = integr
return P
def CorrelationFunction(self, z, R=None, term='ii',
R_s=None, R3=0.0, Th=500., Tc=1., Ts=None, k=None, Tk=None, Ja=None):
"""
Compute the correlation function of some general term.
"""
Qi = self.MeanIonizedFraction(z)
Qh = self.MeanIonizedFraction(z, ion=False)
if R is None:
use_R_tab = True
R = self.halos.tab_R
else:
use_R_tab = False
if Qi == 1:
return np.zeros_like(R)
Tcmb = self.cosm.TCMB(z)
Tgas = self.cosm.Tgas(z)
##
# Check cache for match
##
cached_result = self._cache_cf(z, term)
if cached_result is not None:
_R, _cf = cached_result
if _R.size == R.size:
if np.allclose(_R, R):
return _cf
return np.interp(R, _R, _cf)
##
# 21-cm correlation function
##
if term in ['21', 'phi', 'psi']:
#if term in ['21', 'phi']:
# ev_2pt, ev_2pt_1, ev_2pt_2 = \
# self.ExpectationValue2pt(z, zeta, R=R, term='phi',
# R_s=R_s, R3=R3, Th=Th, Ts=Ts)
# avg_phi = self.ExpectationValue1pt(z, zeta, term='phi',
# R_s=R_s, Th=Th, Ts=Ts)
#
# cf_21 = ev_2pt - avg_phi**2
#
#else:
ev_2pt, ev_2pt_1, ev_2pt_2 = \
self.ExpectationValue2pt(z, R=R, term='psi',
R_s=R_s, R3=R3, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
avg_psi = self.ExpectationValue1pt(z, term='psi',
R_s=R_s, Th=Th, Ts=Ts, Tk=Tk, Ja=Ja)
cf_psi = ev_2pt - avg_psi**2
##
# Temperature fluctuations
##
include_temp = self.pf['ps_include_temp']
include_lya = self.pf['ps_include_lya']
if (include_temp or include_lya) and term in ['phi', '21']:
ev_oo, o1, o2 = self.ExpectationValue2pt(z, R=R,
term='oo', R_s=R_s, Ts=Ts, Tk=Tk, Th=Th, Ja=Ja, k=k)
avg_oo = self.ExpectationValue1pt(z, term='oo',
R_s=R_s, Ts=Ts, Tk=Tk, Th=Th, Ja=Ja, R3=R3)
cf_omega = ev_oo - avg_oo
cf_21 = cf_psi + cf_omega # i.e., cf_phi
else:
cf_21 = cf_psi
if term == '21':
cf = cf_21
elif term == 'phi':
cf = cf_21
elif term == 'psi':
cf = cf_psi
elif term == 'nn':
cf = -self.CorrelationFunction(z, R, term='ii',
R_s=R_s, R3=R3, Th=Th, Ts=Ts)
return cf
elif term == 'nc':
cf = -self.CorrelationFunction(z, R, term='ic',
R_s=R_s, R3=R3, Th=Th, Ts=Ts)
return cf
elif term == 'nd':
cf = -self.CorrelationFunction(z, R, term='id',
R_s=R_s, R3=R3, Th=Th, Ts=Ts)
return cf
##
# Matter correlation function -- we have this tabulated already.
##
elif term in ['dd', 'mm']:
if not self.pf['ps_include_density']:
cf = np.zeros_like(R)
self._cache_cf_[z][term] = R, cf
return cf
iz = np.argmin(np.abs(z - self.halos.tab_z_ps))
if use_R_tab:
cf = self.halos.tab_cf_mm[iz]
else:
cf = np.interp(np.log(R), np.log(self.halos.tab_R),
self.halos.tab_cf_mm[iz])
##
# Ionization correlation function
##
elif term == 'ii':
if not self.pf['ps_include_ion']:
cf = | np.zeros_like(R) | numpy.zeros_like |
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
More or less a python port of Stewart method from R SpatialPositon package
(https://github.com/Groupe-ElementR/SpatialPosition/).
@author: mthh
"""
import numpy as np
from matplotlib.pyplot import contourf
from shapely import speedups
from shapely.ops import unary_union, transform
from shapely.geometry import Polygon, MultiPolygon
from geopandas import GeoDataFrame
try:
from jenkspy import jenks_breaks
except: jenks_breaks = None
from .helpers_classif import get_opt_nb_class, maximal_breaks, head_tail_breaks
if speedups.available and not speedups.enabled: speedups.enable()
def quick_idw(input_geojson_points, variable_name, power, nb_class,
nb_pts=10000, resolution=None, disc_func=None,
mask=None, user_defined_breaks=None,
variable_name2=None, output='GeoJSON', **kwargs):
"""
Function acting as a one-shot wrapper around SmoothIdw object.
Read a file of point values and optionnaly a mask file,
return the smoothed representation as GeoJSON or GeoDataFrame.
Parameters
----------
input_geojson_points : str
Path to file to use as input (Points/Polygons) or GeoDataFrame object,
must contains a relevant numerical field.
variable_name : str
The name of the variable to use (numerical field only).
power : int or float
The power of the function.
nb_class : int, optionnal
The number of class, if unset will most likely be 8.
(default: None)
nb_pts: int, optionnal
The number of points to use for the underlying grid.
(default: 10000)
resolution : int, optionnal
The resolution to use (in meters), if not set a default
resolution will be used in order to make a grid containing around
10000 pts (default: None).
disc_func: str, optionnal
The name of the classification function to be used to decide on which
break values to use to create the contour layer.
(default: None)
mask : str, optionnal
Path to the file (Polygons only) to use as clipping mask,
can also be a GeoDataFrame (default: None).
user_defined_breaks : list or tuple, optionnal
A list of ordered break to use to construct the contours
(overrides `nb_class` and `disc_func` values if any, default: None).
variable_name2 : str, optionnal
The name of the 2nd variable to use (numerical field only); values
computed from this variable will be will be used as to divide
values computed from the first variable (default: None)
output : string, optionnal
The type of output expected (not case-sensitive)
in {"GeoJSON", "GeoDataFrame"} (default: "GeoJSON").
Returns
-------
smoothed_result : bytes or GeoDataFrame,
The result, dumped as GeoJSON (utf-8 encoded) or as a GeoDataFrame.
Examples
--------
Basic usage, output to raw geojson (bytes):
>>> result = quick_idw("some_file.geojson", "some_variable", power=2)
More options, returning a GeoDataFrame:
>>> smooth_gdf = quick_stewart("some_file.geojson", "some_variable",
nb_class=8, disc_func="percentiles",
output="GeoDataFrame")
"""
return SmoothIdw(input_geojson_points,
variable_name,
power,
nb_pts,
resolution,
variable_name2,
mask,
**kwargs
).render(nb_class=nb_class,
disc_func=disc_func,
user_defined_breaks=user_defined_breaks,
output=output)
def quick_stewart(input_geojson_points, variable_name, span,
beta=2, typefct='exponential',nb_class=None,
nb_pts=10000, resolution=None, mask=None,
user_defined_breaks=None, variable_name2=None,
output="GeoJSON", **kwargs):
"""
Function acting as a one-shot wrapper around SmoothStewart object.
Read a file of point values and optionnaly a mask file,
return the smoothed representation as GeoJSON or GeoDataFrame.
Parameters
----------
input_geojson_points : str
Path to file to use as input (Points/Polygons) or GeoDataFrame object,
must contains a relevant numerical field.
variable_name : str
The name of the variable to use (numerical field only).
span : int
The span (meters).
beta : float
The beta!
typefct : str, optionnal
The type of function in {"exponential", "pareto"} (default: "exponential").
nb_class : int, optionnal
The number of class, if unset will most likely be 8
(default: None)
nb_pts: int, optionnal
The number of points to use for the underlying grid.
(default: 10000)
resolution : int, optionnal
The resolution to use (in meters), if not set a default
resolution will be used in order to make a grid containing around
10000 pts (default: None).
mask : str, optionnal
Path to the file (Polygons only) to use as clipping mask,
can also be a GeoDataFrame (default: None).
user_defined_breaks : list or tuple, optionnal
A list of ordered break to use to construct the contours
(override `nb_class` value if any, default: None).
variable_name2 : str, optionnal
The name of the 2nd variable to use (numerical field only); values
computed from this variable will be will be used as to divide
values computed from the first variable (default: None)
output : string, optionnal
The type of output expected (not case-sensitive)
in {"GeoJSON", "GeoDataFrame"} (default: "GeoJSON").
Returns
-------
smoothed_result : bytes or GeoDataFrame,
The result, dumped as GeoJSON (utf-8 encoded) or as a GeoDataFrame.
Examples
--------
Basic usage, output to raw geojson (bytes):
>>> result = quick_stewart("some_file.geojson", "some_variable",
span=12500, beta=3, typefct="exponential")
More options, returning a GeoDataFrame:
>>> smooth_gdf = quick_stewart("some_file.geojson", "some_variable",
span=12500, beta=3, typefct="pareto",
output="GeoDataFrame")
"""
return SmoothStewart(
input_geojson_points,
variable_name,
span,
beta,
typefct,
nb_pts,
resolution,
variable_name2,
mask,
**kwargs
).render(
nb_class=nb_class,
user_defined_breaks=user_defined_breaks,
output=output)
def make_regular_points_with_no_res(bounds, nb_points=10000):
"""
Return a regular grid of points within `bounds` with the specified
number of points (or a close approximate value).
Parameters
----------
bounds : 4-floats tuple
The bbox of the grid, as xmin, ymin, xmax, ymax.
nb_points : int, optionnal
The desired number of points (default: 10000)
Returns
-------
points : numpy.array
An array of coordinates
shape : 2-floats tuple
The number of points on each dimension (width, height)
"""
minlon, minlat, maxlon, maxlat = bounds
minlon, minlat, maxlon, maxlat = bounds
offset_lon = (maxlon - minlon) / 8
offset_lat = (maxlat - minlat) / 8
minlon -= offset_lon
maxlon += offset_lon
minlat -= offset_lat
maxlat += offset_lat
nb_x = int(nb_points**0.5)
nb_y = int(nb_points**0.5)
return (
np.linspace(minlon, maxlon, nb_x),
np.linspace(minlat, maxlat, nb_y),
(nb_y, nb_x)
)
def make_regular_points(bounds, resolution, longlat=True):
"""
Return a regular grid of points within `bounds` with the specified
resolution.
Parameters
----------
bounds : 4-floats tuple
The bbox of the grid, as xmin, ymin, xmax, ymax.
resolution : int
The resolution to use, in the same unit as `bounds`
Returns
-------
points : numpy.array
An array of coordinates
shape : 2-floats tuple
The number of points on each dimension (width, height)
"""
# xmin, ymin, xmax, ymax = bounds
minlon, minlat, maxlon, maxlat = bounds
offset_lon = (maxlon - minlon) / 8
offset_lat = (maxlat - minlat) / 8
minlon -= offset_lon
maxlon += offset_lon
minlat -= offset_lat
maxlat += offset_lat
if longlat:
height = hav_dist(
np.array([(maxlon + minlon) / 2, minlat]),
np.array([(maxlon + minlon) / 2, maxlat])
)
width = hav_dist(
np.array([minlon, (maxlat + minlat) / 2]),
np.array([maxlon, (maxlat + minlat) / 2])
)
else:
height = np.linalg.norm(
np.array([(maxlon + minlon) / 2, minlat])
- np.array([(maxlon + minlon) / 2, maxlat]))
width = np.linalg.norm(
np.array([minlon, (maxlat + minlat) / 2])
- np.array([maxlon, (maxlat + minlat) / 2]))
nb_x = int(round(width / resolution))
nb_y = int(round(height / resolution))
if nb_y * 0.6 > nb_x:
nb_x = int(nb_x + nb_x / 3)
elif nb_x * 0.6 > nb_y:
nb_y = int(nb_y + nb_y / 3)
return (
np.linspace(minlon, maxlon, nb_x),
np.linspace(minlat, maxlat, nb_y),
(nb_y, nb_x)
)
def _compute_centroids(geometries):
res = []
for geom in geometries:
if hasattr(geom, '__len__'):
ix_biggest = np.argmax([g.area for g in geom])
res.append(geom[ix_biggest].centroid)
else:
res.append(geom.centroid)
return res
def make_dist_mat(xy1, xy2, longlat=True):
"""
Return a distance matrix between two set of coordinates.
Use geometric distance (default) or haversine distance (if longlat=True).
Parameters
----------
xy1 : numpy.array
The first set of coordinates as [(x, y), (x, y), (x, y)].
xy2 : numpy.array
The second set of coordinates as [(x, y), (x, y), (x, y)].
longlat : boolean, optionnal
Whether the coordinates are in geographic (longitude/latitude) format
or not (default: False)
Returns
-------
mat_dist : numpy.array
The distance matrix between xy1 and xy2
"""
if longlat:
return hav_dist(xy1[:, None], xy2)
else:
d0 = np.subtract.outer(xy1[:, 0], xy2[:, 0])
d1 = np.subtract.outer(xy1[:, 1], xy2[:, 1])
return np.hypot(d0, d1)
def hav_dist(locs1, locs2):
"""
Return a distance matrix between two set of coordinates.
Use geometric distance (default) or haversine distance (if longlat=True).
Parameters
----------
locs1 : numpy.array
The first set of coordinates as [(long, lat), (long, lat)].
locs2 : numpy.array
The second set of coordinates as [(long, lat), (long, lat)].
Returns
-------
mat_dist : numpy.array
The distance matrix between locs1 and locs2
"""
# locs1 = np.radians(locs1)
# locs2 = np.radians(locs2)
cos_lat1 = np.cos(locs1[..., 0])
cos_lat2 = np.cos(locs2[..., 0])
cos_lat_d = np.cos(locs1[..., 0] - locs2[..., 0])
cos_lon_d = | np.cos(locs1[..., 1] - locs2[..., 1]) | numpy.cos |
import os
import random
import pickle
import numpy as np
import cv2
import torch
import torch.utils.data as data
import torchvision.transforms as transforms
from PIL import Image
from torch.utils.data import DataLoader
import librosa
import time
import copy
import python_speech_features
#import utils
EIGVECS = np.load('../basics/S.npy')
MS = np.load('../basics/mean_shape.npy')
class LRW_1D_lstm_landmark_pca(data.Dataset):
def __init__(self,
dataset_dir,
train='train'):
self.train = train
self.num_frames = 16
self.lmark_root_path = '../dataset/landmark1d'
self.pca = torch.FloatTensor(np.load('../basics/U_lrw1.npy')[:,:6] )
self.mean = torch.FloatTensor(np.load('../basics/mean_lrw1.npy'))
if self.train=='train':
_file = open(os.path.join(dataset_dir, "lmark_train.pkl"), "rb")
self.train_data = pickle.load(_file)
_file.close()
elif self.train =='test':
_file = open(os.path.join(dataset_dir, "lmark_test.pkl"), "rb")
self.test_data = pickle.load(_file)
_file.close()
elif self.train =='demo' :
_file = open(os.path.join(dataset_dir, "img_demo.pkl"), "rb")
self.demo_data = pickle.load(_file)
_file.close()
def __getitem__(self, index):
if self.train=='train':
lmark_path = os.path.join(self.lmark_root_path , self.train_data[index][0] , self.train_data[index][1],self.train_data[index][2], self.train_data[index][2] + '.npy')
mfcc_path = os.path.join('../dataset/mfcc/', self.train_data[index][0], self.train_data[index][1], self.train_data[index][2] + '.npy')
lmark = np.load(lmark_path) * 5.0
lmark = torch.FloatTensor(lmark)
lmark = lmark - self.mean.expand_as(lmark)
lmark = torch.mm(lmark,self.pca)
mfcc = np.load(mfcc_path)
r = random.choice(
[x for x in range(3,8)])
example_landmark =lmark[r,:]
example_mfcc = mfcc[(r -3) * 4 : (r + 4) * 4, 1 :]
mfccs = []
for ind in range(1,17):
t_mfcc =mfcc[(r + ind - 3)*4: (r + ind + 4)*4, 1:]
t_mfcc = torch.FloatTensor(t_mfcc)
mfccs.append(t_mfcc)
mfccs = torch.stack(mfccs, dim = 0)
landmark =lmark[r+1 : r + 17,:]
example_mfcc = torch.FloatTensor(example_mfcc)
return example_landmark, example_mfcc, landmark, mfccs
if self.train=='test':
lmark_path = os.path.join(self.lmark_root_path , self.test_data[index][0] , self.test_data[index][1],self.test_data[index][2], self.test_data[index][2] + '.npy')
mfcc_path = os.path.join('../dataset/mfcc/', self.test_data[index][0], self.test_data[index][1], self.test_data[index][2] + '.npy')
lmark = np.load(lmark_path) * 5.0
lmark = torch.FloatTensor(lmark)
lmark = lmark - self.mean.expand_as(lmark)
lmark = torch.mm(lmark,self.pca)
mfcc = np.load(mfcc_path)
r = random.choice(
[x for x in range(3,8)])
example_landmark =lmark[r,:]
example_mfcc = mfcc[(r -3) * 4 : (r + 4) * 4, 1 :]
mfccs = []
for ind in range(1,17):
t_mfcc =mfcc[(r + ind - 3)*4: (r + ind + 4)*4, 1:]
t_mfcc = torch.FloatTensor(t_mfcc)
mfccs.append(t_mfcc)
mfccs = torch.stack(mfccs, dim = 0)
landmark =lmark[r+1 : r + 17,:]
example_mfcc = torch.FloatTensor(example_mfcc)
return example_landmark, example_mfcc, landmark, mfccs
def __len__(self):
if self.train=='train':
return len(self.train_data)
elif self.train=='test':
return len(self.test_data)
else:
pas
class LRW_1D_single_landmark_pca(data.Dataset):
def __init__(self,
dataset_dir,
train='train'):
self.train = train
self.num_frames = 16
self.lmark_root_path = '../dataset/landmark1d'
self.audio_root_path = '../dataset/audio'
self.pca = torch.FloatTensor(np.load('../basics/U_lrw1.npy')[:,:6] )
self.mean = torch.FloatTensor(np.load('../basics/mean_lrw1.npy'))
if self.train=='train':
_file = open(os.path.join(dataset_dir, "lmark_train.pkl"), "rb")
self.train_data = pickle.load(_file)
_file.close()
elif self.train =='test':
_file = open(os.path.join(dataset_dir, "lmark_test.pkl"), "rb")
self.test_data = pickle.load(_file)
_file.close()
elif self.train =='demo' :
_file = open(os.path.join(dataset_dir, "img_demo.pkl"), "rb")
self.demo_data = pickle.load(_file)
_file.close()
def __getitem__(self, index):
# In training phase, it return real_image, wrong_image, text
if self.train=='train':
lmark_path = os.path.join(self.lmark_root_path , self.train_data[index][0] , self.train_data[index][1],self.train_data[index][2], self.train_data[index][2] + '.npy')
mfcc_path = os.path.join('../dataset/mfcc/', self.train_data[index][0], self.train_data[index][1], self.train_data[index][2] + '.npy')
lmark = np.load(lmark_path)
lmark = torch.FloatTensor(lmark) * 5.0
lmark = lmark - self.mean.expand_as(lmark)
lmark = torch.mm(lmark,self.pca)
mfcc = np.load(mfcc_path)
r = random.choice(
[x for x in range(3,25)])
example_landmark =lmark[r,:]
example_mfcc = mfcc[(r -3) * 4 : (r + 4) * 4, 1 :]
while True:
current_frame_id = random.choice(
[x for x in range(3,25)])
if current_frame_id != r:
break
t_mfcc =mfcc[( current_frame_id - 3)*4: (current_frame_id + 4)*4, 1:]
t_mfcc = torch.FloatTensor(t_mfcc)
landmark =lmark[current_frame_id , :]
example_landmark = torch.FloatTensor(example_landmark)
example_mfcc = torch.FloatTensor(example_mfcc)
landmark = torch.FloatTensor(landmark)
landmark = landmark
return example_landmark, example_mfcc, landmark, t_mfcc
if self.train=='test':
mfcc_path = os.path.join('../dataset/mfcc/', self.test_data[index][0], self.test_data[index][1], self.test_data[index][2] + '.npy')
lmark_path = os.path.join(self.lmark_root_path , self.test_data[index][0] , self.test_data[index][1],self.test_data[index][2], self.test_data[index][2] + '.npy')
lmark = np.load(lmark_path)
mfcc = np.load(mfcc_path)
example_landmark =lmark[3,:]
example_mfcc = mfcc[0 : 7 * 4, 1 :]
r =3
ind = self.test_data[index][3]
t_mfcc =mfcc[(r + ind - 3)*4: (r + ind + 4)*4, 1:]
t_mfcc = torch.FloatTensor(t_mfcc)
landmark =lmark[r+ ind,:]
# example_audio = torch.FloatTensor(example_audio)
example_mfcc = torch.FloatTensor(example_mfcc)
# audio = torch.FloatTensor(audio)
# mfccs = torch.FloatTensor(mfccs)
landmark = torch.FloatTensor(landmark)
# landmark = self.transform(landmark)
landmark = landmark * 5.0
example_landmark = torch.FloatTensor(example_landmark).view(1,-1)
example_landmark = example_landmark - self.mean.expand_as(example_landmark)
example_landmark = torch.mm(example_landmark,self.pca)
return example_landmark[0], example_mfcc, landmark, t_mfcc
def __len__(self):
if self.train=='train':
return len(self.train_data)
elif self.train=='test':
return len(self.test_data)
else:
pass
class LRWdataset1D_single_gt(data.Dataset):
def __init__(self,
dataset_dir,
output_shape=[128, 128],
train='train'):
self.train = train
self.dataset_dir = dataset_dir
self.output_shape = tuple(output_shape)
if not len(output_shape) in [2, 3]:
raise ValueError("[*] output_shape must be [H,W] or [C,H,W]")
if self.train=='train':
_file = open(os.path.join(dataset_dir, "new_img_full_gt_train.pkl"), "rb")
self.train_data = pickle.load(_file)
_file.close()
elif self.train =='test':
_file = open(os.path.join(dataset_dir, "new_img_full_gt_test.pkl"), "rb")
self.test_data = pickle.load(_file)
_file.close()
elif self.train =='demo' :
_file = open(os.path.join(dataset_dir, "new_img_full_gt_demo.pkl"), "rb")
self.demo_data = pickle.load(_file)
_file.close()
self.transform = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize(mean=(0.5, 0.5, 0.5), std=(0.5, 0.5, 0.5))
])
def __getitem__(self, index):
# In training phase, it return real_image, wrong_image, text
if self.train=='train':
#load righ img
image_path = '../dataset/regions/' + self.train_data[index][0]
landmark_path = '../dataset/landmark1d/' + self.train_data[index][0][:-8] + '.npy'
landmark = np.load(landmark_path) * 5.0
right_landmark = landmark[self.train_data[index][1] - 1]
right_landmark = torch.FloatTensor(right_landmark.reshape(-1))
im = cv2.imread(image_path)
im = cv2.cvtColor(im, cv2.COLOR_BGR2RGB)
im = cv2.resize(im, self.output_shape)
im = self.transform(im)
right_img = torch.FloatTensor(im)
r = random.choice(
[x for x in range(1,30)])
example_path = image_path[:-8] + '_%03d.jpg'%r
example_landmark = landmark[r - 1]
example_landmark = torch.FloatTensor(example_landmark.reshape(-1))
example_img = cv2.imread(example_path)
example_img = cv2.cvtColor(example_img, cv2.COLOR_BGR2RGB)
example_img = cv2.resize(example_img, self.output_shape)
example_img = self.transform(example_img)
return example_img, example_landmark, right_img,right_landmark
elif self.train =='test':
# try:
#load righ img
image_path = '../dataset/regions/' + self.test_data[index][0]
landmark_path = '../dataset/landmark1d/' + self.test_data[index][0][:-8] + '.npy'
landmark = np.load(landmark_path) * 5.0
right_landmark = landmark[self.test_data[index][1] - 1]
right_landmark = torch.FloatTensor(right_landmark.reshape(-1))
im = cv2.imread(image_path)
im = cv2.cvtColor(im, cv2.COLOR_BGR2RGB)
im = cv2.resize(im, self.output_shape)
im = self.transform(im)
right_img = torch.FloatTensor(im)
example_path = '../image/musk1_region.jpg'
example_landmark = np.load('../image/musk1.npy')
example_landmark = torch.FloatTensor(example_landmark.reshape(-1)) * 5.0
example_img = cv2.imread(example_path)
example_img = cv2.cvtColor(example_img, cv2.COLOR_BGR2RGB)
example_img = cv2.resize(example_img, self.output_shape)
example_img = self.transform(example_img)
return example_img, example_landmark, right_img,right_landmark
class LRWdataset1D_lstm_gt(data.Dataset):
def __init__(self,
dataset_dir,
output_shape=[128, 128],
train='train'):
self.train = train
self.dataset_dir = dataset_dir
self.output_shape = tuple(output_shape)
if not len(output_shape) in [2, 3]:
raise ValueError("[*] output_shape must be [H,W] or [C,H,W]")
if self.train=='train':
_file = open(os.path.join(dataset_dir, "new_16_full_gt_train.pkl"), "rb")
self.train_data = pickle.load(_file)
_file.close()
elif self.train =='test':
_file = open(os.path.join(dataset_dir, "new_16_full_gt_test.pkl"), "rb")
self.test_data = pickle.load(_file)
_file.close()
elif self.train =='demo' :
_file = open(os.path.join(dataset_dir, "new_16_full_gt_demo.pkl"), "rb")
self.demo_data = pickle.load(_file)
_file.close()
self.transform = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize(mean=(0.5, 0.5, 0.5), std=(0.5, 0.5, 0.5))
])
def __getitem__(self, index):
# In training phase, it return real_image, wrong_image, text
if self.train=='train':
#load righ img
image_path = '../dataset/regions/' + self.train_data[index][0]
landmark_path = '../dataset/landmark1d/' + self.train_data[index][0][:-8] + '.npy'
current_frame_id =self.train_data[index][1]
right_img = torch.FloatTensor(16,3,self.output_shape[0],self.output_shape[1])
for jj in range(16):
this_frame = current_frame_id + jj
image_path = '../dataset/regions/' + self.train_data[index][0][:-7] + '%03d.jpg'%this_frame
im = cv2.imread(image_path)
im = cv2.cvtColor(im, cv2.COLOR_BGR2RGB)
im = cv2.resize(im, self.output_shape)
im = self.transform(im)
right_img[jj,:,:,:] = torch.FloatTensor(im)
landmark = np.load(landmark_path) * 5.0
right_landmark = landmark[self.train_data[index][1] - 1 : self.train_data[index][1] + 15 ]
right_landmark = torch.FloatTensor(right_landmark.reshape(16,136))
r = random.choice(
[x for x in range(1,30)])
example_path = image_path[:-8] + '_%03d.jpg'%r
example_landmark = landmark[r - 1]
example_landmark = torch.FloatTensor(example_landmark.reshape(-1))
example_img = cv2.imread(example_path)
example_img = cv2.cvtColor(example_img, cv2.COLOR_BGR2RGB)
example_img = cv2.resize(example_img, self.output_shape)
example_img = self.transform(example_img)
# print (right_landmark.size())
return example_img, example_landmark, right_img,right_landmark
elif self.train =='test':
#load righ img
image_path = '../dataset/regions/' + self.test_data[index][0]
landmark_path = '../dataset/landmark1d/' + self.test_data[index][0][:-8] + '.npy'
current_frame_id =self.test_data[index][1]
right_img = torch.FloatTensor(16,3,self.output_shape[0],self.output_shape[1])
for jj in range(16):
this_frame = current_frame_id + jj
image_path = '../dataset/regions/' + self.test_data[index][0][:-7] + '%03d.jpg'%this_frame
im = cv2.imread(image_path)
im = cv2.cvtColor(im, cv2.COLOR_BGR2RGB)
im = cv2.resize(im, self.output_shape)
im = self.transform(im)
right_img[jj,:,:,:] = torch.FloatTensor(im)
landmark = np.load(landmark_path) * 5.0
right_landmark = landmark[self.test_data[index][1] - 1 : self.test_data[index][1] + 15 ]
right_landmark = torch.FloatTensor(right_landmark.reshape(16,136))
r = random.choice(
[x for x in range(1,30)])
r = current_frame_id
example_path = image_path[:-8] + '_%03d.jpg'%r
example_landmark = landmark[r - 1]
example_landmark = torch.FloatTensor(example_landmark.reshape(-1))
example_img = cv2.imread(example_path)
example_img = cv2.cvtColor(example_img, cv2.COLOR_BGR2RGB)
example_img = cv2.resize(example_img, self.output_shape)
example_img = self.transform(example_img)
# print (right_landmark.size())
return example_img, example_landmark, right_img,right_landmark
def __len__(self):
if self.train=='train':
return len(self.train_data)
elif self.train=='test':
return len(self.test_data)
else:
return len(self.demo_data)
class LRWdataset1D_single(data.Dataset):
def __init__(self,
dataset_dir,
output_shape=[128, 128],
train='train'):
self.train = train
self.dataset_dir = dataset_dir
self.output_shape = tuple(output_shape)
if not len(output_shape) in [2, 3]:
raise ValueError("[*] output_shape must be [H,W] or [C,H,W]")
if self.train=='train':
_file = open(os.path.join(dataset_dir, "new_img_small_train.pkl"), "rb")
self.train_data = pickle.load(_file)
_file.close()
elif self.train =='test':
_file = open(os.path.join(dataset_dir, "new_img_small_test.pkl"), "rb")
self.test_data = pickle.load(_file)
_file.close()
elif self.train =='demo' :
_file = open(os.path.join(dataset_dir, "img_demo.pkl"), "rb")
self.demo_data = pickle.load(_file)
_file.close()
self.transform = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize(mean=(0.5, 0.5, 0.5), std=(0.5, 0.5, 0.5))
])
def __getitem__(self, index):
# In training phase, it return real_image, wrong_image, text
if self.train=='train':
while True:
# try:
#load righ img
image_path = self.train_data[index][0]
landmark_path = self.train_data[index][1]
landmark = np.load(landmark_path)
right_landmark = landmark[self.train_data[index][2]]
tp = ( np.dot(right_landmark.reshape(1,6), EIGVECS))[0,:].reshape(68,3)
tp = tp[:,:-1].reshape(-1)
right_landmark = torch.FloatTensor(tp)
im = cv2.imread(image_path)
if im is None:
raise IOError
im = cv2.cvtColor(im, cv2.COLOR_BGR2RGB)
im = cv2.resize(im, self.output_shape)
im = self.transform(im)
right_img = torch.FloatTensor(im)
r = random.choice(
[x for x in range(1,30)])
example_path = image_path[:-8] + '_%03d.jpg'%r
example_landmark = landmark[r]
tp = ( np.dot(example_landmark.reshape(1,6), EIGVECS))[0,:].reshape(68,3)
tp = tp[:,:-1].reshape(-1)
example_landmark = torch.FloatTensor(tp)
example_img = cv2.imread(example_path)
if example_img is None:
raise IOError
example_img = cv2.cvtColor(example_img, cv2.COLOR_BGR2RGB)
example_img = cv2.resize(example_img, self.output_shape)
example_img = self.transform(example_img)
return example_img, example_landmark, right_img,right_landmark
elif self.train =='test':
while True:
image_path = self.test_data[index][0]
landmark_path = self.test_data[index][1]
landmark = np.load(landmark_path)
right_landmark = landmark[self.test_data[index][2]]
right_landmark = torch.FloatTensor((MS + np.dot(right_landmark.reshape(1,6), EIGVECS)).reshape(-1))
print (right_landmark.shape)
im = cv2.imread(image_path)
if im is None:
raise IOError
im = cv2.cvtColor(im, cv2.COLOR_BGR2RGB)
im = cv2.resize(im, self.output_shape)
im = self.transform(im)
right_img = torch.FloatTensor(im)
r = random.choice(
[x for x in range(1,30)])
#load example image
example_path = image_path[:-8] + '_%03d.jpg'%r
example_landmark = landmark[self.train_data[r][2]]
example_landmark = torch.FloatTensor((MS + np.dot(example_landmark.reshape(1,6), EIGVECS)).reshape(-1))
example_img = cv2.imread(example_path)
if example_img is None:
raise IOError
example_img = cv2.cvtColor(example_img, cv2.COLOR_BGR2RGB)
example_img = cv2.resize(example_img, self.output_shape)
example_img = self.transform(example_img)
return example_img, example_landmark, right_img,right_landmark
elif self.train =='demo':
landmarks = np.load('/home/lchen63/obama_fake.npy')
landmarks =np.reshape(landmarks, (landmarks.shape[0], 136))
while True:
# try:
image_path = self.demo_data[index][0]
im = cv2.imread(image_path)
im = cv2.cvtColor(im, cv2.COLOR_BGR2RGB)
im = cv2.resize(im, self.output_shape)
im = self.transform(im)
right_img = torch.FloatTensor(im)
example_path = '/mnt/disk1/dat/lchen63/lrw/demo/musk1_region.jpg'
example_landmark = landmarks[0]
example_lip = cv2.imread(example_path)
example_lip = cv2.cvtColor(example_lip, cv2.COLOR_BGR2RGB)
example_lip = cv2.resize(example_lip, self.output_shape)
example_lip = self.transform(example_lip)
right_landmark = torch.FloatTensor(landmarks[index-1])
wrong_landmark = right_landmark
return example_lip, example_landmark, right_img,right_landmark, wrong_landmark
def __len__(self):
if self.train=='train':
return len(self.train_data)
elif self.train=='test':
return len(self.test_data)
else:
return len(self.demo_data)
#############################################################grid
class GRIDdataset1D_single_gt(data.Dataset):
def __init__(self,
dataset_dir,
output_shape=[128, 128],
train='train'):
self.train = train
self.dataset_dir = dataset_dir
self.output_shape = tuple(output_shape)
if not len(output_shape) in [2, 3]:
raise ValueError("[*] output_shape must be [H,W] or [C,H,W]")
if self.train=='train':
_file = open(os.path.join(dataset_dir, "lmark_train.pkl"), "rb")
self.train_data = pickle.load(_file)
_file.close()
elif self.train =='test':
_file = open(os.path.join(dataset_dir, "lmark_test.pkl"), "rb")
self.test_data = pickle.load(_file)
_file.close()
elif self.train =='demo' :
_file = open(os.path.join(dataset_dir, "new_img_full_gt_demo.pkl"), "rb")
self.demo_data = pickle.load(_file)
_file.close()
self.transform = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize(mean=(0.5, 0.5, 0.5), std=(0.5, 0.5, 0.5))
])
def __getitem__(self, index):
# In training phase, it return real_image, wrong_image, text
if self.train=='train':
#load righ img
image_path = os.path.join('/mnt/ssd0/dat/lchen63/grid/data' , self.train_data[index][0], self.train_data[index][0], '%05d.jpg'%(self.train_data[index][1] + 1))
landmark_path = os.path.join('/mnt/ssd0/dat/lchen63/grid/data' , self.train_data[index][0], self.train_data[index][0] + '_norm_lmarks.npy')
landmark = np.load(landmark_path)
right_landmark = landmark[self.train_data[index][1]]
right_landmark = torch.FloatTensor(right_landmark.reshape(-1))
im = cv2.imread(image_path)
im = cv2.cvtColor(im, cv2.COLOR_BGR2RGB)
im = cv2.resize(im, self.output_shape)
im = self.transform(im)
right_img = torch.FloatTensor(im)
r = random.choice(
[x for x in range(1, 76)])
example_path = os.path.join('/mnt/ssd0/dat/lchen63/grid/data' , self.train_data[index][0], self.train_data[index][0], '%05d.jpg'%(r))
example_landmark = landmark[r - 1]
example_landmark = torch.FloatTensor(example_landmark.reshape(-1))
example_img = cv2.imread(example_path)
example_img = cv2.cvtColor(example_img, cv2.COLOR_BGR2RGB)
example_img = cv2.resize(example_img, self.output_shape)
example_img = self.transform(example_img)
return example_img, example_landmark, right_img,right_landmark
elif self.train =='test':
# try:
#load righ img
image_path = os.path.join('/mnt/ssd0/dat/lchen63/grid/data' , self.test_data[index][0], self.test_data[index][0], '%05d.jpg'%(self.test_data[index][1] + 1))
landmark_path = os.path.join('/mnt/ssd0/dat/lchen63/grid/data' , self.test_data[index][0], self.test_data[index][0] + '_norm_lmarks.npy')
landmark = np.load(landmark_path)
right_landmark = landmark[self.test_data[index][1]]
right_landmark = torch.FloatTensor(right_landmark.reshape(-1))
im = cv2.imread(image_path)
im = cv2.cvtColor(im, cv2.COLOR_BGR2RGB)
im = cv2.resize(im, self.output_shape)
im = self.transform(im)
right_img = torch.FloatTensor(im)
r = random.choice(
[x for x in range(1, 76)])
example_path = os.path.join('/mnt/ssd0/dat/lchen63/grid/data' , self.test_data[index][0], self.test_data[index][0], '%05d.jpg'%(r))
example_landmark = landmark[r - 1]
example_landmark = torch.FloatTensor(example_landmark.reshape(-1))
example_img = cv2.imread(example_path)
example_img = cv2.cvtColor(example_img, cv2.COLOR_BGR2RGB)
example_img = cv2.resize(example_img, self.output_shape)
example_img = self.transform(example_img)
return example_img, example_landmark, right_img,right_landmark
elif self.train =='demo':
# try:
#load righ img
image_path = '/mnt/ssd0/dat/lchen63/lrw/demo/regions/' + self.demo_data[index][0]
landmark_path = '/mnt/ssd0/dat/lchen63/lrw/demo/landmark1d/' + self.demo_data[index][1].replace('obama_', 'obama_ge_')
right_landmark = np.load(landmark_path)
right_landmark = torch.FloatTensor(right_landmark.reshape(-1))
# print ('=========================')
# print ('real path: ' + image_path)
im = cv2.imread(image_path)
if im is None:
print (image_path)
raise IOError
im = cv2.cvtColor(im, cv2.COLOR_BGR2RGB)
im = cv2.resize(im, self.output_shape)
im = self.transform(im)
right_img = torch.FloatTensor(im)
example_path = '../image/musk1_region.jpg'
example_landmark = np.load('../image/musk1.npy')
# tp = ( np.dot(example_landmark.reshape(1,6), EIGVECS))[0,:].reshape(68,3)
# tp = tp[:,:-1].reshape(-1)
example_landmark = torch.FloatTensor(example_landmark.reshape(-1))
example_img = cv2.imread(example_path)
example_img = cv2.cvtColor(example_img, cv2.COLOR_BGR2RGB)
example_img = cv2.resize(example_img, self.output_shape)
example_img = self.transform(example_img)
# print (right_landmark.size())
return example_img, example_landmark, right_img,right_landmark
def __len__(self):
if self.train=='train':
return len(self.train_data)
elif self.train=='test':
return len(self.test_data)
else:
return len(self.demo_data)
class GRIDdataset1D_lstm_gt(data.Dataset):
def __init__(self,
dataset_dir,
output_shape=[128, 128],
train='train'):
self.train = train
self.dataset_dir = dataset_dir
self.output_shape = tuple(output_shape)
if not len(output_shape) in [2, 3]:
raise ValueError("[*] output_shape must be [H,W] or [C,H,W]")
if self.train=='train':
_file = open(os.path.join(dataset_dir, "lmark_16_train.pkl"), "rb")
self.train_data = pickle.load(_file)
_file.close()
elif self.train =='test':
_file = open(os.path.join(dataset_dir, "lmark_16_test.pkl"), "rb")
self.test_data = pickle.load(_file)
_file.close()
elif self.train =='demo' :
_file = open(os.path.join(dataset_dir, "new_16_full_gt_demo.pkl"), "rb")
self.demo_data = pickle.load(_file)
_file.close()
self.transform = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize(mean=(0.5, 0.5, 0.5), std=(0.5, 0.5, 0.5))
])
def __getitem__(self, index):
# In training phase, it return real_image, wrong_image, text
if self.train=='train':
#load righ img
image_path_root = os.path.join('/mnt/ssd0/dat/lchen63/grid/data' , self.train_data[index][0], self.train_data[index][0])
landmark_path = os.path.join('/mnt/ssd0/dat/lchen63/grid/data' , self.train_data[index][0], self.train_data[index][0] + '_norm_lmarks.npy')
current_frame_id =self.train_data[index][1]
right_img = torch.FloatTensor(16,3,self.output_shape[0],self.output_shape[1])
for jj in range(16):
this_frame = current_frame_id + jj
image_path = os.path.join(image_path_root, '%05d.jpg'%this_frame)
im = cv2.imread(image_path)
im = cv2.cvtColor(im, cv2.COLOR_BGR2RGB)
im = cv2.resize(im, self.output_shape)
im = self.transform(im)
right_img[jj,:,:,:] = torch.FloatTensor(im)
landmark = np.load(landmark_path)
right_landmark = landmark[self.train_data[index][1] - 1 : self.train_data[index][1] + 15 ]
right_landmark = torch.FloatTensor(right_landmark.reshape(16,136))
r = random.choice(
[x for x in range(1,76)])
example_path = os.path.join(image_path_root, '%05d.jpg'%r)
example_landmark = landmark[r - 1]
example_landmark = torch.FloatTensor(example_landmark.reshape(-1))
example_img = cv2.imread(example_path)
example_img = cv2.cvtColor(example_img, cv2.COLOR_BGR2RGB)
example_img = cv2.resize(example_img, self.output_shape)
example_img = self.transform(example_img)
return example_img, example_landmark, right_img,right_landmark
elif self.train =='test':
image_path_root = os.path.join('/mnt/ssd0/dat/lchen63/grid/data' , self.test_data[index][0], self.test_data[index][0])
landmark_path = os.path.join('/mnt/ssd0/dat/lchen63/grid/data' , self.test_data[index][0], self.test_data[index][0] + '_norm_lmarks.npy')
current_frame_id =self.test_data[index][1]
right_img = torch.FloatTensor(16,3,self.output_shape[0],self.output_shape[1])
for jj in range(16):
this_frame = current_frame_id + jj
image_path = os.path.join(image_path_root, '%05d.jpg'%this_frame)
im = cv2.imread(image_path)
im = cv2.cvtColor(im, cv2.COLOR_BGR2RGB)
im = cv2.resize(im, self.output_shape)
im = self.transform(im)
right_img[jj,:,:,:] = torch.FloatTensor(im)
landmark = np.load(landmark_path)
right_landmark = landmark[self.test_data[index][1] - 1 : self.test_data[index][1] + 15 ]
right_landmark = torch.FloatTensor(right_landmark.reshape(16,136))
r = random.choice(
[x for x in range(1,76)])
example_path = os.path.join(image_path_root, '%05d.jpg'%r)
example_landmark = landmark[r - 1]
example_landmark = torch.FloatTensor(example_landmark.reshape(-1))
example_img = cv2.imread(example_path)
example_img = cv2.cvtColor(example_img, cv2.COLOR_BGR2RGB)
example_img = cv2.resize(example_img, self.output_shape)
example_img = self.transform(example_img)
return example_img, example_landmark, right_img,right_landmark
def __len__(self):
if self.train=='train':
return len(self.train_data)
elif self.train=='test':
return len(self.test_data)
else:
return len(self.demo_data)
class GRID_1D_lstm_landmark_pca(data.Dataset):
def __init__(self,
dataset_dir,
train='train'):
self.train = train
self.num_frames = 16
self.root_path = '/mnt/ssd0/dat/lchen63/grid/data'
self.pca = torch.FloatTensor(np.load('../basics/U_grid.npy')[:,:6] )
self.mean = torch.FloatTensor(np.load('../basics/mean_grid.npy'))
if self.train=='train':
_file = open(os.path.join(dataset_dir, "lmark_train.pkl"), "rb")
self.train_data = pickle.load(_file)
_file.close()
elif self.train =='test':
_file = open(os.path.join(dataset_dir, "lmark_test.pkl"), "rb")
self.test_data = pickle.load(_file)
_file.close()
elif self.train =='demo' :
_file = open(os.path.join(dataset_dir, "img_demo.pkl"), "rb")
self.demo_data = pickle.load(_file)
_file.close()
def __getitem__(self, index):
# In training phase, it return real_image, wrong_image, text
if self.train=='train':
try:
lmark_path = os.path.join(self.root_path , self.train_data[index][0] , self.train_data[index][0] + '_norm_lmarks.npy')
mfcc_path = os.path.join(self.root_path, self.train_data[index][0], self.train_data[index][0] +'_mfcc.npy')
lmark = np.load(lmark_path) * 5.0
lmark = torch.FloatTensor(lmark)
lmark = lmark - self.mean.expand_as(lmark)
lmark = torch.mm(lmark,self.pca)
mfcc = np.load(mfcc_path)
r = random.choice(
[x for x in range(6,50)])
example_landmark =lmark[r,:]
example_mfcc = mfcc[(r -3) * 4 : (r + 4) * 4, 1 :]
mfccs = []
for ind in range(1,17):
t_mfcc =mfcc[(r + ind - 3)*4: (r + ind + 4)*4, 1:]
t_mfcc = torch.FloatTensor(t_mfcc)
mfccs.append(t_mfcc)
mfccs = torch.stack(mfccs, dim = 0)
landmark =lmark[r+1 : r + 17,:]
example_mfcc = torch.FloatTensor(example_mfcc)
return example_landmark, example_mfcc, landmark, mfccs
except:
self.__getitem__(index + 1)
if self.train=='test':
lmark_path = os.path.join(self.root_path , self.test_data[index][0] , self.test_data[index][0] + '_norm_lmarks.npy')
mfcc_path = os.path.join(self.root_path, self.test_data[index][0], self.test_data[index][0] +'_mfcc.npy')
lmark = np.load(lmark_path) * 5.0
lmark = torch.FloatTensor(lmark)
lmark = lmark - self.mean.expand_as(lmark)
lmark = torch.mm(lmark,self.pca)
mfcc = np.load(mfcc_path)
r = random.choice(
[x for x in range(3,70)])
example_landmark =lmark[r,:]
example_mfcc = mfcc[(r -3) * 4 : (r + 4) * 4, 1 :]
mfccs = []
for ind in range(1,17):
t_mfcc =mfcc[(r + ind - 3)*4: (r + ind + 4)*4, 1:]
t_mfcc = torch.FloatTensor(t_mfcc)
mfccs.append(t_mfcc)
mfccs = torch.stack(mfccs, dim = 0)
landmark =lmark[r+1 : r + 17,:]
example_mfcc = torch.FloatTensor(example_mfcc)
return example_landmark, example_mfcc, landmark, mfccs
def __len__(self):
if self.train=='train':
return len(self.train_data)
elif self.train=='test':
return len(self.test_data)
else:
pass
class GRID_1D_single_landmark_pca(data.Dataset):
def __init__(self,
dataset_dir,
train='train'):
self.train = train
self.num_frames = 16
self.root_path = '/mnt/ssd0/dat/lchen63/grid/data'
self.pca = torch.FloatTensor(np.load('../basics/U_grid.npy')[:,:6] )
self.mean = torch.FloatTensor(np.load('../basics/mean_grid.npy'))
if self.train=='train':
_file = open(os.path.join(dataset_dir, "lmark_train.pkl"), "rb")
self.train_data = pickle.load(_file)
_file.close()
elif self.train =='test':
_file = open(os.path.join(dataset_dir, "lmark_test.pkl"), "rb")
self.test_data = pickle.load(_file)
_file.close()
elif self.train =='demo' :
_file = open(os.path.join(dataset_dir, "img_demo.pkl"), "rb")
self.demo_data = pickle.load(_file)
_file.close()
def __getitem__(self, index):
# In training phase, it return real_image, wrong_image, text
if self.train=='train':
# try:
lmark_path = os.path.join(self.root_path , self.train_data[index][0] , self.train_data[index][0] + '_norm_lmarks.npy')
mfcc_path = os.path.join(self.root_path, self.train_data[index][0], self.train_data[index][0] +'_mfcc.npy')
ind = self.train_data[index][1]
lmark = | np.load(lmark_path) | numpy.load |
"""Authors: <NAME>, <NAME>, and <NAME>."""
from typing import Iterable, Tuple, Optional
import numpy as np
import psutil
from abc import abstractmethod
from itertools import product
from hdmf.data_utils import AbstractDataChunkIterator, DataChunk
class GenericDataChunkIterator(AbstractDataChunkIterator):
"""DataChunkIterator that lets the user specify chunk and buffer shapes."""
def _set_chunk_shape(self, chunk_mb):
"""
Select chunk size less than the threshold of chunk_mb, keeping the dimensional ratios of the original data.
Parameters
----------
chunk_mb : float
H5 reccomends setting this to around 1 MB for optimal performance.
"""
n_dims = len(self.maxshape)
itemsize = self.dtype.itemsize
chunk_bytes = chunk_mb * 1e6
v = np.floor( | np.array(self.maxshape) | numpy.array |
from sklearn import preprocessing
import numpy as np
from .preprocessing import Preprocessor
import os
import pickle
import pandas as pd
def get_X_y(df, target):
X = np.array(df.loc[:, df.columns != target])
y = np.array(df.loc[:, df.columns == target])
return X, y
def sample_df_dataset(df_train_name, df_valid_name, df_test_name, run_seed=1234, max_num_row=10000):
# always same samples here
np.random.seed(1234)
df_train = pd.read_csv(df_train_name)
df_train = df_train.sample(n=min(max_num_row, df_train.shape[0]), random_state=1234)
| np.random.seed(run_seed) | numpy.random.seed |
# Copyright (c) 2018 <NAME>
#
# Distributed under the Boost Software License, Version 1.0. (See accompanying
# file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
import numpy as np
from phylanx import Phylanx
@Phylanx
def test_arange_float():
arange_float = | np.arange(3, dtype='float') | numpy.arange |
import numpy as np
from collections import defaultdict
from typing import Any, Callable, Dict, List, Optional, Set, Tuple, Union
def _voc_ap(
rec,
prec,
use_07_metric=False,
):
"""Compute VOC AP given precision and recall. If use_07_metric is true, uses
the VOC 07 11-point method (default:False).
"""
if use_07_metric:
# 11 point metric
ap = 0.0
for t in np.arange(0.0, 1.1, 0.1):
if np.sum(rec >= t) == 0:
p = 0
else:
p = np.max(prec[rec >= t])
ap = ap + p / 11.0
else:
# correct AP calculation
# first append sentinel values at the end
mrec = np.concatenate(([0.0], rec, [1.0]))
mpre = np.concatenate(([0.0], prec, [0.0]))
# compute the precision envelope
for i in range(mpre.size - 1, 0, -1):
mpre[i - 1] = np.maximum(mpre[i - 1], mpre[i])
# to calculate area under PR curve, look for points
# where X axis (recall) changes value
i = np.where(mrec[1:] != mrec[:-1])[0]
# and sum (\Delta recall) * prec
ap = np.sum((mrec[i + 1] - mrec[i]) * mpre[i + 1])
return ap
def voc_ap_score(
p_bboxes: List[np.ndarray],
p_scores: List[np.ndarray],
p_classes: List[np.ndarray],
gt_bboxes: List[np.ndarray],
gt_classes: List[np.ndarray],
class_id: int = None,
threshold: float = 0.5,
):
"""
Args:
p_bboxes: a list of predict bboxes
p_scores: a list of predict score for bbox
p_classes: a list of predict class id for bbox
gt_bboxes: a list of ground truth bboxes
gt_classes: a list of true class id for each true bbox
class_id: the class id to compute ap score
threshold: the threshold to ap score
"""
if class_id is not None:
gt_bboxes = [gt_bbox[gt_class == class_id] for gt_class, gt_bbox in zip(gt_classes, gt_bboxes)]
p_bboxes = [p_bbox[p_class == class_id] for p_class, p_bbox in zip(p_classes, p_bboxes)]
p_scores = [p_score[p_class == class_id] for p_class, p_score in zip(p_classes, p_scores)]
p_indexes = [np.array([i] * len(p_bboxes[i])) for i in range(len(p_bboxes))]
p_bboxes, p_scores, p_indexes = (
np.concatenate(p_bboxes),
np.concatenate(p_scores),
np.concatenate(p_indexes),
)
p_sort_indexes = | np.argsort(-p_scores) | numpy.argsort |
import sys
import numpy as np
import matplotlib.pyplot as plt
from sklearn.manifold import TSNE
from sklearn.neighbors import KNeighborsClassifier
from sklearn.model_selection import StratifiedShuffleSplit
def example1(Ntr, d, seed=1991):
np.random.seed(seed)
N = 2 * Ntr
# view 1: uniform in sphere
# class 0 in radius [0,2], class 1 in radius [3,4]
r1 = 2 * np.random.rand(N)
theta1 = np.pi * np.random.rand(N)
phi1 = 2 * np.pi * np.random.rand(N)
r2 = 3 + np.random.rand(N)
theta2 = np.pi * np.random.rand(N)
phi2 = 2 * np.pi * np.random.rand(N)
X1 = np.vstack((r1 * np.sin(theta1) * np.cos(phi1), r1 * | np.sin(theta1) | numpy.sin |
from elasticsearch import Elasticsearch
from elasticsearch_dsl import Search
import numpy as np
##Connect with elasticsearch client
es = Elasticsearch(['localhost'],port=9200)
##Some initial variables
label_fields = ["title"]
fields = ["title","cast","country","description"]
weight_fields =["title^2","cast^1","country^1","description^3"]
label_id =[]
Similarity_score=[]
Similarity_id = []
Similarity_title = []
Similarity_name =[]
tmp_precision =0
tmp_recall =0
tmp_f_measure =0
w_tmp_precision =0
w_tmp_recall =0
w_tmp_f_measure =0
Ag_precision = []
Ag_recall = []
Ag_f_measure = []
W_Ag_precision = []
W_Ag_recall = []
W_Ag_f_measure =[]
##Give label_query to return our label_id through this function
def label(index,label_query,label_fields):
label_id=[]
s = Search(using=es, index=index)
results = s.query("simple_query_string", query=label_query, fields=label_fields,
auto_generate_synonyms_phrase_query=True).execute()
for hit in results:
label_id.append(hit.meta.id)
# print('This is label_id:', label_id)
return label_id
##Use different models to search and match the query and return the score, id and name
def Similarity_module(index,query,fields):
Similarity_score=[]
Similarity_id =[]
Similarity_title = []
s = Search(using=es, index=index)
results = s.query("simple_query_string", query=query, fields=fields,
auto_generate_synonyms_phrase_query=True).execute()
for hit in results:
Similarity_score.append(hit.meta.score)
Similarity_id.append(hit.meta.id)
Similarity_title.append(hit.title)
# print('This is Similarity_score:', Similarity_score)
# print('This is Similarity_id:', Similarity_id)
Similarity_score = score_normalized(Similarity_score)
return Similarity_score,Similarity_id,Similarity_title
##Use different models to search and match the query and return the score, id and name,
##Added each term in the field, giving different weights.
def Similarity_module_weight(index,query,weight_fields):
Similarity_score=[]
Similarity_id =[]
Similarity_title = []
s = Search(using=es, index=index)
results = s.query("simple_query_string", query=query, fields=weight_fields,
auto_generate_synonyms_phrase_query=True).execute()
for hit in results:
Similarity_score.append(hit.meta.score)
Similarity_id.append(hit.meta.id)
Similarity_title.append(hit.title)
# print('This is Similarity_score:', Similarity_score)
# print('This is Similarity_id:', Similarity_id)
Similarity_score=score_normalized(Similarity_score)
return Similarity_score,Similarity_id,Similarity_title
##Calculate model accuracy, recall rate and Harmonic Mean
def cal_rec_pre(label_id,search_id):
tmp = [val for val in label_id if val in search_id]
precision = len(tmp) / len(label_id)
recall = len(tmp) / len(search_id)
f_measure = (2*precision*recall)/(precision+recall)
return precision,recall,f_measure
##Normalize the returned document score (min-max)
def score_normalized(Similarity_score):
normalize_score = []
min_score = min(Similarity_score)
max_score = max(Similarity_score)
while True:
try:
for i in range(len(Similarity_score)):
if len(Similarity_score) == 1:
normalize_score.append(Similarity_score[0] / Similarity_score[0])
else:
normalize_score.append((Similarity_score[i] - min_score) / (max_score - min_score))
return normalize_score
except:
break
## Calculation of diversity between models
def Kendall_rank_correlation(model1,model2,query,fields):
model1_score,model1_id,_=Similarity_module(model1,query,fields)
model2_score, model2_id,_ = Similarity_module(model2, query, fields)
Same_results = [val for val in model1_id if val in model2_id]
N = len(model1_id)
C = len(Same_results)
D = N - 2 * C
tau = (C - D) / (N * (N+1) / 2)
return tau
##Ranking combination, you can combine multiple models and return the new document score, id and name
def rank_combination(query,index,fields):
score = []
id = []
name = []
rank = []
for i in range(len(index)):
_, Similarity_id, Similarity_name = Similarity_module(index[i], query, fields)
rank += [1,2,3,4,5,6,7,8,9,10]
id += Similarity_id
name += Similarity_name
# print(id)
id_unique = sorted(set(id), key=id.index)
rank_unique = []
name_unique = sorted(set(name), key=name.index)
sum_rank = 0
for j in range (len(id_unique)):
location = [i for i, a in enumerate(id) if a == id_unique[j]]
for k in range(len(location)):
sum_rank = sum_rank + rank[location[k]]
avg_rank = sum_rank/len(location)
rank_unique.append(float(avg_rank))
sum_rank = 0
rank_unique = np.array(rank_unique, dtype=np.float32)
id_unique = np.array(id_unique, dtype=np.int32)
name_unique = np.array(name_unique)
rank_unique = rank_unique[np.argsort(rank_unique)]
id_unique = id_unique[ | np.argsort(rank_unique) | numpy.argsort |
import json
import os
import time
import numpy as np
import matplotlib.pyplot as plt
import logging
import re
from datetime import datetime
from qcodes.instrument.base import Instrument
from qcodes.utils import validators
from qcodes.instrument.parameter import ManualParameter
import zhinst.ziPython as zi
log = logging.getLogger(__name__)
##########################################################################
# Module level functions
##########################################################################
def gen_waveform_name(ch, cw):
"""
Return a standard waveform name based on channel and codeword number.
Note the use of 1-based indexing of the channels. To clarify, the
'ch' argument to this function is 0-based, but the naming of the actual
waveforms as well as the signal outputs of the instruments are 1-based.
The function will map 'logical' channel 0 to physical channel 1, and so on.
"""
return 'wave_ch{}_cw{:03}'.format(ch+1, cw)
def gen_partner_waveform_name(ch, cw):
"""
Return a standard waveform name for the partner waveform of a dual-channel
waveform. The physical channel indexing is 1-based where as the logical channel
indexing (i.e. the argument to this function) is 0-based. To clarify, the
'ch' argument to this function is 0-based, but the naming of the actual
waveforms as well as the signal outputs of the instruments are 1-based.
The function will map 'logical' channel 0 to physical channel 1, and so on.
"""
return gen_waveform_name(2*(ch//2) + ((ch + 1) % 2), cw)
def merge_waveforms(chan0=None, chan1=None, marker=None):
"""
Merges waveforms for channel 0, channel 1 and marker bits into a single
numpy array suitable for being written to the instrument. Channel 1 and marker
data is optional. Use named arguments to combine, e.g. channel 0 and marker data.
"""
chan0_uint = None
chan1_uint = None
marker_uint = None
# The 'array_format' variable is used internally in this function in order to
# control the order and number of uint16 words that we put together for each
# sample of the final array. The variable is essentially interpreted as a bit
# mask where each bit indicates which channels/marker values to include in
# the final array. Bit 0 for chan0 data, 1 for chan1 data and 2 for marker data.
array_format = 0
if chan0 is not None:
chan0_uint = np.array((np.power(2, 15)-1)*chan0, dtype=np.uint16)
array_format += 1
if chan1 is not None:
chan1_uint = np.array((np.power(2, 15)-1)*chan1, dtype=np.uint16)
array_format += 2
if marker is not None:
marker_uint = np.array(marker, dtype=np.uint16)
array_format += 4
if array_format == 1:
return chan0_uint
elif array_format == 2:
return chan1_uint
elif array_format == 3:
return np.vstack((chan0_uint, chan1_uint)).reshape((-2,), order='F')
elif array_format == 4:
return marker_uint
elif array_format == 5:
return np.vstack((chan0_uint, marker_uint)).reshape((-2,), order='F')
elif array_format == 6:
return np.vstack((chan1_uint, marker_uint)).reshape((-2,), order='F')
elif array_format == 7:
return np.vstack((chan0_uint, chan1_uint, marker_uint)).reshape((-2,), order='F')
else:
return []
def plot_timing_diagram(data, bits, line_length=30):
"""
Takes list of 32-bit integer values as read from the 'raw/dios/0/data' device nodes and creates
a timing diagram of the result. The timing diagram can be used for verifying that e.g. the
strobe signal (A.K.A the toggle signal) is periodic.
"""
def _plot_lines(ax, pos, *args, **kwargs):
if ax == 'x':
for p in pos:
plt.axvline(p, *args, **kwargs)
else:
for p in pos:
plt.axhline(p, *args, **kwargs)
def _plot_timing_diagram(data, bits):
plt.figure(figsize=(20, 0.5*len(bits)))
t = np.arange(len(data))
_plot_lines('y', 2*np.arange(len(bits)), color='.5', linewidth=2)
_plot_lines('x', t[0:-1:2], color='.5', linewidth=0.5)
for n, i in enumerate(reversed(bits)):
line = [((x >> i) & 1) for x in data]
plt.step(t, np.array(line) + 2*n, 'r', linewidth=2, where='post')
plt.text(-0.5, 2*n, str(i))
plt.xlim([t[0], t[-1]])
plt.ylim([0, 2*len(bits)+1])
plt.gca().axis('off')
plt.show()
while len(data) > 0:
if len(data) > line_length:
d = data[0:line_length]
data = data[line_length:]
else:
d = data
data = []
_plot_timing_diagram(d, bits)
def plot_codeword_diagram(ts, cws, range=None):
"""
Takes a list of timestamps (X) and codewords (Y) and produces a simple 'stem' plot of the two.
The plot is useful for visually checking that the codewords are detected at regular intervals.
Can also be used for visual verification of standard codeword patterns such as the staircase used
for calibration.
"""
plt.figure(figsize=(20, 10))
plt.stem((np.array(ts)-ts[0])*10.0/3, np.array(cws))
if range is not None:
plt.xlim(range[0], range[1])
xticks = np.arange(range[0], range[1], step=20)
while len(xticks) > 20:
xticks = xticks[::2]
plt.xticks(xticks)
plt.xlabel('Time (ns)')
plt.ylabel('Codeword (#)')
plt.grid()
plt.show()
def _gen_set_cmd(dev_set_func, node_path: str):
"""
Generates a set function based on the dev_set_type method (e.g., seti)
and the node_path (e.g., '/dev8003/sigouts/1/mode'
"""
def set_cmd(val):
return dev_set_func(node_path, val)
return set_cmd
def _gen_get_cmd(dev_get_func, node_path: str):
"""
Generates a get function based on the dev_set_type method (e.g., geti)
and the node_path (e.g., '/dev8003/sigouts/1/mode'
"""
def get_cmd():
return dev_get_func(node_path)
return get_cmd
##########################################################################
# Exceptions
##########################################################################
class ziDAQError(Exception):
"""Exception raised when no DAQ has been connected."""
pass
class ziModuleError(Exception):
"""Exception raised when a module generates an error."""
pass
class ziValueError(Exception):
"""Exception raised when a wrong or empty value is returned."""
pass
class ziCompilationError(Exception):
"""Exception raised when an AWG program fails to compile."""
pass
class ziDeviceError(Exception):
"""Exception raised when a class is used with the wrong device type."""
pass
class ziOptionsError(Exception):
"""Exception raised when a device does not have the right options installed."""
pass
class ziVersionError(Exception):
"""Exception raised when a device does not have the right firmware versions."""
pass
class ziReadyError(Exception):
"""Exception raised when a device was started which is not ready."""
pass
class ziRuntimeError(Exception):
"""Exception raised when a device detects an error at runtime."""
pass
class ziConfigurationError(Exception):
"""Exception raised when a wrong configuration is detected."""
pass
##########################################################################
# Mock classes
##########################################################################
class MockDAQServer():
"""
This class implements a mock version of the DAQ object used for
communicating with the instruments. It contains dummy declarations of
the most important methods implemented by the server and used by
the instrument drivers.
Important: The Mock server creates some default 'nodes' (basically
just entries in a 'dict') based on the device name that is used when
connecting to a device. These nodes differ depending on the instrument
type, which is determined by the number in the device name: dev2XXX are
UHFQA instruments, dev8XXX are HDAWG8 instruments, dev10XXX are PQSC
instruments.
"""
def __init__(self, server, port, apilevel, verbose=False):
self.server = server
self.port = port
self.apilevel = apilevel
self.device = None
self.interface = None
self.nodes = {'/zi/devices/connected': {'type': 'String', 'value': ''}}
self.devtype = None
self.poll_nodes = []
self.verbose = verbose
def awgModule(self):
return MockAwgModule(self)
def setDebugLevel(self, debuglevel: int):
print('Setting debug level to {}'.format(debuglevel))
def connectDevice(self, device, interface):
if self.device is not None:
raise ziDAQError(
'Trying to connect to a device that is already connected!')
if self.interface is not None and self.interface != interface:
raise ziDAQError(
'Trying to change interface on an already connected device!')
self.device = device
self.interface = interface
if self.device.lower().startswith('dev2'):
self.devtype = 'UHFQA'
elif self.device.lower().startswith('dev8'):
self.devtype = 'HDAWG8'
elif self.device.lower().startswith('dev10'):
self.devtype = 'PQSC'
# Add paths
filename = os.path.join(os.path.dirname(os.path.abspath(
__file__)), 'zi_parameter_files', 'node_doc_{}.json'.format(self.devtype))
if not os.path.isfile(filename):
raise ziRuntimeError(
'No parameter file available for devices of type ' + self.devtype)
# NB: defined in parent class
self._load_parameter_file(filename=filename)
# Update connected status
self.nodes['/zi/devices/connected']['value'] = self.device
# Set the LabOne revision
self.nodes['/zi/about/revision'] = {'type': 'Integer', 'value': 200802104}
self.nodes[f'/{self.device}/features/devtype'] = {'type': 'String', 'value': self.devtype}
self.nodes[f'/{self.device}/system/fwrevision'] = {'type': 'Integer', 'value': 99999}
self.nodes[f'/{self.device}/system/fpgarevision'] = {'type': 'Integer', 'value': 99999}
self.nodes[f'/{self.device}/system/slaverevision'] = {'type': 'Integer', 'value': 99999}
if self.devtype == 'UHFQA':
self.nodes[f'/{self.device}/features/options'] = {'type': 'String', 'value': 'QA\nAWG'}
for i in range(16):
self.nodes[f'/{self.device}/awgs/0/waveform/waves/{i}'] = {'type': 'ZIVectorData', 'value': np.array([])}
for i in range(10):
self.nodes[f'/{self.device}/qas/0/integration/weights/{i}/real'] = {'type': 'ZIVectorData', 'value': np.array([])}
self.nodes[f'/{self.device}/qas/0/integration/weights/{i}/imag'] = {'type': 'ZIVectorData', 'value': np.array([])}
self.nodes[f'/{self.device}/qas/0/result/data/{i}/wave'] = {'type': 'ZIVectorData', 'value': np.array([])}
self.nodes[f'/{self.device}/raw/dios/0/delay'] = {'type': 'Integer', 'value': 0}
self.nodes[f'/{self.device}/dios/0/extclk'] = {'type': 'Integer', 'value': 0}
self.nodes[f'/{self.device}/dios/0/drive'] = {'type': 'Integer', 'value': 0}
self.nodes[f'/{self.device}/dios/0/mode'] = {'type': 'Integer', 'value': 0}
elif self.devtype == 'HDAWG8':
self.nodes[f'/{self.device}/features/options'] = {'type': 'String', 'value': 'PC\nME'}
self.nodes[f'/{self.device}/raw/error/json/errors'] = {
'type': 'String', 'value': '{"sequence_nr" : 0, "new_errors" : 0, "first_timestamp" : 0, "timestamp" : 0, "timestamp_utc" : "2019-08-07 17 : 33 : 55", "messages" : []}'}
for i in range(32):
self.nodes['/' + self.device +
'/raw/dios/0/delays/' + str(i) + '/value'] = {'type': 'Integer', 'value': 0}
self.nodes[f'/{self.device}/raw/error/blinkseverity'] = {'type': 'Integer', 'value': 0}
self.nodes[f'/{self.device}/raw/error/blinkforever'] = {'type': 'Integer', 'value': 0}
self.nodes[f'/{self.device}/dios/0/extclk'] = {'type': 'Integer', 'value': 0}
for awg_nr in range(4):
for i in range(2048):
self.nodes[f'/{self.device}/awgs/{awg_nr}/waveform/waves/{i}'] = {
'type': 'ZIVectorData', 'value': np.array([])}
self.nodes[f'/{self.device}/awgs/{awg_nr}/waveform/waves/{i}'] = {
'type': 'ZIVectorData', 'value': np.array([])}
self.nodes[f'/{self.device}/awgs/{awg_nr}/waveform/waves/{i}'] = {
'type': 'ZIVectorData', 'value': np.array([])}
self.nodes[f'/{self.device}/awgs/{awg_nr}/waveform/waves/{i}'] = {
'type': 'ZIVectorData', 'value': np.array([])}
for sigout_nr in range(8):
self.nodes[f'/{self.device}/sigouts/{sigout_nr}/precompensation/fir/coefficients'] = {
'type': 'ZIVectorData', 'value': np.array([])}
self.nodes[f'/{self.device}/dios/0/mode'] = {'type': 'Integer', 'value': 0}
self.nodes[f'/{self.device}/dios/0/extclk'] = {'type': 'Integer', 'value': 0}
self.nodes[f'/{self.device}/dios/0/drive'] = {'type': 'Integer', 'value': 0}
for dio_nr in range(32):
self.nodes[f'/{self.device}/raw/dios/0/delays/{dio_nr}/value'] = {'type': 'Integer', 'value': 0}
self.nodes[f'/{self.device}/raw/error/clear'] = {
'type': 'Integer', 'value': 0}
elif self.devtype == 'PQSC':
self.nodes[f'/{self.device}/raw/error/json/errors'] = {
'type': 'String', 'value': '{"sequence_nr" : 0, "new_errors" : 0, "first_timestamp" : 0, "timestamp" : 0, "timestamp_utc" : "2019-08-07 17 : 33 : 55", "messages" : []}'}
self.nodes[f'/{self.device}/raw/error/clear'] = {
'type': 'Integer', 'value': 0}
def listNodesJSON(self, path):
pass
def getString(self, path):
if path not in self.nodes:
raise ziRuntimeError("Unknown node '" + path +
"' used with mocked server and device!")
if self.nodes[path]['type'] != 'String':
raise ziRuntimeError(
"Trying to node '" + path + "' as string, but the type is '" + self.nodes[path]['type'] + "'!")
return self.nodes[path]['value']
def getInt(self, path):
if path not in self.nodes:
raise ziRuntimeError("Unknown node '" + path +
"' used with mocked server and device!")
if self.verbose:
print('getInt', path, int(self.nodes[path]['value']))
return int(self.nodes[path]['value'])
def getDouble(self, path):
if path not in self.nodes:
raise ziRuntimeError("Unknown node '" + path +
"' used with mocked server and device!")
if self.verbose:
print('getDouble', path, float(self.nodes[path]['value']))
return float(self.nodes[path]['value'])
def setInt(self, path, value):
if path not in self.nodes:
raise ziRuntimeError("Unknown node '" + path +
"' used with mocked server and device!")
if self.verbose:
print('setInt', path, value)
self.nodes[path]['value'] = value
def setDouble(self, path, value):
if path not in self.nodes:
raise ziRuntimeError("Unknown node '" + path +
"' used with mocked server and device!")
if self.verbose:
print('setDouble', path, value)
self.nodes[path]['value'] = value
def setVector(self, path, value):
if path not in self.nodes:
raise ziRuntimeError("Unknown node '" + path +
"' used with mocked server and device!")
if self.nodes[path]['type'] != 'ZIVectorData':
raise ziRuntimeError("Unable to set node '" + path + "' of type " +
self.nodes[path]['type'] + " using setVector!")
self.nodes[path]['value'] = value
def setComplex(self, path, value):
if path not in self.nodes:
raise ziRuntimeError("Unknown node '" + path +
"' used with mocked server and device!")
if not self.nodes[path]['type'].startswith('Complex'):
raise ziRuntimeError("Unable to set node '" + path + "' of type " +
self.nodes[path]['type'] + " using setComplex!")
if self.verbose:
print('setComplex', path, value)
self.nodes[path]['value'] = value
def getComplex(self, path):
if path not in self.nodes:
raise ziRuntimeError("Unknown node '" + path +
"' used with mocked server and device!")
if not self.nodes[path]['type'].startswith('Complex'):
raise ziRuntimeError("Unable to get node '" + path + "' of type " +
self.nodes[path]['type'] + " using getComplex!")
if self.verbose:
print('getComplex', path, self.nodes[path]['value'])
return self.nodes[path]['value']
def get(self, path, flat, flags):
if path not in self.nodes:
raise ziRuntimeError("Unknown node '" + path +
"' used with mocked server and device!")
return {path: [{'vector': self.nodes[path]['value']}]}
def getAsEvent(self, path):
self.poll_nodes.append(path)
def poll(self, poll_time, timeout, flags, flat):
poll_data = {}
for path in self.poll_nodes:
if self.verbose:
print('poll', path)
m = re.match(r'/(\w+)/qas/0/result/data/(\d+)/wave', path)
if m:
poll_data[path] = [{'vector': np.random.rand(
self.getInt('/' + m.group(1) + '/qas/0/result/length'))}]
continue
m = re.match(r'/(\w+)/qas/0/monitor/inputs/(\d+)/wave', path)
if m:
poll_data[path] = [{'vector': np.random.rand(
self.getInt('/' + m.group(1) + '/qas/0/monitor/length'))}]
continue
m = re.match(r'/(\w+)/awgs/(\d+)/ready', path)
if m:
poll_data[path] = {'value': [1]}
continue
poll_data[path] = {'value': [0]}
return poll_data
def subscribe(self, path):
if self.verbose:
print('subscribe', path)
self.poll_nodes.append(path)
def unsubscribe(self, path):
if self.verbose:
print('unsubscribe', path)
if path in self.poll_nodes:
self.poll_nodes.remove(path)
def sync(self):
"""The sync method does not need to do anything as there are no
device delays to deal with when using the mock server.
"""
pass
def _load_parameter_file(self, filename: str):
"""
Takes in a node_doc JSON file auto generates paths based on
the contents of this file.
"""
with open(filename) as fo:
f = fo.read()
node_pars = json.loads(f)
for par in node_pars.values():
node = par['Node'].split('/')
# The parfile is valid for all devices of a certain type
# so the device name has to be split out.
parpath = '/' + self.device + '/' + '/'.join(node)
if par['Type'].startswith('Integer'):
self.nodes[parpath.lower()] = {'type': par['Type'], 'value': 0}
elif par['Type'].startswith('Double'):
self.nodes[parpath.lower()] = {
'type': par['Type'], 'value': 0.0}
elif par['Type'].startswith('Complex'):
self.nodes[parpath.lower()] = {
'type': par['Type'], 'value': 0 + 0j}
elif par['Type'].startswith('String'):
self.nodes[parpath.lower()] = {
'type': par['Type'], 'value': ''}
class MockAwgModule():
"""
This class implements a mock version of the awgModule object used for
compiling and uploading AWG programs. It doesn't actually compile anything, but
only maintains a counter of how often the compilation method has been executed.
For the future, the class could be updated to allow the user to select whether
the next compilation should be successful or not in order to enable more
flexibility in the unit tests of the actual drivers.
"""
def __init__(self, daq):
self._daq = daq
self._device = None
self._index = None
self._sourcestring = None
self._compilation_count = {}
if not os.path.isdir('awg/waves'):
os.makedirs('awg/waves')
def get_compilation_count(self, index):
if index not in self._compilation_count:
raise ziModuleError(
'Trying to access compilation count of invalid index ' + str(index) + '!')
return self._compilation_count[index]
def set(self, path, value):
if path == 'awgModule/device':
self._device = value
elif path == 'awgModule/index':
self._index = value
if self._index not in self._compilation_count:
self._compilation_count[self._index] = 0
elif path == 'awgModule/compiler/sourcestring':
# The compiled program is stored in _sourcestring
self._sourcestring = value
if self._index not in self._compilation_count:
raise ziModuleError(
'Trying to compile AWG program, but no AWG index has been configured!')
if self._device is None:
raise ziModuleError(
'Trying to compile AWG program, but no AWG device has been configured!')
self._compilation_count[self._index] += 1
self._daq.setInt('/' + self._device + '/' +
'awgs/' + str(self._index) + '/ready', 1)
def get(self, path):
if path == 'awgModule/device':
value = [self._device]
elif path == 'awgModule/index':
value[self._index]
elif path == 'awgModule/compiler/statusstring':
value = ['File successfully uploaded']
else:
value = ['']
for elem in reversed(path.split('/')[1:]):
rv = {elem: value}
value = rv
return rv
def execute(self):
pass
##########################################################################
# Class
##########################################################################
class ZI_base_instrument(Instrument):
"""
This is a base class for Zurich Instruments instrument drivers.
It includes functionality that is common to all instruments. It maintains
a list of available nodes as JSON files in the 'zi_parameter_files'
subfolder. The parameter files should be regenerated when newer versions
of the firmware are installed on the instrument.
The base class also manages waveforms for the instruments. The waveforms
are kept in a table, which is kept synchronized with CSV files in the
awg/waves folder belonging to LabOne. The base class will select whether
to compile and configure an instrument based on changes to the waveforms
and to the requested AWG program. Basically, if a waveform changes length
or if the AWG program changes, then the program will be compiled and
uploaded the next time the user executes the 'start' method. If a waveform
has changed, but the length is the same, then the waveform will simply
be updated on the instrument using a a fast waveform upload technique. Again,
this is triggered when the 'start' method is called.
"""
##########################################################################
# Constructor
##########################################################################
def __init__(self,
name: str,
device: str,
interface: str= '1GbE',
server: str= 'localhost',
port: int= 8004,
apilevel: int= 5,
num_codewords: int= 0,
awg_module: bool=True,
logfile: str = None,
**kw) -> None:
"""
Input arguments:
name: (str) name of the instrument as seen by the user
device (str) the name of the device e.g., "dev8008"
interface (str) the name of the interface to use ('1GbE' or 'USB')
server (str) the host where the ziDataServer is running
port (int) the port to connect to for the ziDataServer (don't change)
apilevel (int) the API version level to use (don't change unless you know what you're doing)
awg_module (bool) create an awgModule
num_codewords (int) the number of codeword-based waveforms to prepare
logfile (str) file name where all commands should be logged
"""
t0 = time.time()
super().__init__(name=name, **kw)
# Decide which server to use based on name
if server == 'emulator':
log.info('Connecting to mock DAQ server')
self.daq = MockDAQServer(server, port, apilevel)
else:
log.info('Connecting to DAQ server')
self.daq = zi.ziDAQServer(server, port, apilevel)
if not self.daq:
raise(ziDAQError())
self.daq.setDebugLevel(0)
# Handle absolute path
self.use_setVector = "setVector" in dir(self.daq)
# Connect a device
if not self._is_device_connected(device):
log.info(f'Connecting to device {device}')
self.daq.connectDevice(device, interface)
self.devname = device
self.devtype = self.gets('features/devtype')
# We're now connected, so do some sanity checking
self._check_devtype()
self._check_versions()
self._check_options()
# Default waveform length used when initializing waveforms to zero
self._default_waveform_length = 32
# add qcodes parameters based on JSON parameter file
# FIXME: we might want to skip/remove/(add to _params_to_skip_update) entries like AWGS/*/ELF/DATA,
# AWGS/*/SEQUENCER/ASSEMBLY, AWGS/*/DIO/DATA
filename = os.path.join(os.path.dirname(os.path.abspath(
__file__)), 'zi_parameter_files', 'node_doc_{}.json'.format(self.devtype))
if not os.path.isfile(filename):
log.info(f"{self.devname}: Parameter file not found, creating '{filename}''")
self._create_parameter_file(filename=filename)
try:
# NB: defined in parent class
log.info(f'{self.devname}: Loading parameter file')
self._load_parameter_file(filename=filename)
except FileNotFoundError:
# Should never happen as we just created the file above
log.error(f"{self.devname}: parameter file for data parameters {filename} not found")
raise
# Create modules
if awg_module:
self._awgModule = self.daq.awgModule()
self._awgModule.set('awgModule/device', device)
self._awgModule.execute()
# Will hold information about all configured waveforms
self._awg_waveforms = {}
# Asserted when AWG needs to be reconfigured
self._awg_needs_configuration = [False]*(self._num_channels()//2)
self._awg_program = [None]*(self._num_channels()//2)
# Create waveform parameters
self._num_codewords = 0
# CH: this Delft function should not be needed for us, and removing it
# should save time in the init script. Please let me know if you
# experience any issues with the init of HDAWG/UHF.
# self._add_codeword_waveform_parameters(num_codewords)
else:
self._awgModule = None
# Create other neat parameters
self._add_extra_parameters()
# A list of all subscribed paths
self._subscribed_paths = []
self._awg_source_strings = {}
# Structure for storing errors
self._errors = None
# Structure for storing errors that should be demoted to warnings
self._errors_to_ignore = []
# Make initial error check
self.check_errors()
# Optionally setup log file
if logfile is not None:
self._logfile = open(logfile, 'w')
else:
self._logfile = None
# Show some info
serial = self.get('features_serial')
options = self.get('features_options')
fw_revision = self.get('system_fwrevision')
fpga_revision = self.get('system_fpgarevision')
log.info('{}: serial={}, options={}, fw_revision={}, fpga_revision={}'
.format(self.devname, serial, options.replace('\n', '|'), fw_revision, fpga_revision))
self.connect_message(begin_time=t0)
##########################################################################
# Private methods: Abstract Base Class methods
##########################################################################
def _check_devtype(self):
"""
Checks that the driver is used with the correct device-type.
"""
raise NotImplementedError('Virtual method with no implementation!')
def _check_options(self):
"""
Checks that the correct options are installed on the instrument.
"""
raise NotImplementedError('Virtual method with no implementation!')
def _check_versions(self):
"""
Checks that sufficient versions of the firmware are available.
"""
raise NotImplementedError('Virtual method with no implementation!')
def _check_awg_nr(self, awg_nr):
"""
Checks that the given AWG index is valid for the device.
"""
raise NotImplementedError('Virtual method with no implementation!')
def _update_num_channels(self):
raise NotImplementedError('Virtual method with no implementation!')
def _update_awg_waveforms(self):
raise NotImplementedError('Virtual method with no implementation!')
def _num_channels(self):
raise NotImplementedError('Virtual method with no implementation!')
def _add_extra_parameters(self) -> None:
"""
Adds extra useful parameters to the instrument.
"""
log.info(f'{self.devname}: Adding extra parameters')
self.add_parameter(
'timeout',
unit='s',
initial_value=30,
parameter_class=ManualParameter,
vals=validators.Ints())
##########################################################################
# Private methods
##########################################################################
def _add_codeword_waveform_parameters(self, num_codewords) -> None:
"""
Adds parameters that are used for uploading codewords.
It also contains initial values for each codeword to ensure
that the "upload_codeword_program" works.
"""
docst = ('Specifies a waveform for a specific codeword. ' +
'The waveforms must be uploaded using ' +
'"upload_codeword_program". The channel number corresponds' +
' to the channel as indicated on the device (1 is lowest).')
self._params_to_skip_update = []
log.info(f'{self.devname}: Adding codeword waveform parameters')
for ch in range(self._num_channels()):
for cw in range(max(num_codewords, self._num_codewords)):
# NB: parameter naming identical to QWG
wf_name = gen_waveform_name(ch, cw)
if cw >= self._num_codewords and wf_name not in self.parameters:
# Add parameter
self.add_parameter(
wf_name,
label='Waveform channel {} codeword {:03}'.format(
ch+1, cw),
vals=validators.Arrays(), # min_value, max_value = unknown
set_cmd=self._gen_write_waveform(ch, cw),
get_cmd=self._gen_read_waveform(ch, cw),
docstring=docst)
self._params_to_skip_update.append(wf_name)
# Make sure the waveform data is up-to-date
self._gen_read_waveform(ch, cw)()
elif cw >= num_codewords:
# Delete parameter as it's no longer needed
if wf_name in self.parameters:
self.parameters.pop(wf_name)
self._awg_waveforms.pop(wf_name)
# Update the number of codewords
self._num_codewords = num_codewords
def _load_parameter_file(self, filename: str):
"""
Takes in a node_doc JSON file auto generates parameters based on
the contents of this file.
"""
with open(filename) as fo:
f = fo.read()
node_pars = json.loads(f)
for par in node_pars.values():
node = par['Node'].split('/')
# The parfile is valid for all devices of a certain type
# so the device name has to be split out.
parname = '_'.join(node).lower()
parpath = '/' + self.devname + '/' + '/'.join(node)
# This block provides the mapping between the ZI node and QCoDes
# parameter.
par_kw = {}
par_kw['name'] = parname
if par['Unit'] != 'None':
par_kw['unit'] = par['Unit']
else:
par_kw['unit'] = 'arb. unit'
par_kw['docstring'] = par['Description']
if "Options" in par.keys():
# options can be done better, this is not sorted
par_kw['docstring'] += '\nOptions:\n' + str(par['Options'])
# Creates type dependent get/set methods
if par['Type'] == 'Integer (64 bit)':
par_kw['set_cmd'] = _gen_set_cmd(self.seti, parpath)
par_kw['get_cmd'] = _gen_get_cmd(self.geti, parpath)
# min/max not implemented yet for ZI auto docstrings #352
par_kw['vals'] = validators.Ints()
elif par['Type'] == 'Integer (enumerated)':
par_kw['set_cmd'] = _gen_set_cmd(self.seti, parpath)
par_kw['get_cmd'] = _gen_get_cmd(self.geti, parpath)
par_kw['vals'] = validators.Ints(min_value=0,
max_value=len(par["Options"]))
elif par['Type'] == 'Double':
par_kw['set_cmd'] = _gen_set_cmd(self.setd, parpath)
par_kw['get_cmd'] = _gen_get_cmd(self.getd, parpath)
# min/max not implemented yet for ZI auto docstrings #352
par_kw['vals'] = validators.Numbers()
elif par['Type'] == 'Complex Double':
par_kw['set_cmd'] = _gen_set_cmd(self.setc, parpath)
par_kw['get_cmd'] = _gen_get_cmd(self.getc, parpath)
# min/max not implemented yet for ZI auto docstrings #352
par_kw['vals'] = validators.Anything()
elif par['Type'] == 'ZIVectorData':
par_kw['set_cmd'] = _gen_set_cmd(self.setv, parpath)
par_kw['get_cmd'] = _gen_get_cmd(self.getv, parpath)
# min/max not implemented yet for ZI auto docstrings #352
par_kw['vals'] = validators.Arrays()
elif par['Type'] == 'String':
par_kw['set_cmd'] = _gen_set_cmd(self.sets, parpath)
par_kw['get_cmd'] = _gen_get_cmd(self.gets, parpath)
par_kw['vals'] = validators.Strings()
elif par['Type'] == 'CoreString':
par_kw['get_cmd'] = _gen_get_cmd(self.getd, parpath)
par_kw['set_cmd'] = None # Not implemented
par_kw['vals'] = validators.Strings()
elif par['Type'] == 'ZICntSample':
par_kw['get_cmd'] = None # Not implemented
par_kw['set_cmd'] = None # Not implemented
par_kw['vals'] = None # Not implemented
elif par['Type'] == 'ZITriggerSample':
par_kw['get_cmd'] = None # Not implemented
par_kw['set_cmd'] = None # Not implemented
par_kw['vals'] = None # Not implemented
elif par['Type'] == 'ZIDIOSample':
par_kw['get_cmd'] = None # Not implemented
par_kw['set_cmd'] = None # Not implemented
par_kw['vals'] = None # Not implemented
elif par['Type'] == 'ZIAuxInSample':
par_kw['get_cmd'] = None # Not implemented
par_kw['set_cmd'] = None # Not implemented
par_kw['vals'] = None # Not implemented
elif par['Type'] == 'ZIScopeWave':
par_kw['get_cmd'] = None # Not implemented
par_kw['set_cmd'] = None # Not implemented
par_kw['vals'] = None # Not implemented
else:
raise NotImplementedError(
"Parameter '{}' of type '{}' not supported".format(
parname, par['Type']))
# If not readable/writable the methods are removed after the type
# dependent loop to keep this more readable.
if 'Read' not in par['Properties']:
par_kw['get_cmd'] = None
if 'Write' not in par['Properties']:
par_kw['set_cmd'] = None
self.add_parameter(**par_kw)
def _create_parameter_file(self, filename: str):
"""
This generates a json file Containing the node_docs as extracted
from the ZI instrument API.
Replaces the use of the s_node_pars and d_node_pars files.
"""
# Get all interesting nodes
nodes = json.loads(self.daq.listNodesJSON('/' + self.devname))
modified_nodes = {}
# Do some name mangling
for name, node in nodes.items():
name = name.replace('/' + self.devname.upper() + '/', '')
node['Node'] = name
modified_nodes[name] = node
# Dump the nodes
with open(filename, "w") as json_file:
json.dump(modified_nodes, json_file, indent=4, sort_keys=True)
def _is_device_connected(self, device):
"""
Return true if the given device is already connected to the server.
"""
if device.lower() in [x.lower() for x in self.daq.getString('/zi/devices/connected').split(',')]:
return True
else:
return False
def _get_full_path(self, paths):
"""
Concatenates the device name with one or more paths to create a fully
qualified path for use in the server.
"""
if type(paths) is list:
for p, n in enumerate(paths):
if p[0] != '/':
paths[n] = ('/' + self.devname + '/' + p).lower()
else:
paths[n] = paths[n].lower()
else:
if paths[0] != '/':
paths = ('/' + self.devname + '/' + paths).lower()
else:
paths = paths.lower()
return paths
def _get_awg_directory(self):
"""
Returns the AWG directory where waveforms should be stored.
"""
return os.path.join(self._awgModule.get('awgModule/directory')['directory'][0], 'awg')
def _initialize_waveform_to_zeros(self):
"""
Generates all zeros waveforms for all codewords.
"""
t0 = time.time()
wf = np.zeros(self._default_waveform_length)
waveform_params = [value for key, value in self.parameters.items()
if 'wave_ch' in key.lower()]
for par in waveform_params:
par(wf)
t1 = time.time()
log.debug(
'Set all waveforms to zeros in {:.1f} ms'.format(1.0e3*(t1-t0)))
def _gen_write_waveform(self, ch, cw):
def write_func(waveform):
log.debug(f"{self.devname}: Writing waveform (len {len(waveform)}) to ch{ch} cw{cw}")
# Determine which AWG this waveform belongs to
awg_nr = ch//2
# Name of this waveform
wf_name = gen_waveform_name(ch, cw)
# Check that we're allowed to modify this waveform
if self._awg_waveforms[wf_name]['readonly']:
raise ziConfigurationError(
'Trying to modify read-only waveform on '
'codeword {}, channel {}'.format(cw, ch))
# The length of HDAWG waveforms should be a multiple of 8 samples.
if (len(waveform) % 8) != 0:
log.debug(f"{self.devname}: waveform is not a multiple of 8 samples, appending zeros.")
extra_zeros = 8-(len(waveform) % 8)
waveform = np.concatenate([waveform, np.zeros(extra_zeros)])
# If the length has changed, we need to recompile the AWG program
if len(waveform) != len(self._awg_waveforms[wf_name]['waveform']):
log.debug(f"{self.devname}: Length of waveform has changed. Flagging awg as requiring recompilation.")
self._awg_needs_configuration[awg_nr] = True
# Update the associated CSV file
log.debug(f"{self.devname}: Updating csv waveform {wf_name}, for ch{ch}, cw{cw}")
self._write_csv_waveform(ch=ch, cw=cw, wf_name=wf_name,
waveform=waveform)
# And the entry in our table and mark it for update
self._awg_waveforms[wf_name]['waveform'] = waveform
log.debug(f"{self.devname}: Marking waveform as dirty.")
self._awg_waveforms[wf_name]['dirty'] = True
return write_func
def _write_csv_waveform(self, ch: int, cw: int, wf_name: str, waveform) -> None:
filename = os.path.join(
self._get_awg_directory(), 'waves',
self.devname + '_' + wf_name + '.csv')
np.savetxt(filename, waveform, delimiter=",")
def _gen_read_waveform(self, ch, cw):
def read_func():
# AWG
awg_nr = ch//2
# Name of this waveform
wf_name = gen_waveform_name(ch, cw)
log.debug(f"{self.devname}: Reading waveform {wf_name} for ch{ch} cw{cw}")
# Check if the waveform data is in our dictionary
if wf_name not in self._awg_waveforms:
log.debug(f"{self.devname}: Waveform not in self._awg_waveforms: reading from csv file.")
# Initialize elements
self._awg_waveforms[wf_name] = {
'waveform': None, 'dirty': False, 'readonly': False}
# Make sure everything gets recompiled
log.debug(f"{self.devname}: Flagging awg as requiring recompilation.")
self._awg_needs_configuration[awg_nr] = True
# It isn't, so try to read the data from CSV
waveform = self._read_csv_waveform(ch, cw, wf_name)
# Check whether we got something
if waveform is None:
log.debug(f"{self.devname}: Waveform CSV does not exist, initializing to zeros.")
# Nope, initialize to zeros
waveform = np.zeros(32)
self._awg_waveforms[wf_name]['waveform'] = waveform
# write the CSV file
self._write_csv_waveform(ch, cw, wf_name, waveform)
else:
# Got data, update dictionary
self._awg_waveforms[wf_name]['waveform'] = waveform
# Get the waveform data from our dictionary, which must now
# have the data
return self._awg_waveforms[wf_name]['waveform']
return read_func
def _read_csv_waveform(self, ch: int, cw: int, wf_name: str):
filename = os.path.join(
self._get_awg_directory(), 'waves',
self.devname + '_' + wf_name + '.csv')
try:
log.debug(f"{self.devname}: reading waveform from csv '{filename}'")
return np.genfromtxt(filename, delimiter=',')
except OSError as e:
# if the waveform does not exist yet dont raise exception
log.warning(e)
return None
def _length_match_waveforms(self, awg_nr):
"""
Adjust the length of a codeword waveform such that each individual
waveform of the pair has the same length
"""
log.info('Length matching waveforms for dynamic waveform upload.')
wf_table = self._get_waveform_table(awg_nr)
matching_updated = False
iter_id = 0
# We iterate over the waveform table
while(matching_updated or iter_id == 0):
iter_id += 1
if iter_id > 10:
raise StopIteration
log.info('Length matching iteration {}.'.format(iter_id))
matching_updated = False
for wf_name, other_wf_name in wf_table:
len_wf = len(self._awg_waveforms[wf_name]['waveform'])
len_other_wf = len(self._awg_waveforms[other_wf_name]['waveform'])
# First one is shorter
if len_wf < len_other_wf:
log.info(f"{self.devname}: Modifying {wf_name} for length matching.")
# Temporarily unset the readonly flag to be allowed to append zeros
readonly = self._awg_waveforms[wf_name]['readonly']
self._awg_waveforms[wf_name]['readonly'] = False
self.set(wf_name, np.concatenate(
(self._awg_waveforms[wf_name]['waveform'], np.zeros(len_other_wf-len_wf))))
self._awg_waveforms[wf_name]['dirty'] = True
self._awg_waveforms[wf_name]['readonly'] = readonly
matching_updated = True
elif len_other_wf < len_wf:
log.info(f"{self.devname}: Modifying {other_wf_name} for length matching.")
readonly = self._awg_waveforms[other_wf_name]['readonly']
self._awg_waveforms[other_wf_name]['readonly'] = False
self.set(other_wf_name, np.concatenate(
(self._awg_waveforms[other_wf_name]['waveform'], np.zeros(len_wf-len_other_wf))))
self._awg_waveforms[other_wf_name]['dirty'] = True
self._awg_waveforms[other_wf_name]['readonly'] = readonly
matching_updated = True
def _clear_dirty_waveforms(self, awg_nr):
"""
Adjust the length of a codeword waveform such that each individual
waveform of the pair has the same length
"""
log.info(f"{self.devname}: Clearing dirty waveform tag for AWG {awg_nr}")
for cw in range(self._num_codewords):
wf_name = gen_waveform_name(2*awg_nr+0, cw)
self._awg_waveforms[wf_name]['dirty'] = False
other_wf_name = gen_waveform_name(2*awg_nr+1, cw)
self._awg_waveforms[other_wf_name]['dirty'] = False
def _clear_readonly_waveforms(self, awg_nr):
"""
Clear the read-only flag of all configured waveforms. Typically used when switching
configurations (i.e. programs).
"""
for cw in range(self._num_codewords):
wf_name = gen_waveform_name(2*awg_nr+0, cw)
self._awg_waveforms[wf_name]['readonly'] = False
other_wf_name = gen_waveform_name(2*awg_nr+1, cw)
self._awg_waveforms[other_wf_name]['readonly'] = False
def _set_readonly_waveform(self, ch: int, cw: int):
"""
Mark a waveform as being read-only. Typically used to limit which waveforms the user
is allowed to change based on the overall configuration of the instrument and the type
of AWG program being executed.
"""
# Sanity check
if cw >= self._num_codewords:
raise ziConfigurationError(
'Codeword {} is out of range of the configured number of codewords ({})!'.format(cw, self._num_codewords))
if ch >= self._num_channels():
raise ziConfigurationError(
'Channel {} is out of range of the configured number of channels ({})!'.format(ch, self._num_channels()))
# Name of this waveform
wf_name = gen_waveform_name(ch, cw)
# Check if the waveform data is in our dictionary
if wf_name not in self._awg_waveforms:
raise ziConfigurationError(
'Trying to mark waveform {} as read-only, but the waveform has not been configured yet!'.format(wf_name))
self._awg_waveforms[wf_name]['readonly'] = True
def _upload_updated_waveforms(self, awg_nr):
"""
Loop through all configured waveforms and use dynamic waveform uploading
to update changed waveforms on the instrument as needed.
"""
# Fixme. the _get_waveform_table should also be implemented for the UFH
log.info(f"{self.devname}: Using dynamic waveform update for AWG {awg_nr}.")
wf_table = self._get_waveform_table(awg_nr)
for dio_cw, (wf_name, other_wf_name) in enumerate(wf_table):
if self._awg_waveforms[wf_name]['dirty'] or self._awg_waveforms[other_wf_name]['dirty']:
# Combine the waveforms and upload
wf_data = merge_waveforms(self._awg_waveforms[wf_name]['waveform'],
self._awg_waveforms[other_wf_name]['waveform'])
# Write the new waveform
self.setv(
'awgs/{}/waveform/waves/{}'.format(awg_nr, dio_cw), wf_data)
def _codeword_table_preamble(self, awg_nr):
"""
Defines a snippet of code to use in the beginning of an AWG program in order to define the waveforms.
The generated code depends on the instrument type. For the HDAWG instruments, we use the setDIOWaveform
function. For the UHF-QA we simply define the raw waveforms.
"""
raise NotImplementedError('Virtual method with no implementation!')
def _configure_awg_from_variable(self, awg_nr):
"""
Configures an AWG with the program stored in the object in the self._awg_program[awg_nr] member.
"""
log.info(f"{self.devname}: Configuring AWG {awg_nr} with predefined codeword program")
if self._awg_program[awg_nr] is not None:
full_program = \
'// Start of automatically generated codeword table\n' + \
self._codeword_table_preamble(awg_nr) + \
'// End of automatically generated codeword table\n' + \
self._awg_program[awg_nr]
self.configure_awg_from_string(awg_nr, full_program)
else:
logging.info(f"{self.devname}: No program configured for awg_nr {awg_nr}.")
def _write_cmd_to_logfile(self, cmd):
if self._logfile is not None:
now = datetime.now()
now_str = now.strftime("%d/%m/%Y %H:%M:%S")
self._logfile.write(f'#{now_str}\n')
self._logfile.write(f'{self.name}.{cmd}\n')
def _flush_logfile(self):
if self._logfile is not None:
self._logfile.flush()
##########################################################################
# Public methods: node helpers
##########################################################################
def setd(self, path, value) -> None:
self._write_cmd_to_logfile(f'daq.setDouble("{path}", {value})')
self.daq.setDouble(self._get_full_path(path), value)
def getd(self, path):
return self.daq.getDouble(self._get_full_path(path))
def seti(self, path, value) -> None:
self._write_cmd_to_logfile(f'daq.setDouble("{path}", {value})')
self.daq.setInt(self._get_full_path(path), value)
def geti(self, path):
return self.daq.getInt(self._get_full_path(path))
def sets(self, path, value) -> None:
self._write_cmd_to_logfile(f'daq.setString("{path}", {value})')
self.daq.setString(self._get_full_path(path), value)
def gets(self, path):
return self.daq.getString(self._get_full_path(path))
def setc(self, path, value) -> None:
self._write_cmd_to_logfile(f'daq.setComplex("{path}", {value})')
self.daq.setComplex(self._get_full_path(path), value)
def getc(self, path):
return self.daq.getComplex(self._get_full_path(path))
def setv(self, path, value) -> None:
# Handle absolute path
if self.use_setVector:
self._write_cmd_to_logfile(f'daq.setVector("{path}", np.array({np.array2string(value, separator=",")}))')
self.daq.setVector(self._get_full_path(path), value)
else:
self._write_cmd_to_logfile(f'daq.vectorWrite("{path}", np.array({np.array2string(value, separator=",")}))')
self.daq.vectorWrite(self._get_full_path(path), value)
def getv(self, path):
path = self._get_full_path(path)
value = self.daq.get(path, True, 0)
if path not in value:
raise ziValueError('No value returned for path ' + path)
else:
return value[path][0]['vector']
def getdeep(self, path, timeout=5.0):
path = self._get_full_path(path)
self.daq.getAsEvent(path)
while timeout > 0.0:
value = self.daq.poll(0.01, 500, 4, True)
if path in value:
return value[path]
else:
timeout -= 0.01
return None
def subs(self, path:str) -> None:
full_path = self._get_full_path(path)
if full_path not in self._subscribed_paths:
self._subscribed_paths.append(full_path)
self.daq.subscribe(full_path)
def unsubs(self, path:str=None) -> None:
if path is None:
for path in self._subscribed_paths:
self.daq.unsubscribe(path)
self._subscribed_paths.clear()
else:
full_path = self._get_full_path(path)
if full_path in self._subscribed_paths:
del self._subscribed_paths[self._subscribed_paths.index(full_path)]
self.daq.unsubscribe(full_path)
def poll(self, poll_time=0.1):
# The timeout of 1ms (second argument) is smaller than in the Delft
# driver version (500ms) to allow fast spectroscopy.
return self.daq.poll(poll_time, 1, 4, True)
def sync(self) -> None:
self.daq.sync()
##########################################################################
# Public methods
##########################################################################
def start(self, **kw):
""" Start the sequencer
:param kw: currently ignored, added for compatibilty with other
instruments that accept kwargs in start().
"""
log.info(f"{self.devname}: Starting '{self.name}'")
self.check_errors()
# Loop through each AWG and check whether to reconfigure it
for awg_nr in range(self._num_channels()//2):
self._length_match_waveforms(awg_nr)
# If the reconfiguration flag is set, upload new program
if self._awg_needs_configuration[awg_nr]:
log.debug(f"{self.devname}: Detected awg configuration tag for AWG {awg_nr}.")
self._configure_awg_from_variable(awg_nr)
self._awg_needs_configuration[awg_nr] = False
self._clear_dirty_waveforms(awg_nr)
else:
log.debug(f"{self.devname}: Did not detect awg configuration tag for AWG {awg_nr}.")
# Loop through all waveforms and update accordingly
self._upload_updated_waveforms(awg_nr)
self._clear_dirty_waveforms(awg_nr)
# Start all AWG's
for awg_nr in range(self._num_channels()//2):
# Skip AWG's without programs
if self._awg_program[awg_nr] is None:
# to configure all awgs use "upload_codeword_program" or specify
# another program
logging.info(f"{self.devname}: Not starting awg_nr {awg_nr}.")
continue
# Check that the AWG is ready
if not self.get('awgs_{}_ready'.format(awg_nr)):
raise ziReadyError(
'Tried to start AWG {} that is not ready!'.format(awg_nr))
# Enable it
self.set('awgs_{}_enable'.format(awg_nr), 1)
log.info(f"{self.devname}: Started '{self.name}'")
def stop(self):
log.info('Stopping {}'.format(self.name))
# Stop all AWG's
for awg_nr in range(self._num_channels()//2):
self.set('awgs_{}_enable'.format(awg_nr), 0)
self.check_errors()
# FIXME: temporary solution for issue
def FIXMEclose(self) -> None:
try:
# Disconnect application server
self.daq.disconnect()
except AttributeError:
pass
super().close()
def check_errors(self, errors_to_ignore=None) -> None:
raise NotImplementedError('Virtual method with no implementation!')
def clear_errors(self) -> None:
raise NotImplementedError('Virtual method with no implementation!')
def demote_error(self, code: str):
"""
Demote a ZIRuntime error to a warning.
Arguments
code (str)
The error code of the exception to ignore.
The error code gets logged as an error before the exception
is raised. The code is a string like "DIOCWCASE".
"""
self._errors_to_ignore.append(code)
def reset_waveforms_zeros(self):
"""
Sets all waveforms to an array of 48 zeros.
"""
t0 = time.time()
wf = | np.zeros(48) | numpy.zeros |
import numpy as np
from numpy import ma
from pyindi import *
from scipy import ndimage, sqrt, stats, misc, signal
pi = PyINDI(verbose=False)
# define 2D gaussian for fitting PSFs
def gaussian_x(x, mu, sig):
shape_gaussian = np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.)))
return shape_gaussian
def find_airy_psf(image):
if True:
#imageThis = numpy.copy(image)
'''
if (PSFside == 'left'):
imageThis[:,1024:-1] = 0
elif (PSFside == 'right'):
imageThis[:,0:1024] = 0
'''
image[np.isnan(image)] = np.nanmedian(image) # if there are NaNs, replace them with the median image value
imageG = ndimage.gaussian_filter(image, 6) # further remove effect of bad pixels (somewhat redundant?)
loc = np.argwhere(imageG==imageG.max())
cx = loc[0,1]
cy = loc[0,0]
#plt.imshow(imageG, origin="lower")
#
#plt.scatter([cx,cx],[cy,cy], c='r', s=50)
#plt.colorbar()
#plt.show()
#print [cy, cx] # check
return [cy, cx]
def find_grism_psf(image, sig, length_y):
if True:
# generate the Gaussian to correlate with the image
mu_x_center = 0.5*image.shape[1] # initially center the probe shape for correlation
x_probe_gaussian = gaussian_x(np.arange(image.shape[1]), mu_x_center, sig)
# generate a top hat for correlating it to a grism-ed PSF in y
y_abcissa = np.arange(image.shape[0])
y_probe_tophat = np.zeros(image.shape[0])
y_probe_tophat[np.logical_and(y_abcissa > 0.5*image.shape[0]-0.5*length_y,
y_abcissa <= 0.5*image.shape[0]+0.5*length_y)] = 1
# dampen edge effects
repl_val = np.median(image)
image[0:4,:] = repl_val
image[-5:-1,:] = repl_val
image[:,0:4] = repl_val
image[:,-5:-1] = repl_val
# correlate real PSF and probe shape in x
corr_x = signal.correlate(np.sum(image,axis=0), x_probe_gaussian, mode='same')
# correlate real PSF and probe shape in y
# (first, we have to integrate along x and subtract the background shape)
profile_y = np.subtract(np.sum(image,axis=1), image.shape[1]*np.median(image,axis=1))
corr_y = signal.correlate(profile_y, y_probe_tophat, mode='same')
# find centers of psfs
psf_center_x = np.argmax(corr_x)
psf_center_y = np.argmax(corr_y)
return [psf_center_y, psf_center_x]
class fft_img:
# take FFT of a 2D image
def __init__(self, image):
self.image = image
def fft(self, padding=int(0), pad_mode='constant', mask_thresh=1e-10, mask=True):
padI = np.pad(self.image, padding, pad_mode)
# arguments: image, pad size, pad mode, threshold for masking, mask flag
padI = np.fft.fftshift(padI)
PhaseExtract = np.fft.fft2(padI)
PhaseExtract = np.fft.fftshift(PhaseExtract)
AmpPE = np.absolute(PhaseExtract)
ArgPE = np.multiply(np.angle(PhaseExtract),180./np.pi)
if mask:
# mask out low-power regions
AmpPE_masked = | ma.masked_where(AmpPE < mask_thresh, AmpPE, copy=False) | numpy.ma.masked_where |
#%%
import random
import matplotlib.pyplot as plt
import tensorflow as tf
import tensorflow.keras as keras
from itertools import product
import pandas as pd
import numpy as np
import pickle
from math import log2, ceil
import sys
sys.path.append("../../src/")
from lifelong_dnn import LifeLongDNN
from joblib import Parallel, delayed
import tensorflow as tf
import warnings
warnings.filterwarnings(action='once')
#%%
############################
### Main hyperparameters ###
############################
ntrees = 50
hybrid_comp_trees = 25
estimation_set = 0.63
validation_set= 1-estimation_set
num_points_per_task = 5000
num_points_per_forest = 500
reps = 30
task_10_sample = 10*np.array([10, 50, 100, 200, 350, 500])
#%%
def sort_data(data_x, data_y, num_points_per_task, total_task=10, shift=1):
x = data_x.copy()
y = data_y.copy()
idx = [np.where(data_y == u)[0] for u in np.unique(data_y)]
train_x_across_task = []
train_y_across_task = []
test_x_across_task = []
test_y_across_task = []
batch_per_task=5000//num_points_per_task
sample_per_class = num_points_per_task//total_task
test_data_slot=100//batch_per_task
for task in range(total_task):
for batch in range(batch_per_task):
for class_no in range(task*10,(task+1)*10,1):
indx = np.roll(idx[class_no],(shift-1)*100)
if batch==0 and class_no==task*10:
train_x = x[indx[batch*sample_per_class:(batch+1)*sample_per_class],:]
train_y = y[indx[batch*sample_per_class:(batch+1)*sample_per_class]]
test_x = x[indx[batch*test_data_slot+500:(batch+1)*test_data_slot+500],:]
test_y = y[indx[batch*test_data_slot+500:(batch+1)*test_data_slot+500]]
else:
train_x = np.concatenate((train_x, x[indx[batch*sample_per_class:(batch+1)*sample_per_class],:]), axis=0)
train_y = np.concatenate((train_y, y[indx[batch*sample_per_class:(batch+1)*sample_per_class]]), axis=0)
test_x = np.concatenate((test_x, x[indx[batch*test_data_slot+500:(batch+1)*test_data_slot+500],:]), axis=0)
test_y = np.concatenate((test_y, y[indx[batch*test_data_slot+500:(batch+1)*test_data_slot+500]]), axis=0)
train_x_across_task.append(train_x)
train_y_across_task.append(train_y)
test_x_across_task.append(test_x)
test_y_across_task.append(test_y)
return train_x_across_task, train_y_across_task, test_x_across_task, test_y_across_task
# %%
def voter_predict_proba(voter, nodes_across_trees):
def worker(tree_idx):
#get the node_ids_to_posterior_map for this tree
node_ids_to_posterior_map = voter.tree_idx_to_node_ids_to_posterior_map[tree_idx]
#get the nodes of X
nodes = nodes_across_trees[tree_idx]
posteriors = []
node_ids = node_ids_to_posterior_map.keys()
#loop over nodes of X
for node in nodes:
#if we've seen this node before, simply get the posterior
if node in node_ids:
posteriors.append(node_ids_to_posterior_map[node])
#if we haven't seen this node before, simply use the uniform posterior
else:
posteriors.append(np.ones((len(np.unique(voter.classes_)))) / len(voter.classes_))
return posteriors
if voter.parallel:
return Parallel(n_jobs=-1)(
delayed(worker)(tree_idx) for tree_idx in range(voter.n_estimators)
)
else:
return [worker(tree_idx) for tree_idx in range(voter.n_estimators)]
#%%
def estimate_posteriors(l2f, X, representation = 0, decider = 0):
l2f.check_task_idx_(decider)
if representation == "all":
representation = range(l2f.n_tasks)
elif isinstance(representation, int):
representation = np.array([representation])
def worker(transformer_task_idx):
transformer = l2f.transformers_across_tasks[transformer_task_idx]
voter = l2f.voters_across_tasks_matrix[decider][transformer_task_idx]
return voter_predict_proba(voter,transformer(X))
'''if l2f.parallel:
posteriors_across_tasks = np.array(
Parallel(n_jobs=-1)(
delayed(worker)(transformer_task_idx) for transformer_task_idx in representation
)
)
else:'''
posteriors_across_tasks = np.array([worker(transformer_task_idx) for transformer_task_idx in representation])
return posteriors_across_tasks
# %%
(X_train, y_train), (X_test, y_test) = keras.datasets.cifar100.load_data()
data_x = np.concatenate([X_train, X_test])
data_x = data_x.reshape((data_x.shape[0], data_x.shape[1] * data_x.shape[2] * data_x.shape[3]))
data_y = np.concatenate([y_train, y_test])
data_y = data_y[:, 0]
train_x_across_task, train_y_across_task, test_x_across_task, test_y_across_task = sort_data(
data_x,data_y,num_points_per_task
)
# %%
hybrid = np.zeros(reps,dtype=float)
building = np.zeros(reps,dtype=float)
recruiting= np.zeros(reps,dtype=float)
uf = np.zeros(reps,dtype=float)
mean_accuracy_dict = {'hybrid':[],'building':[],'recruiting':[],'UF':[]}
std_accuracy_dict = {'hybrid':[],'building':[],'recruiting':[],'UF':[]}
for ns in task_10_sample:
estimation_sample_no = ceil(estimation_set*ns)
validation_sample_no = ns - estimation_sample_no
for rep in range(reps):
print("doing {} samples for {} th rep".format(ns,rep))
## estimation
l2f = LifeLongDNN(model = "uf", parallel = True)
for task in range(9):
indx = np.random.choice(num_points_per_task, num_points_per_forest, replace=False)
l2f.new_forest(
train_x_across_task[task][indx],
train_y_across_task[task][indx],
max_depth=ceil(log2(num_points_per_forest)),
n_estimators=ntrees
)
task_10_train_indx = | np.random.choice(num_points_per_task, ns, replace=False) | numpy.random.choice |
# Advent of Code 2018, Day 13
# (c) blu3r4y
from collections import defaultdict
from enum import IntEnum
from itertools import tee
import networkx as nx
import numpy as np
def part1(graph: nx.Graph, carts):
return solve(graph, carts)
def part2(graph: nx.Graph, carts):
return solve(graph, carts, True)
def solve(graph: nx.Graph, carts, delete_on_crash=False):
# save the turning strategy with the cart location (x, y) as its key
turns = defaultdict(lambda: TurnStrategy.Left)
while True:
# iterate over cart positions
for pos in sorted(carts.keys()):
# a previous crash could might removed this cart already
if pos not in carts:
continue
# neigbors, which also exist in the graph
options = list(filter(lambda tup: graph.has_edge(pos, tup[1]), carts[pos].next_neighbors(pos)))
new_facing, new_pos = options[0]
# intersection? (use turn-rule and set next turn)
if len(options) > 1:
new_facing, new_pos = options[turns[pos]]
turns[pos] = turns.pop(pos).next_turn()
if new_pos in carts:
# crash detected
if delete_on_crash:
del carts[pos]
del carts[new_pos]
else:
# (part 1) first crash position
return ','.join(map(str, reversed(new_pos)))
else:
# cart moved (change position key)
carts[new_pos] = new_facing
turns[new_pos] = turns[pos]
del carts[pos]
# (part 2) position of single cart left
if delete_on_crash and len(carts) == 1:
return ','.join(map(str, reversed(next(iter(carts.keys())))))
class TurnStrategy(IntEnum):
Left = 0
Straight = 1
Right = 2
def next_turn(self):
# Left -> Straight -> Right -> Left -> ...
return TurnStrategy((self + 1) % 3)
class Direction(IntEnum):
Up = 0
Down = 1
Left = 2
Right = 3
@staticmethod
def from_char(ch):
if ch == '^':
return Direction.Up
elif ch == 'v':
return Direction.Down
elif ch == '<':
return Direction.Left
elif ch == '>':
return Direction.Right
def as_offset(self):
# offset within the matrix if you go in this direction
if self == Direction.Up:
return np.array((-1, 0))
elif self == Direction.Down:
return | np.array((1, 0)) | numpy.array |
#!/usr/bin/env python
# Copyright (c) 2020, NVIDIA CORPORATION. All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
# * Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
# * Neither the name of NVIDIA CORPORATION nor the names of its
# contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
# EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
# PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
# OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
import argparse
import numpy as np
from PIL import Image
import sys
from functools import partial
import os
import tritongrpcclient
import tritongrpcclient.model_config_pb2 as mc
import tritonhttpclient
from tritonclientutils.utils import triton_to_np_dtype
from tritonclientutils.utils import InferenceServerException
if sys.version_info >= (3, 0):
import queue
else:
import Queue as queue
class UserData:
def __init__(self):
self._completed_requests = queue.Queue()
# Callback function used for async_stream_infer()
def completion_callback(user_data, result, error):
# passing error raise and handling out
user_data._completed_requests.put((result, error))
FLAGS = None
def parse_model_grpc(model_metadata, model_config):
"""
Check the configuration of a model to make sure it meets the
requirements for an image classification network (as expected by
this client)
"""
if len(model_metadata.inputs) != 1:
raise Exception("expecting 1 input, got {}".format(
len(model_metadata.inputs)))
if len(model_metadata.outputs) != 1:
raise Exception("expecting 1 output, got {}".format(
len(model_metadata.outputs)))
if len(model_config.input) != 1:
raise Exception(
"expecting 1 input in model configuration, got {}".format(
len(model_config.input)))
input_metadata = model_metadata.inputs[0]
input_config = model_config.input[0]
output_metadata = model_metadata.outputs[0]
if output_metadata.datatype != "FP32":
raise Exception("expecting output datatype to be FP32, model '" +
model_metadata.name + "' output type is " +
output_metadata.datatype)
# Output is expected to be a vector. But allow any number of
# dimensions as long as all but 1 is size 1 (e.g. { 10 }, { 1, 10
# }, { 10, 1, 1 } are all ok).
non_one_cnt = 0
for dim in output_metadata.shape:
if dim > 1:
non_one_cnt += 1
if non_one_cnt > 1:
raise Exception("expecting model output to be a vector")
# Model input must have 3 dims, either CHW or HWC
if len(input_metadata.shape) != 3:
raise Exception(
"expecting input to have 3 dimensions, model '{}' input has {}".
format(model_name, len(input_metadata.shape)))
if ((input_config.format != mc.ModelInput.FORMAT_NCHW) and
(input_config.format != mc.ModelInput.FORMAT_NHWC)):
raise Exception("unexpected input format " +
mc.ModelInput.Format.Name(input_config.format) +
", expecting " +
mc.ModelInput.Format.Name(mc.ModelInput.FORMAT_NCHW) +
" or " +
mc.ModelInput.Format.Name(mc.ModelInput.FORMAT_NHWC))
if input_config.format == mc.ModelInput.FORMAT_NHWC:
h = input_metadata.shape[0]
w = input_metadata.shape[1]
c = input_metadata.shape[2]
else:
c = input_metadata.shape[0]
h = input_metadata.shape[1]
w = input_metadata.shape[2]
return (model_config.max_batch_size, input_metadata.name,
output_metadata.name, c, h, w, input_config.format,
input_metadata.datatype)
def parse_model_http(model_metadata, model_config):
"""
Check the configuration of a model to make sure it meets the
requirements for an image classification network (as expected by
this client)
"""
if len(model_metadata['inputs']) != 1:
raise Exception("expecting 1 input, got {}".format(
len(model_metadata['inputs'])))
if len(model_metadata['outputs']) != 1:
raise Exception("expecting 1 output, got {}".format(
len(model_metadata['outputs'])))
if len(model_config['input']) != 1:
raise Exception(
"expecting 1 input in model configuration, got {}".format(
len(model_config['input'])))
input_metadata = model_metadata['inputs'][0]
input_config = model_config['input'][0]
output_metadata = model_metadata['outputs'][0]
if output_metadata['datatype'] != "FP32":
raise Exception("expecting output datatype to be FP32, model '" +
model_metadata['name'] + "' output type is " +
output_metadata['datatype'])
# Output is expected to be a vector. But allow any number of
# dimensions as long as all but 1 is size 1 (e.g. { 10 }, { 1, 10
# }, { 10, 1, 1 } are all ok).
non_one_cnt = 0
for dim in output_metadata['shape']:
if dim > 1:
non_one_cnt += 1
if non_one_cnt > 1:
raise Exception("expecting model output to be a vector")
# Model input must have 3 dims, either CHW or HWC
if len(input_metadata['shape']) != 3:
raise Exception(
"expecting input to have 3 dimensions, model '{}' input has {}".
format(model_metadata.name, len(input_metadata['shape'])))
if ((input_config['format'] != "FORMAT_NCHW") and
(input_config['format'] != "FORMAT_NHWC")):
raise Exception("unexpected input format " + input_config['format'] +
", expecting FORMAT_NCHW or FORMAT_NHWC")
if input_config['format'] == "FORMAT_NHWC":
h = input_metadata['shape'][0]
w = input_metadata['shape'][1]
c = input_metadata['shape'][2]
else:
c = input_metadata['shape'][0]
h = input_metadata['shape'][1]
w = input_metadata['shape'][2]
max_batch_size = 0
if 'max_batch_size' in model_config:
max_batch_size = model_config['max_batch_size']
return (max_batch_size, input_metadata['name'], output_metadata['name'], c,
h, w, input_config['format'], input_metadata['datatype'])
def preprocess(img, format, dtype, c, h, w, scaling, protocol):
"""
Pre-process an image to meet the size, type and format
requirements specified by the parameters.
"""
# np.set_printoptions(threshold='nan')
if c == 1:
sample_img = img.convert('L')
else:
sample_img = img.convert('RGB')
resized_img = sample_img.resize((w, h), Image.BILINEAR)
resized = np.array(resized_img)
if resized.ndim == 2:
resized = resized[:, :, np.newaxis]
npdtype = triton_to_np_dtype(dtype)
typed = resized.astype(npdtype)
if scaling == 'INCEPTION':
scaled = (typed / 128) - 1
elif scaling == 'VGG':
if c == 1:
scaled = typed - np.asarray((128,), dtype=npdtype)
else:
scaled = typed - | np.asarray((123, 117, 104), dtype=npdtype) | numpy.asarray |
import numpy as np
import matplotlib
#print ("Matplotlib Version :",matplotlib.__version__)
import pylab as pl
import time, sys, os
import decimal
import glob
from subprocess import call
from IPython.display import Image
from matplotlib.pyplot import figure, imshow, axis
from matplotlib.image import imread
#from sympy import *
#from mpmath import quad
from scipy.integrate import quad
import random
import string
vol_frac = 0.5
radius_cyl = np.sqrt(vol_frac/np.pi)
rho = 1000
mu = 0.001
L = 2*radius_cyl
def Reynolds( V_mean, L, rho=1000, mu=0.001):
Re_actual = rho*V_mean*L/mu
return Re_actual
def majorAxis(alpha):
return np.sqrt((0.5/np.pi)/alpha)
def createFolder(directory):
try:
if not os.path.exists(directory):
os.makedirs(directory)
except OSError:
print ('Error: Creating directory. ' + directory)
def plot_fourier_curve(shape):
# input( coeffs ): the fourier coefficients of dimension 2,2*M+1, where M is the maximum degree.
# output plot: Plots the shape
coeffs = shape["coeffs"]
name =shape["name"]
x_coeffs = coeffs[0,:]
y_coeffs = coeffs[1,:]
M = (np.shape(coeffs)[1] -1 ) // 2
start_t = 0.0
t = np.linspace(start_t,start_t+2.0*np.pi,num=100,endpoint=True)
#print((t))
x = np.zeros(np.shape(t))
y = np.zeros(np.shape(t))
x += 0.5*x_coeffs[0] ; y += 0.5*y_coeffs[0]
for mi in range(1,M+1):
x += x_coeffs[2*mi-1]*np.cos(mi*t) + x_coeffs[2*mi]*np.sin(mi*t)
y += y_coeffs[2*mi-1]*np.cos(mi*t) + y_coeffs[2*mi]*np.sin(mi*t)
pl.plot(x,y,'k-')
head = "shape "+name
curve = np.column_stack((x,y))
np.savetxt(name,curve,delimiter=" ")#,header=head)
pl.axis('equal')
pl.title('Shape from Fourier Coeffs.')
pl.show()
coords = {"x":x,
"y":y}
return coords
def minkowski_fourier_curve(coeffs):
# input( shape ): contains the key "coeffs" -the fourier coefficients of dimension 2,2*M+1, where M is the maximum degree.
# and the key "name" for shape name.
# output (W) : Dictionary containing the four 2D minkowski tensors W020, W120, W220, W102 and the area
# and perimeter of the curve/shape.
#coeffs = shape["coeffs"]
t=symbols("t") # parameter of the curve
x_coeffs = coeffs[0,:]
y_coeffs = coeffs[1,:]
# m =0 , zeroth degree terms, also gives the centroid of the shape.
expr_X = "0.5*"+str(coeffs[0,0])
expr_Y = "0.5*"+str(coeffs[1,0])
M = (np.shape(coeffs)[1] -1)//2
# X and Y coodinates as parametric representation using fourier series.
for mi in range(1,M+1):
expr_X += "+" + str(x_coeffs[2*mi-1]) + "*cos("+str(mi)+"*t) + " +str(x_coeffs[2*mi])+"*sin("+str(mi)+"*t)"
expr_Y += "+" + str(y_coeffs[2*mi-1]) + "*cos("+str(mi)+"*t) + " +str(y_coeffs[2*mi])+"*sin("+str(mi)+"*t)"
# derivative terms required for normal and curvature computation
sym_x = sympify(expr_X)
sym_y = sympify(expr_Y)
# dx/dt
sym_dx = diff(sym_x,t)
# d^2x/dt^2
sym_ddx = diff(sym_dx,t)
# dA = ydx infinitesimal area
sym_ydx = sym_y*sym_dx
sym_dy = diff(sym_y,t)
sym_ddy = diff(sym_dy,t)
# ds = sqrt(x'^2 + y'^2) , the infinitesimal arc-length
sym_ds = sqrt(sym_dx**2 + sym_dy**2)
# position vector r
sym_r = [sym_x, sym_y]
# unit normal vector n
sym_norm_mag = sqrt(sym_dx**2 + sym_dy**2)
sym_norm = [sym_dx/sym_norm_mag, sym_dy/sym_norm_mag]
#print("Computed derivatives")
# Area = \int ydx
area = Integral(sym_ydx,(t,0,2*pi)).evalf(5)
perimeter = Integral(sym_ds,(t,0,2*pi)).evalf(5)
kappa = (sym_dx*sym_ddy - sym_dy*sym_ddx)/(sym_dx**2 + sym_dy**2)**(3/2)
#print("Computing integrals ...")
#Initialize the minkowski tensors
W020 = np.zeros((2,2))
W120 = np.zeros((2,2))
W220 = np.zeros((2,2))
W102 = np.zeros((2,2))
x = symbols('x')
#tensor computation
for ia in range(2):
for ib in range(2):
# W020[ia,ib] = Integral(sym_r[ia]*sym_r[ib]*sym_ydx, (t,0,2*pi)).evalf(5)
# print("Computing W120 ...")
# W120[ia,ib] = 0.5* Integral(sym_r[ia]*sym_r[ib]*sym_ds, (t,0,2*pi)).evalf(5)
# W220[ia,ib] = 0.5* Integral(kappa*sym_r[ia]*sym_r[ib]*sym_ds, (t,0,2*pi)).evalf(5)
# print("Computing W102 ...")
# W102[ia,ib] = 0.5* Integral(sym_norm[ia] * sym_norm[ib]*sym_ds,(t,0,2*pi)).evalf(5)
f = lambdify(t,sym_r[ia]*sym_r[ib]*sym_ydx)
W020[ia,ib],err = quad( f, 0,2*np.pi)
#print(W020[ia,ib])
#print("Computing W120 ...")
f = lambdify(t,sym_r[ia]*sym_r[ib]*sym_ds)
W120[ia,ib],err = quad(f, 0,2*np.pi)
W120[ia,ib] = 0.5* W120[ia,ib]
f = lambdify(t,kappa*sym_r[ia]*sym_r[ib]*sym_ds)
W220[ia,ib],err = quad(f, 0,2*np.pi)
W220[ia,ib] = 0.5*W220[ia,ib]
#print("Computing W102 ...")
f = lambdify(t,sym_norm[ia] * sym_norm[ib]*sym_ds)
W102[ia,ib], err = quad(f, 0,2*np.pi)
W102[ia,ib] = 0.5* W102[ia,ib]
#dictionary with computed quantities
W={"W020":W020,
"W120":W120,
"W220":W220,
"W102":W102,
"area":area,
"perimeter":perimeter
}
return W
# def simulate_flow():
# DIR = './shapes/coords'
# createFolder('./simulations')
# start_t = time.time()
# name_list = []
# num = 0
# #n_angles =20
# n_shapes = len(os.listdir(DIR))
# for name in os.listdir(DIR):
# if os.path.isfile(os.path.join(DIR,name)):
# update_progress(num/n_shapes,start_t,time.time())
# num += 1
# thisfolder ='./simulations/'+name
# createFolder(thisfolder)
# #print("Shape No. "+str(num)+" : "+name)
# #for angle in range(n_angles):
# #theta = random.uniform(0.0,np.pi)
# # thisfolder ='./simulations/'+name+'/theta_'+str(round(theta,3))
# # createFolder(thisfolder)
# call(["cp","vorticity.gfs",thisfolder+'/.'])
# call(["cp","xprofile",thisfolder+'/.'])
# f=open(thisfolder+"/shape.gts","w")
# call(["shapes",os.path.join(DIR,name)],stdout=f) #+" > "+thisfolder+"/shape.gts"])
# os.chdir(thisfolder)
# call(["gerris2D","vorticity.gfs"])
# #xp = (np.loadtxt('xprof', delimiter=" "))
# #pl.plot(xp[:,6],xp[:,2],label=r'$\theta =$') #thets
# #Vel_mean[i,1] = np.mean(xp[:,6])
# #Vel_mean[i,0] = theta
# #Image("velocity.png")
# os.chdir('../../')
# #name_list.append(name)
# n_simulations = n_shapes
def simulate_flow(dp=0.000001,DIR='./shapes_low0/coords'):
# DIR = './shapes_low0/coords'
# dp_0 = 0.000001
# p_ratio = round(dp_0/dp,2)
dp_string = '{:.0e}'.format(decimal.Decimal(str(dp)))
folder_name ='./simulations_dP_'+dp_string
input_file ='vorticity_'+dp_string+'.gfs'
with open('vorticity.gfs','r') as fin:
# # with is like your try .. finally block in this case
input_string = fin.readlines()
for index, line in enumerate(input_string):
if line.strip().startswith('Source {} U'):
input_string[index] = 'Source {} U '+str(dp)
with open(input_file, 'w') as file:
file.writelines( input_string )
createFolder(folder_name)
start_t = time.time()
name_list = []
num = 0
#n_angles =20
n_shapes = len(os.listdir(DIR))
for name in os.listdir(DIR):
if os.path.isfile(os.path.join(DIR,name)):
update_progress(num/n_shapes,start_t,time.time())
num += 1
thisfolder =folder_name + '/' + name
createFolder(thisfolder)
#print("Shape No. "+str(num)+" : "+name)
#for angle in range(n_angles):
#theta = random.uniform(0.0,np.pi)
# thisfolder ='./simulations/'+name+'/theta_'+str(round(theta,3))
# createFolder(thisfolder)
call(["cp", input_file ,thisfolder+'/.'])
call(["cp","xprofile",thisfolder+'/.'])
f=open(thisfolder+"/shape.gts","w")
call(["shapes",os.path.join(DIR,name)],stdout=f) #+" > "+thisfolder+"/shape.gts"])
os.chdir(thisfolder)
call(["gerris2D",input_file])
#xp = (np.loadtxt('xprof', delimiter=" "))
#pl.plot(xp[:,6],xp[:,2],label=r'$\theta =$') #thets
#Vel_mean[i,1] = np.mean(xp[:,6])
#Vel_mean[i,0] = theta
#Image("velocity.png")
os.chdir('../../')
#name_list.append(name)
n_simulations = n_shapes
def fourier2Cart(coeffs,t):
#x_coeffs = coeffs[0,:]
#y_coeffs = coeffs[1,:]
#M = (np.shape(coeffs)[1] -1 ) // 2
#x = np.zeros(np.shape(t))
#y = np.zeros(np.shape(t))
#x += 0.5*x_coeffs[0] ; y += 0.5*y_coeffs[0]
#for mi in range(1,M+1):
# x += x_coeffs[2*mi-1]*np.cos(mi*t) + x_coeffs[2*mi]*np.sin(mi*t)
# y += y_coeffs[2*mi-1]*np.cos(mi*t) + y_coeffs[2*mi]*np.sin(mi*t)
#t.reshape(len(t))
#t=t[:,np.newaxis].T
tt = np.row_stack((t,t))
#print(np.shape(tt))
coords = np.zeros(np.shape(tt))
coords += 0.5*coeffs[:,0,np.newaxis]
M = (np.shape(coeffs)[1] -1 ) // 2
for mi in range(1,M+1):
coords += coeffs[:,2*mi-1,np.newaxis]*np.cos( mi*tt) + coeffs[:,2*mi,np.newaxis]*np.sin(mi*tt)
#coords = np.row_stack((x,y))
return coords
def generateShape(res=200,M=4):
t = np.linspace(0, 2.0*np.pi, num=res, endpoint=True)
dt = t[1]-t[0]
coeffs = np.zeros((2,2*M+1))
bad_shape = True
n_attempts = 0
while bad_shape == True:
alpha = np.random.uniform(1.0,2.0)
a = majorAxis(alpha)
b = alpha*a
#a = 1
#b = 1
#print("the major and minor axes are:"+str(a)+","+str(b))
coeffs[0,1] = a # create an ellipse as starting point
coeffs[1,2] = b # create an ellipse as starting point
coeffs[:,3::] = coeffs[:,3::] + 0.25*a*(np.random.rand(2,2*M-2) -0.5)#-0.5
coords = fourier2Cart(coeffs,t)
#pl.plot(coords[0,:],coords[1,:],'-')
dx = np.gradient(coords,axis=1)
ddx = np.gradient(dx, axis=1)
num = dx[0,:] * ddx[1,:] - ddx[0,:] * dx[1,:]
denom = dx[0,:] * dx[0,:] + dx[1,:] * dx[1,:]
denom = np.sqrt(denom)
denom = denom * denom * denom
curvature = num / denom
sharp_edge = False
outside_domain = False
if (np.amax(np.absolute(curvature)) > 20):
sharp_edge = True
coords_prime = np.gradient(coords,dt,axis=1)
integrand = coords_prime[1,:] * coords[0,:]
area = np.trapz(integrand, x=t)
scale = np.sqrt(0.5 / np.absolute(area))
coeffs = scale * coeffs
coords = fourier2Cart(coeffs,t)
if(np.any(np.abs(coords) >= 0.5)):
outside_domain = True
bad_shape = sharp_edge or outside_domain
n_attempts +=1
#if(bad_shape):
# print( "This shape is bad:"+str(sharp_edge)+str(outside_domain))
#x_coeffs_prime = x_coeffs[1:]
#y_coeffs_prime = y_coeffs[1:]
coords_prime = np.gradient(coords,dt,axis=1)
integrand = coords[1,:] * coords_prime[0,:]
area = np.trapz(integrand, x=t)
# x = np.append(x, x[0])
# y = np.append(y, y[0])
length = np.sum( np.sqrt(np.ediff1d(coords[0,:]) * np.ediff1d(coords[0,:]) + np.ediff1d(coords[1,:]) * np.ediff1d(coords[1,:])) )
print('x-coefficients: ' + str(coeffs[0,:]))
print('y-coefficients: ' + str(coeffs[1,:]))
print('enclosed area: ' + str(np.absolute(area)))
print('curve length: ' + str(length))
shape={"coeffs":coeffs,
"coords":coords}
pl.plot(coords[0,:],coords[1,:],'-')
return shape
def check_self_intersection(coords):
result = False
for i in range(2,np.shape(coords)[1]-1):
p = coords[:,i]
dp = coords[:,i+1] - p
for j in range(0,i-2):
if (result==False):
q = coords[:,j]
dq = coords[:,j+1] - q
dpdq = np.cross(dp,dq)
t = np.cross(q-p,dq)/dpdq
u = np.cross(q-p,dp)/dpdq
if(dpdq != 0):
if(0<= t <= 1):
if(0<= u <= 1):
result = True
return result
def check_domain_intersection(coords):
result = np.any(np.abs(coords)>= 0.5)
return result
def generate_Npoint_shape(N=10,M=4, res=100):
#random.seed(1516)
bad_shape =True
while bad_shape == True:
pos_r = np.random.uniform(0,0.5,(N))
#pos_thet = np.random.uniform(0,2*np.pi,(1,N))
pos_thet =np.linspace(0,2*np.pi,num=N,endpoint=False)
posx = pos_r*np.cos(pos_thet)
posy = pos_r*np.sin(pos_thet)
pos = | np.row_stack((posx,posy)) | numpy.row_stack |
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""Aqueous Helgeson Equation of State with Bromley activity model
This file implements an aqueous equation of state (EOS) named the
Helgeson EOS with Bromley activity model. It is specifically
the version of the that EOS that is described in Jager et. al. (2003),
which is linked in the readme.md file. The file consists of a single
class, 'HegBromEos' that will take as arguments a list of components
and a pressure and a temperature. Pressure and temperature can be
modified after an instance of HegBromEos is created; however, the number
of components and actual component list cannot. The method 'calc' is the
main calculation of the class, which uses other methods to determine
the partial fugacity of each component given mole fractions, pressure,
and temperature.
Functions
----------
pure_water_vol_intgrt :
Calculates integrated change in the volume of pure water from P_0 to P
at fixed T.
pure_water_vol :
Calculates volume of pure water at P and T.
dielectric_const :
Calculates dielectric constant of pure water at P and T.
molality :
Calculates molality of each solute in the aqueous phase.
solute_vol_integrated:
Calculates volume of each component as a solute.
"""
import numpy as np
# Constants for EOS
R = 8.3144621 # Gas constant in J/mol-K
T_0 = 298.15 # Reference temperature in K
P_0 = 1 # Reference pressure in bar
# Constants for solute model
theta = 228.0
psi = 2600
s10 = 243.9576
s11 = -0.7520846
s12 = 6.60648e-4
s20 = 0.039037
s21 = -2.12309e-4
s22 = 3.18021e-7
s30 = -1.0126e-5
s31 = 6.04961e-8
s32 = -9.3334e-11
# Constants produced by symbolic integration for h_ast funum_compstion
f1 = 73786976294838206464
f2 = 8151985141053725
f3 = 3249460376862603
f4 = 9444732965739290427392
f5 = 4722366482869645213696
f6 = 1043454098054876800
# Constants for pure water
gw_pure = -237129
hw_pure = -285830
cp_a0 = R * 8.712
cp_a1 = R * 1e-2 * 0.125
cp_a2 = R * 1e-5 * -0.018
cp_a3 = 0
a10 = 31.1251
a11 = -1.14154e-1
a12 = 3.10034e-4
a13 = -2.48318e-7
a20 = -2.46176e-2
a21 = 2.15663e-4
a22 = -6.48160e-7
a23 = 6.47521e-10
a30 = 8.69425e-6
a31 = -7.96939e-8
a32 = 2.45391e-10
a33 = -2.51773e-13
a40 = -6.03348e-10
a41 = 5.57791e-12
a42 = -1.72577e-14
a43 = 1.77978e-17
"""The above global variables may be used throughout the calculation."""
def pure_water_vol_intgrt(T, P):
"""Volume of pure water integrate wrt pressure.
Parameters
----------
T : float
Temperature in Kelvin.
P : float
Pressure in bar.
Returns
----------
v_w : float
Volume of water integrated in cm^3 - bar.
"""
v_w = ((a10 * P + a20 * P ** 2 / 2 + a30 * P ** 3 / 3 + a40 * P ** 4 / 4)
+ (a11 * P + a21 * P ** 2 / 2 + a31 * P ** 3 / 3 + a41 * P ** 4 / 4) * T
+ (a12 * P + a22 * P ** 2 / 2 + a32 * P ** 3 / 3 + a42 * P ** 4 / 4) * T ** 2
+ (a13 * P + a23 * P ** 2 / 2 + a33 * P ** 3 / 3 + a43 * P ** 4 / 4) * T ** 3)
return v_w
def pure_water_vol(T, P):
"""Volume of pure water.
Parameters
----------
T : float
Temperature in Kelvin.
P : float
Pressure in bar.
Returns
----------
v_w : float
Volume of water in cm^3.
"""
v_w = ((a10 + a20 * P + a30 * P ** 2 + a40 * P ** 3)
+ (a11 + a21 * P + a31 * P ** 2 + a41 * P ** 3) * T
+ (a12 + a22 * P + a32 * P ** 2 + a42 * P ** 3) * T ** 2
+ (a13 + a23 * P + a33 * P ** 2 + a43 * P ** 3) * T ** 3)
return v_w
def dielectric_const(T, P):
"""Dielectric constant of pure water.
Parameters
----------
T : float
Temperature in Kelvin.
P : float
Pressure in bar.
Returns
----------
eps : float
Dielectric constant of water (no units) .
"""
eps = ((s10 + s20 * P + s30 * P ** 2)
+ (s11 + s21 * P + s31 * P ** 2) * T
+ (s12 + s22 * P + s32 * P ** 2) * T ** 2)
return eps
def molality(xc, xw):
"""Calculates molality of each solute in the aqueous phase.
Parameters
----------
xc : float
Mole fraction of component.
xw : float
Mole fraction water.
Returns
----------
float
Molality of component in mol[component] / kg[water].
"""
return xc / (xw * 0.018015)
def solute_vol_integrated(comp, T, P):
"""Volume of solute integrated wrt pressure.
Parameters
----------
comp : object
Instance of Component class for each component
T : float
Temperature at initialization in Kelvin.
P : float
Pressure at initialization in bar.
Returns
----------
v_ast_P : float
Volume of solute integrated wrt pressure in cm^3 - bar
"""
omega = comp.AqHB['omega_born']
v1 = comp.AqHB['v']['v1']
v2 = comp.AqHB['v']['v2']
v3 = comp.AqHB['v']['v3']
v4 = comp.AqHB['v']['v4']
tau = ((5.0 / 6.0) * T - theta) / (1.0 + np.exp((T - 273.15) / 5.0))
v_ast_P = (
(v1 * P + v2 * np.log(psi + P)
+ (v3 * P + v4 * np.log(psi + P)) * (1.0 / (T - theta - tau))
+ omega / dielectric_const(T, P)) / (R * T)
)
return v_ast_P
class HegBromEos(object):
"""The main class for this EOS that perform various calculations.
Methods
----------
make_constant_mats :
Performs calculations that only depend on pressure and temperature.
fugacity :
Calculates fugacity of each component in the aqueous phase.
calc:
Main calculation for aqueous phase EOS.
"""
def __init__(self, comps, T, P):
"""Aqueous EOS object for fugacity calculations.
Parameters
----------
comps : list
List of components as 'Component' objects created with
'component_properties.py'.
T : float
Temperature at initialization in Kelvin.
P : float
Pressure at initialization in bar.
Attributes
----------
water_ind : int
Index of for water component in all lists.
comps : list
List of 'Component' classes passed into 'HegBromEos'.
comp_names : list
List of components names.
num_comps : int
Number of components.
T : float
Temperature at initialization in Kelvin.
P : float
Pressure at initialization in bar.
g_io_vec : numpy array
Pre-allocated array for gibbs energy of each component
in ideal gas state.
molality_vec : numpy array
Pre-allocated array for molality of each component.
activity_vec : numpy array
Pre-allocated array for activity of each component
in Bromley activity model.
gamma_p1_vec : numpy array
Pre-allocated array for gamma_{p1} variable of each
component in Bromley activity model.
mu_ik_RT_vec : numpy array
Pre-allocated array chemical potential of each component.
"""
try:
self.water_ind = [ii for ii, x in enumerate(comps)
if x.compname == 'h2o'][0]
except ValueError:
raise RuntimeError(
"""Aqueous EOS requires water to be present!
\nPlease provide water in your component list.""")
self.comps = comps
self.comp_names = [x.compname for x in comps]
self.num_comps = len(comps)
self.T = T
self.P = P
self.g_io_vec = np.zeros(self.num_comps)
self.molality_vec = np.zeros(self.num_comps)
self.activity_vec = np.zeros(self.num_comps)
self.gamma_p1_vec = np.zeros(self.num_comps)
self.mu_ik_rt_cons = | np.zeros(self.num_comps) | numpy.zeros |
import numpy as np
class LabFrame:
def __init__(self, velocity):
self.update(velocity)
def update(self, velocity):
self.velocity = velocity
self.gamma = 1 / np.sqrt(1 - | np.linalg.norm(velocity) | numpy.linalg.norm |
"""Filter design.
"""
from __future__ import division, print_function, absolute_import
import warnings
import numpy
from numpy import (atleast_1d, poly, polyval, roots, real, asarray, allclose,
resize, pi, absolute, logspace, r_, sqrt, tan, log10,
arctan, arcsinh, sin, exp, cosh, arccosh, ceil, conjugate,
zeros, sinh, append, concatenate, prod, ones, array)
from numpy import mintypecode
import numpy as np
from scipy import special, optimize
from scipy.special import comb
from scipy.misc import factorial
from numpy.polynomial.polynomial import polyval as npp_polyval
import math
__all__ = ['findfreqs', 'freqs', 'freqz', 'tf2zpk', 'zpk2tf', 'normalize',
'lp2lp', 'lp2hp', 'lp2bp', 'lp2bs', 'bilinear', 'iirdesign',
'iirfilter', 'butter', 'cheby1', 'cheby2', 'ellip', 'bessel',
'band_stop_obj', 'buttord', 'cheb1ord', 'cheb2ord', 'ellipord',
'buttap', 'cheb1ap', 'cheb2ap', 'ellipap', 'besselap',
'BadCoefficients',
'tf2sos', 'sos2tf', 'zpk2sos', 'sos2zpk', 'group_delay']
class BadCoefficients(UserWarning):
"""Warning about badly conditioned filter coefficients"""
pass
abs = absolute
def findfreqs(num, den, N):
"""
Find array of frequencies for computing the response of an analog filter.
Parameters
----------
num, den : array_like, 1-D
The polynomial coefficients of the numerator and denominator of the
transfer function of the filter or LTI system. The coefficients are
ordered from highest to lowest degree.
N : int
The length of the array to be computed.
Returns
-------
w : (N,) ndarray
A 1-D array of frequencies, logarithmically spaced.
Examples
--------
Find a set of nine frequencies that span the "interesting part" of the
frequency response for the filter with the transfer function
H(s) = s / (s^2 + 8s + 25)
>>> from scipy import signal
>>> signal.findfreqs([1, 0], [1, 8, 25], N=9)
array([ 1.00000000e-02, 3.16227766e-02, 1.00000000e-01,
3.16227766e-01, 1.00000000e+00, 3.16227766e+00,
1.00000000e+01, 3.16227766e+01, 1.00000000e+02])
"""
ep = atleast_1d(roots(den)) + 0j
tz = atleast_1d(roots(num)) + 0j
if len(ep) == 0:
ep = atleast_1d(-1000) + 0j
ez = r_['-1',
numpy.compress(ep.imag >= 0, ep, axis=-1),
numpy.compress((abs(tz) < 1e5) & (tz.imag >= 0), tz, axis=-1)]
integ = abs(ez) < 1e-10
hfreq = numpy.around(numpy.log10(numpy.max(3 * abs(ez.real + integ) +
1.5 * ez.imag)) + 0.5)
lfreq = numpy.around(numpy.log10(0.1 * numpy.min(abs(real(ez + integ)) +
2 * ez.imag)) - 0.5)
w = logspace(lfreq, hfreq, N)
return w
def freqs(b, a, worN=None, plot=None):
"""
Compute frequency response of analog filter.
Given the M-order numerator `b` and N-order denominator `a` of an analog
filter, compute its frequency response::
b[0]*(jw)**M + b[1]*(jw)**(M-1) + ... + b[M]
H(w) = ----------------------------------------------
a[0]*(jw)**N + a[1]*(jw)**(N-1) + ... + a[N]
Parameters
----------
b : array_like
Numerator of a linear filter.
a : array_like
Denominator of a linear filter.
worN : {None, int, array_like}, optional
If None, then compute at 200 frequencies around the interesting parts
of the response curve (determined by pole-zero locations). If a single
integer, then compute at that many frequencies. Otherwise, compute the
response at the angular frequencies (e.g. rad/s) given in `worN`.
plot : callable, optional
A callable that takes two arguments. If given, the return parameters
`w` and `h` are passed to plot. Useful for plotting the frequency
response inside `freqs`.
Returns
-------
w : ndarray
The angular frequencies at which `h` was computed.
h : ndarray
The frequency response.
See Also
--------
freqz : Compute the frequency response of a digital filter.
Notes
-----
Using Matplotlib's "plot" function as the callable for `plot` produces
unexpected results, this plots the real part of the complex transfer
function, not the magnitude. Try ``lambda w, h: plot(w, abs(h))``.
Examples
--------
>>> from scipy.signal import freqs, iirfilter
>>> b, a = iirfilter(4, [1, 10], 1, 60, analog=True, ftype='cheby1')
>>> w, h = freqs(b, a, worN=np.logspace(-1, 2, 1000))
>>> import matplotlib.pyplot as plt
>>> plt.semilogx(w, 20 * np.log10(abs(h)))
>>> plt.xlabel('Frequency')
>>> plt.ylabel('Amplitude response [dB]')
>>> plt.grid()
>>> plt.show()
"""
if worN is None:
w = findfreqs(b, a, 200)
elif isinstance(worN, int):
N = worN
w = findfreqs(b, a, N)
else:
w = worN
w = atleast_1d(w)
s = 1j * w
h = polyval(b, s) / polyval(a, s)
if plot is not None:
plot(w, h)
return w, h
def freqz(b, a=1, worN=None, whole=False, plot=None):
"""
Compute the frequency response of a digital filter.
Given the M-order numerator `b` and N-order denominator `a` of a digital
filter, compute its frequency response::
jw -jw -jwM
jw B(e ) b[0] + b[1]e + .... + b[M]e
H(e ) = ---- = -----------------------------------
jw -jw -jwN
A(e ) a[0] + a[1]e + .... + a[N]e
Parameters
----------
b : array_like
numerator of a linear filter
a : array_like
denominator of a linear filter
worN : {None, int, array_like}, optional
If None (default), then compute at 512 frequencies equally spaced
around the unit circle.
If a single integer, then compute at that many frequencies.
If an array_like, compute the response at the frequencies given (in
radians/sample).
whole : bool, optional
Normally, frequencies are computed from 0 to the Nyquist frequency,
pi radians/sample (upper-half of unit-circle). If `whole` is True,
compute frequencies from 0 to 2*pi radians/sample.
plot : callable
A callable that takes two arguments. If given, the return parameters
`w` and `h` are passed to plot. Useful for plotting the frequency
response inside `freqz`.
Returns
-------
w : ndarray
The normalized frequencies at which `h` was computed, in
radians/sample.
h : ndarray
The frequency response.
Notes
-----
Using Matplotlib's "plot" function as the callable for `plot` produces
unexpected results, this plots the real part of the complex transfer
function, not the magnitude. Try ``lambda w, h: plot(w, abs(h))``.
Examples
--------
>>> from scipy import signal
>>> b = signal.firwin(80, 0.5, window=('kaiser', 8))
>>> w, h = signal.freqz(b)
>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> plt.title('Digital filter frequency response')
>>> ax1 = fig.add_subplot(111)
>>> plt.plot(w, 20 * np.log10(abs(h)), 'b')
>>> plt.ylabel('Amplitude [dB]', color='b')
>>> plt.xlabel('Frequency [rad/sample]')
>>> ax2 = ax1.twinx()
>>> angles = np.unwrap(np.angle(h))
>>> plt.plot(w, angles, 'g')
>>> plt.ylabel('Angle (radians)', color='g')
>>> plt.grid()
>>> plt.axis('tight')
>>> plt.show()
"""
b, a = map(atleast_1d, (b, a))
if whole:
lastpoint = 2 * pi
else:
lastpoint = pi
if worN is None:
N = 512
w = numpy.linspace(0, lastpoint, N, endpoint=False)
elif isinstance(worN, int):
N = worN
w = numpy.linspace(0, lastpoint, N, endpoint=False)
else:
w = worN
w = atleast_1d(w)
zm1 = exp(-1j * w)
h = polyval(b[::-1], zm1) / polyval(a[::-1], zm1)
if plot is not None:
plot(w, h)
return w, h
def group_delay(system, w=None, whole=False):
r"""Compute the group delay of a digital filter.
The group delay measures by how many samples amplitude envelopes of
various spectral components of a signal are delayed by a filter.
It is formally defined as the derivative of continuous (unwrapped) phase::
d jw
D(w) = - -- arg H(e)
dw
Parameters
----------
system : tuple of array_like (b, a)
Numerator and denominator coefficients of a filter transfer function.
w : {None, int, array-like}, optional
If None (default), then compute at 512 frequencies equally spaced
around the unit circle.
If a single integer, then compute at that many frequencies.
If array, compute the delay at the frequencies given
(in radians/sample).
whole : bool, optional
Normally, frequencies are computed from 0 to the Nyquist frequency,
pi radians/sample (upper-half of unit-circle). If `whole` is True,
compute frequencies from 0 to ``2*pi`` radians/sample.
Returns
-------
w : ndarray
The normalized frequencies at which the group delay was computed,
in radians/sample.
gd : ndarray
The group delay.
Notes
-----
The similar function in MATLAB is called `grpdelay`.
If the transfer function :math:`H(z)` has zeros or poles on the unit
circle, the group delay at corresponding frequencies is undefined.
When such a case arises the warning is raised and the group delay
is set to 0 at those frequencies.
For the details of numerical computation of the group delay refer to [1]_.
.. versionadded: 0.16.0
See Also
--------
freqz : Frequency response of a digital filter
References
----------
.. [1] <NAME>, "Understanding Digital Signal Processing,
3rd edition", p. 830.
Examples
--------
>>> from scipy import signal
>>> b, a = signal.iirdesign(0.1, 0.3, 5, 50, ftype='cheby1')
>>> w, gd = signal.group_delay((b, a))
>>> import matplotlib.pyplot as plt
>>> plt.title('Digital filter group delay')
>>> plt.plot(w, gd)
>>> plt.ylabel('Group delay [samples]')
>>> plt.xlabel('Frequency [rad/sample]')
>>> plt.show()
"""
if w is None:
w = 512
if isinstance(w, int):
if whole:
w = np.linspace(0, 2 * pi, w, endpoint=False)
else:
w = np.linspace(0, pi, w, endpoint=False)
w = np.atleast_1d(w)
b, a = map(np.atleast_1d, system)
c = np.convolve(b, a[::-1])
cr = c * np.arange(c.size)
z = np.exp(-1j * w)
num = np.polyval(cr[::-1], z)
den = np.polyval(c[::-1], z)
singular = np.absolute(den) < 10 * EPSILON
if np.any(singular):
warnings.warn(
"The group delay is singular at frequencies [{0}], setting to 0".
format(", ".join("{0:.3f}".format(ws) for ws in w[singular]))
)
gd = np.zeros_like(w)
gd[~singular] = np.real(num[~singular] / den[~singular]) - a.size + 1
return w, gd
def _cplxreal(z, tol=None):
"""
Split into complex and real parts, combining conjugate pairs.
The 1D input vector `z` is split up into its complex (`zc`) and real (`zr`)
elements. Every complex element must be part of a complex-conjugate pair,
which are combined into a single number (with positive imaginary part) in
the output. Two complex numbers are considered a conjugate pair if their
real and imaginary parts differ in magnitude by less than ``tol * abs(z)``.
Parameters
----------
z : array_like
Vector of complex numbers to be sorted and split
tol : float, optional
Relative tolerance for testing realness and conjugate equality.
Default is ``100 * spacing(1)`` of `z`'s data type (i.e. 2e-14 for
float64)
Returns
-------
zc : ndarray
Complex elements of `z`, with each pair represented by a single value
having positive imaginary part, sorted first by real part, and then
by magnitude of imaginary part. The pairs are averaged when combined
to reduce error.
zr : ndarray
Real elements of `z` (those having imaginary part less than
`tol` times their magnitude), sorted by value.
Raises
------
ValueError
If there are any complex numbers in `z` for which a conjugate
cannot be found.
See Also
--------
_cplxpair
Examples
--------
>>> a = [4, 3, 1, 2-2j, 2+2j, 2-1j, 2+1j, 2-1j, 2+1j, 1+1j, 1-1j]
>>> zc, zr = _cplxreal(a)
>>> print zc
[ 1.+1.j 2.+1.j 2.+1.j 2.+2.j]
>>> print zr
[ 1. 3. 4.]
"""
z = atleast_1d(z)
if z.size == 0:
return z, z
elif z.ndim != 1:
raise ValueError('_cplxreal only accepts 1D input')
if tol is None:
# Get tolerance from dtype of input
tol = 100 * np.finfo((1.0 * z).dtype).eps
# Sort by real part, magnitude of imaginary part (speed up further sorting)
z = z[np.lexsort((abs(z.imag), z.real))]
# Split reals from conjugate pairs
real_indices = abs(z.imag) <= tol * abs(z)
zr = z[real_indices].real
if len(zr) == len(z):
# Input is entirely real
return array([]), zr
# Split positive and negative halves of conjugates
z = z[~real_indices]
zp = z[z.imag > 0]
zn = z[z.imag < 0]
if len(zp) != len(zn):
raise ValueError('Array contains complex value with no matching '
'conjugate.')
# Find runs of (approximately) the same real part
same_real = np.diff(zp.real) <= tol * abs(zp[:-1])
diffs = numpy.diff(concatenate(([0], same_real, [0])))
run_starts = numpy.where(diffs > 0)[0]
run_stops = numpy.where(diffs < 0)[0]
# Sort each run by their imaginary parts
for i in range(len(run_starts)):
start = run_starts[i]
stop = run_stops[i] + 1
for chunk in (zp[start:stop], zn[start:stop]):
chunk[...] = chunk[np.lexsort([abs(chunk.imag)])]
# Check that negatives match positives
if any(abs(zp - zn.conj()) > tol * abs(zn)):
raise ValueError('Array contains complex value with no matching '
'conjugate.')
# Average out numerical inaccuracy in real vs imag parts of pairs
zc = (zp + zn.conj()) / 2
return zc, zr
def _cplxpair(z, tol=None):
"""
Sort into pairs of complex conjugates.
Complex conjugates in `z` are sorted by increasing real part. In each
pair, the number with negative imaginary part appears first.
If pairs have identical real parts, they are sorted by increasing
imaginary magnitude.
Two complex numbers are considered a conjugate pair if their real and
imaginary parts differ in magnitude by less than ``tol * abs(z)``. The
pairs are forced to be exact complex conjugates by averaging the positive
and negative values.
Purely real numbers are also sorted, but placed after the complex
conjugate pairs. A number is considered real if its imaginary part is
smaller than `tol` times the magnitude of the number.
Parameters
----------
z : array_like
1-dimensional input array to be sorted.
tol : float, optional
Relative tolerance for testing realness and conjugate equality.
Default is ``100 * spacing(1)`` of `z`'s data type (i.e. 2e-14 for
float64)
Returns
-------
y : ndarray
Complex conjugate pairs followed by real numbers.
Raises
------
ValueError
If there are any complex numbers in `z` for which a conjugate
cannot be found.
See Also
--------
_cplxreal
Examples
--------
>>> a = [4, 3, 1, 2-2j, 2+2j, 2-1j, 2+1j, 2-1j, 2+1j, 1+1j, 1-1j]
>>> z = _cplxpair(a)
>>> print(z)
[ 1.-1.j 1.+1.j 2.-1.j 2.+1.j 2.-1.j 2.+1.j 2.-2.j 2.+2.j 1.+0.j
3.+0.j 4.+0.j]
"""
z = atleast_1d(z)
if z.size == 0 or np.isrealobj(z):
return np.sort(z)
if z.ndim != 1:
raise ValueError('z must be 1-dimensional')
zc, zr = _cplxreal(z, tol)
# Interleave complex values and their conjugates, with negative imaginary
# parts first in each pair
zc = np.dstack((zc.conj(), zc)).flatten()
z = np.append(zc, zr)
return z
def tf2zpk(b, a):
r"""Return zero, pole, gain (z, p, k) representation from a numerator,
denominator representation of a linear filter.
Parameters
----------
b : array_like
Numerator polynomial coefficients.
a : array_like
Denominator polynomial coefficients.
Returns
-------
z : ndarray
Zeros of the transfer function.
p : ndarray
Poles of the transfer function.
k : float
System gain.
Notes
-----
If some values of `b` are too close to 0, they are removed. In that case,
a BadCoefficients warning is emitted.
The `b` and `a` arrays are interpreted as coefficients for positive,
descending powers of the transfer function variable. So the inputs
:math:`b = [b_0, b_1, ..., b_M]` and :math:`a =[a_0, a_1, ..., a_N]`
can represent an analog filter of the form:
.. math::
H(s) = \frac
{b_0 s^M + b_1 s^{(M-1)} + \cdots + b_M}
{a_0 s^N + a_1 s^{(N-1)} + \cdots + a_N}
or a discrete-time filter of the form:
.. math::
H(z) = \frac
{b_0 z^M + b_1 z^{(M-1)} + \cdots + b_M}
{a_0 z^N + a_1 z^{(N-1)} + \cdots + a_N}
This "positive powers" form is found more commonly in controls
engineering. If `M` and `N` are equal (which is true for all filters
generated by the bilinear transform), then this happens to be equivalent
to the "negative powers" discrete-time form preferred in DSP:
.. math::
H(z) = \frac
{b_0 + b_1 z^{-1} + \cdots + b_M z^{-M}}
{a_0 + a_1 z^{-1} + \cdots + a_N z^{-N}}
Although this is true for common filters, remember that this is not true
in the general case. If `M` and `N` are not equal, the discrete-time
transfer function coefficients must first be converted to the "positive
powers" form before finding the poles and zeros.
"""
b, a = normalize(b, a)
b = (b + 0.0) / a[0]
a = (a + 0.0) / a[0]
k = b[0]
b /= b[0]
z = roots(b)
p = roots(a)
return z, p, k
def zpk2tf(z, p, k):
"""
Return polynomial transfer function representation from zeros and poles
Parameters
----------
z : array_like
Zeros of the transfer function.
p : array_like
Poles of the transfer function.
k : float
System gain.
Returns
-------
b : ndarray
Numerator polynomial coefficients.
a : ndarray
Denominator polynomial coefficients.
"""
z = atleast_1d(z)
k = atleast_1d(k)
if len(z.shape) > 1:
temp = poly(z[0])
b = zeros((z.shape[0], z.shape[1] + 1), temp.dtype.char)
if len(k) == 1:
k = [k[0]] * z.shape[0]
for i in range(z.shape[0]):
b[i] = k[i] * poly(z[i])
else:
b = k * poly(z)
a = atleast_1d(poly(p))
# Use real output if possible. Copied from numpy.poly, since
# we can't depend on a specific version of numpy.
if issubclass(b.dtype.type, numpy.complexfloating):
# if complex roots are all complex conjugates, the roots are real.
roots = numpy.asarray(z, complex)
pos_roots = numpy.compress(roots.imag > 0, roots)
neg_roots = numpy.conjugate(numpy.compress(roots.imag < 0, roots))
if len(pos_roots) == len(neg_roots):
if numpy.all(numpy.sort_complex(neg_roots) ==
numpy.sort_complex(pos_roots)):
b = b.real.copy()
if issubclass(a.dtype.type, numpy.complexfloating):
# if complex roots are all complex conjugates, the roots are real.
roots = numpy.asarray(p, complex)
pos_roots = numpy.compress(roots.imag > 0, roots)
neg_roots = numpy.conjugate(numpy.compress(roots.imag < 0, roots))
if len(pos_roots) == len(neg_roots):
if numpy.all(numpy.sort_complex(neg_roots) ==
numpy.sort_complex(pos_roots)):
a = a.real.copy()
return b, a
def tf2sos(b, a, pairing='nearest'):
"""
Return second-order sections from transfer function representation
Parameters
----------
b : array_like
Numerator polynomial coefficients.
a : array_like
Denominator polynomial coefficients.
pairing : {'nearest', 'keep_odd'}, optional
The method to use to combine pairs of poles and zeros into sections.
See `zpk2sos`.
Returns
-------
sos : ndarray
Array of second-order filter coefficients, with shape
``(n_sections, 6)``. See `sosfilt` for the SOS filter format
specification.
See Also
--------
zpk2sos, sosfilt
Notes
-----
It is generally discouraged to convert from TF to SOS format, since doing
so usually will not improve numerical precision errors. Instead, consider
designing filters in ZPK format and converting directly to SOS. TF is
converted to SOS by first converting to ZPK format, then converting
ZPK to SOS.
.. versionadded:: 0.16.0
"""
return zpk2sos(*tf2zpk(b, a), pairing=pairing)
def sos2tf(sos):
"""
Return a single transfer function from a series of second-order sections
Parameters
----------
sos : array_like
Array of second-order filter coefficients, must have shape
``(n_sections, 6)``. See `sosfilt` for the SOS filter format
specification.
Returns
-------
b : ndarray
Numerator polynomial coefficients.
a : ndarray
Denominator polynomial coefficients.
Notes
-----
.. versionadded:: 0.16.0
"""
sos = np.asarray(sos)
b = [1.]
a = [1.]
n_sections = sos.shape[0]
for section in range(n_sections):
b = np.polymul(b, sos[section, :3])
a = np.polymul(a, sos[section, 3:])
return b, a
def sos2zpk(sos):
"""
Return zeros, poles, and gain of a series of second-order sections
Parameters
----------
sos : array_like
Array of second-order filter coefficients, must have shape
``(n_sections, 6)``. See `sosfilt` for the SOS filter format
specification.
Returns
-------
z : ndarray
Zeros of the transfer function.
p : ndarray
Poles of the transfer function.
k : float
System gain.
Notes
-----
.. versionadded:: 0.16.0
"""
sos = np.asarray(sos)
n_sections = sos.shape[0]
z = np.empty(n_sections*2, np.complex128)
p = np.empty(n_sections*2, np.complex128)
k = 1.
for section in range(n_sections):
zpk = tf2zpk(sos[section, :3], sos[section, 3:])
z[2*section:2*(section+1)] = zpk[0]
p[2*section:2*(section+1)] = zpk[1]
k *= zpk[2]
return z, p, k
def _nearest_real_complex_idx(fro, to, which):
"""Get the next closest real or complex element based on distance"""
assert which in ('real', 'complex')
order = np.argsort(np.abs(fro - to))
mask = np.isreal(fro[order])
if which == 'complex':
mask = ~mask
return order[np.where(mask)[0][0]]
def zpk2sos(z, p, k, pairing='nearest'):
"""
Return second-order sections from zeros, poles, and gain of a system
Parameters
----------
z : array_like
Zeros of the transfer function.
p : array_like
Poles of the transfer function.
k : float
System gain.
pairing : {'nearest', 'keep_odd'}, optional
The method to use to combine pairs of poles and zeros into sections.
See Notes below.
Returns
-------
sos : ndarray
Array of second-order filter coefficients, with shape
``(n_sections, 6)``. See `sosfilt` for the SOS filter format
specification.
See Also
--------
sosfilt
Notes
-----
The algorithm used to convert ZPK to SOS format is designed to
minimize errors due to numerical precision issues. The pairing
algorithm attempts to minimize the peak gain of each biquadratic
section. This is done by pairing poles with the nearest zeros, starting
with the poles closest to the unit circle.
*Algorithms*
The current algorithms are designed specifically for use with digital
filters. (The output coefficents are not correct for analog filters.)
The steps in the ``pairing='nearest'`` and ``pairing='keep_odd'``
algorithms are mostly shared. The ``nearest`` algorithm attempts to
minimize the peak gain, while ``'keep_odd'`` minimizes peak gain under
the constraint that odd-order systems should retain one section
as first order. The algorithm steps and are as follows:
As a pre-processing step, add poles or zeros to the origin as
necessary to obtain the same number of poles and zeros for pairing.
If ``pairing == 'nearest'`` and there are an odd number of poles,
add an additional pole and a zero at the origin.
The following steps are then iterated over until no more poles or
zeros remain:
1. Take the (next remaining) pole (complex or real) closest to the
unit circle to begin a new filter section.
2. If the pole is real and there are no other remaining real poles [#]_,
add the closest real zero to the section and leave it as a first
order section. Note that after this step we are guaranteed to be
left with an even number of real poles, complex poles, real zeros,
and complex zeros for subsequent pairing iterations.
3. Else:
1. If the pole is complex and the zero is the only remaining real
zero*, then pair the pole with the *next* closest zero
(guaranteed to be complex). This is necessary to ensure that
there will be a real zero remaining to eventually create a
first-order section (thus keeping the odd order).
2. Else pair the pole with the closest remaining zero (complex or
real).
3. Proceed to complete the second-order section by adding another
pole and zero to the current pole and zero in the section:
1. If the current pole and zero are both complex, add their
conjugates.
2. Else if the pole is complex and the zero is real, add the
conjugate pole and the next closest real zero.
3. Else if the pole is real and the zero is complex, add the
conjugate zero and the real pole closest to those zeros.
4. Else (we must have a real pole and real zero) add the next
real pole closest to the unit circle, and then add the real
zero closest to that pole.
.. [#] This conditional can only be met for specific odd-order inputs
with the ``pairing == 'keep_odd'`` method.
.. versionadded:: 0.16.0
Examples
--------
Design a 6th order low-pass elliptic digital filter for a system with a
sampling rate of 8000 Hz that has a pass-band corner frequency of
1000 Hz. The ripple in the pass-band should not exceed 0.087 dB, and
the attenuation in the stop-band should be at least 90 dB.
In the following call to `signal.ellip`, we could use ``output='sos'``,
but for this example, we'll use ``output='zpk'``, and then convert to SOS
format with `zpk2sos`:
>>> from scipy import signal
>>> z, p, k = signal.ellip(6, 0.087, 90, 1000/(0.5*8000), output='zpk')
Now convert to SOS format.
>>> sos = signal.zpk2sos(z, p, k)
The coefficients of the numerators of the sections:
>>> sos[:, :3]
array([[ 0.0014154 , 0.00248707, 0.0014154 ],
[ 1. , 0.72965193, 1. ],
[ 1. , 0.17594966, 1. ]])
The symmetry in the coefficients occurs because all the zeros are on the
unit circle.
The coefficients of the denominators of the sections:
>>> sos[:, 3:]
array([[ 1. , -1.32543251, 0.46989499],
[ 1. , -1.26117915, 0.6262586 ],
[ 1. , -1.25707217, 0.86199667]])
The next example shows the effect of the `pairing` option. We have a
system with three poles and three zeros, so the SOS array will have
shape (2, 6). The means there is, in effect, an extra pole and an extra
zero at the origin in the SOS representation.
>>> z1 = np.array([-1, -0.5-0.5j, -0.5+0.5j])
>>> p1 = np.array([0.75, 0.8+0.1j, 0.8-0.1j])
With ``pairing='nearest'`` (the default), we obtain
>>> signal.zpk2sos(z1, p1, 1)
array([[ 1. , 1. , 0.5 , 1. , -0.75, 0. ],
[ 1. , 1. , 0. , 1. , -1.6 , 0.65]])
The first section has the zeros {-0.5-0.05j, -0.5+0.5j} and the poles
{0, 0.75}, and the second section has the zeros {-1, 0} and poles
{0.8+0.1j, 0.8-0.1j}. Note that the extra pole and zero at the origin
have been assigned to different sections.
With ``pairing='keep_odd'``, we obtain:
>>> signal.zpk2sos(z1, p1, 1, pairing='keep_odd')
array([[ 1. , 1. , 0. , 1. , -0.75, 0. ],
[ 1. , 1. , 0.5 , 1. , -1.6 , 0.65]])
The extra pole and zero at the origin are in the same section.
The first section is, in effect, a first-order section.
"""
# TODO in the near future:
# 1. Add SOS capability to `filtfilt`, `freqz`, etc. somehow (#3259).
# 2. Make `decimate` use `sosfilt` instead of `lfilter`.
# 3. Make sosfilt automatically simplify sections to first order
# when possible. Note this might make `sosfiltfilt` a bit harder (ICs).
# 4. Further optimizations of the section ordering / pole-zero pairing.
# See the wiki for other potential issues.
valid_pairings = ['nearest', 'keep_odd']
if pairing not in valid_pairings:
raise ValueError('pairing must be one of %s, not %s'
% (valid_pairings, pairing))
if len(z) == len(p) == 0:
return array([[k, 0., 0., 1., 0., 0.]])
# ensure we have the same number of poles and zeros, and make copies
p = np.concatenate((p, np.zeros(max(len(z) - len(p), 0))))
z = np.concatenate((z, np.zeros(max(len(p) - len(z), 0))))
n_sections = (max(len(p), len(z)) + 1) // 2
sos = zeros((n_sections, 6))
if len(p) % 2 == 1 and pairing == 'nearest':
p = np.concatenate((p, [0.]))
z = np.concatenate((z, [0.]))
assert len(p) == len(z)
# Ensure we have complex conjugate pairs
# (note that _cplxreal only gives us one element of each complex pair):
z = np.concatenate(_cplxreal(z))
p = np.concatenate(_cplxreal(p))
p_sos = np.zeros((n_sections, 2), np.complex128)
z_sos = np.zeros_like(p_sos)
for si in range(n_sections):
# Select the next "worst" pole
p1_idx = np.argmin(np.abs(1 - np.abs(p)))
p1 = p[p1_idx]
p = np.delete(p, p1_idx)
# Pair that pole with a zero
if np.isreal(p1) and np.isreal(p).sum() == 0:
# Special case to set a first-order section
z1_idx = _nearest_real_complex_idx(z, p1, 'real')
z1 = z[z1_idx]
z = np.delete(z, z1_idx)
p2 = z2 = 0
else:
if not np.isreal(p1) and np.isreal(z).sum() == 1:
# Special case to ensure we choose a complex zero to pair
# with so later (setting up a first-order section)
z1_idx = _nearest_real_complex_idx(z, p1, 'complex')
assert not np.isreal(z[z1_idx])
else:
# Pair the pole with the closest zero (real or complex)
z1_idx = np.argmin(np.abs(p1 - z))
z1 = z[z1_idx]
z = np.delete(z, z1_idx)
# Now that we have p1 and z1, figure out what p2 and z2 need to be
if not np.isreal(p1):
if not np.isreal(z1): # complex pole, complex zero
p2 = p1.conj()
z2 = z1.conj()
else: # complex pole, real zero
p2 = p1.conj()
z2_idx = _nearest_real_complex_idx(z, p1, 'real')
z2 = z[z2_idx]
assert np.isreal(z2)
z = np.delete(z, z2_idx)
else:
if not np.isreal(z1): # real pole, complex zero
z2 = z1.conj()
p2_idx = _nearest_real_complex_idx(p, z1, 'real')
p2 = p[p2_idx]
assert np.isreal(p2)
else: # real pole, real zero
# pick the next "worst" pole to use
idx = np.where(np.isreal(p))[0]
assert len(idx) > 0
p2_idx = idx[np.argmin(np.abs(np.abs(p[idx]) - 1))]
p2 = p[p2_idx]
# find a real zero to match the added pole
assert np.isreal(p2)
z2_idx = _nearest_real_complex_idx(z, p2, 'real')
z2 = z[z2_idx]
assert np.isreal(z2)
z = np.delete(z, z2_idx)
p = np.delete(p, p2_idx)
p_sos[si] = [p1, p2]
z_sos[si] = [z1, z2]
assert len(p) == len(z) == 0 # we've consumed all poles and zeros
del p, z
# Construct the system, reversing order so the "worst" are last
p_sos = np.reshape(p_sos[::-1], (n_sections, 2))
z_sos = np.reshape(z_sos[::-1], (n_sections, 2))
gains = np.ones(n_sections)
gains[0] = k
for si in range(n_sections):
x = zpk2tf(z_sos[si], p_sos[si], gains[si])
sos[si] = np.concatenate(x)
return sos
def _align_nums(nums):
"""
Given an array of numerator coefficient arrays [[a_1, a_2,...,
a_n],..., [b_1, b_2,..., b_m]], this function pads shorter numerator
arrays with zero's so that all numerators have the same length. Such
alignment is necessary for functions like 'tf2ss', which needs the
alignment when dealing with SIMO transfer functions.
"""
try:
# The statement can throw a ValueError if one
# of the numerators is a single digit and another
# is array-like e.g. if nums = [5, [1, 2, 3]]
nums = asarray(nums)
if not np.issubdtype(nums.dtype, np.number):
raise ValueError("dtype of numerator is non-numeric")
return nums
except ValueError:
nums = list(nums)
maxwidth = len(max(nums, key=lambda num: atleast_1d(num).size))
for index, num in enumerate(nums):
num = atleast_1d(num).tolist()
nums[index] = [0] * (maxwidth - len(num)) + num
return atleast_1d(nums)
def normalize(b, a):
"""Normalize polynomial representation of a transfer function.
If values of `b` are too close to 0, they are removed. In that case, a
BadCoefficients warning is emitted.
"""
b = _align_nums(b)
b, a = map(atleast_1d, (b, a))
if len(a.shape) != 1:
raise ValueError("Denominator polynomial must be rank-1 array.")
if len(b.shape) > 2:
raise ValueError("Numerator polynomial must be rank-1 or"
" rank-2 array.")
if len(b.shape) == 1:
b = asarray([b], b.dtype.char)
while a[0] == 0.0 and len(a) > 1:
a = a[1:]
outb = b * (1.0) / a[0]
outa = a * (1.0) / a[0]
if allclose(0, outb[:, 0], atol=1e-14):
warnings.warn("Badly conditioned filter coefficients (numerator): the "
"results may be meaningless", BadCoefficients)
while allclose(0, outb[:, 0], atol=1e-14) and (outb.shape[-1] > 1):
outb = outb[:, 1:]
if outb.shape[0] == 1:
outb = outb[0]
return outb, outa
def lp2lp(b, a, wo=1.0):
"""
Transform a lowpass filter prototype to a different frequency.
Return an analog low-pass filter with cutoff frequency `wo`
from an analog low-pass filter prototype with unity cutoff frequency, in
transfer function ('ba') representation.
"""
a, b = map(atleast_1d, (a, b))
try:
wo = float(wo)
except TypeError:
wo = float(wo[0])
d = len(a)
n = len(b)
M = max((d, n))
pwo = pow(wo, numpy.arange(M - 1, -1, -1))
start1 = max((n - d, 0))
start2 = max((d - n, 0))
b = b * pwo[start1] / pwo[start2:]
a = a * pwo[start1] / pwo[start1:]
return normalize(b, a)
def lp2hp(b, a, wo=1.0):
"""
Transform a lowpass filter prototype to a highpass filter.
Return an analog high-pass filter with cutoff frequency `wo`
from an analog low-pass filter prototype with unity cutoff frequency, in
transfer function ('ba') representation.
"""
a, b = map(atleast_1d, (a, b))
try:
wo = float(wo)
except TypeError:
wo = float(wo[0])
d = len(a)
n = len(b)
if wo != 1:
pwo = pow(wo, numpy.arange(max((d, n))))
else:
pwo = numpy.ones(max((d, n)), b.dtype.char)
if d >= n:
outa = a[::-1] * pwo
outb = resize(b, (d,))
outb[n:] = 0.0
outb[:n] = b[::-1] * pwo[:n]
else:
outb = b[::-1] * pwo
outa = resize(a, (n,))
outa[d:] = 0.0
outa[:d] = a[::-1] * pwo[:d]
return normalize(outb, outa)
def lp2bp(b, a, wo=1.0, bw=1.0):
"""
Transform a lowpass filter prototype to a bandpass filter.
Return an analog band-pass filter with center frequency `wo` and
bandwidth `bw` from an analog low-pass filter prototype with unity
cutoff frequency, in transfer function ('ba') representation.
"""
a, b = map(atleast_1d, (a, b))
D = len(a) - 1
N = len(b) - 1
artype = mintypecode((a, b))
ma = max([N, D])
Np = N + ma
Dp = D + ma
bprime = numpy.zeros(Np + 1, artype)
aprime = numpy.zeros(Dp + 1, artype)
wosq = wo * wo
for j in range(Np + 1):
val = 0.0
for i in range(0, N + 1):
for k in range(0, i + 1):
if ma - i + 2 * k == j:
val += comb(i, k) * b[N - i] * (wosq) ** (i - k) / bw ** i
bprime[Np - j] = val
for j in range(Dp + 1):
val = 0.0
for i in range(0, D + 1):
for k in range(0, i + 1):
if ma - i + 2 * k == j:
val += comb(i, k) * a[D - i] * (wosq) ** (i - k) / bw ** i
aprime[Dp - j] = val
return normalize(bprime, aprime)
def lp2bs(b, a, wo=1.0, bw=1.0):
"""
Transform a lowpass filter prototype to a bandstop filter.
Return an analog band-stop filter with center frequency `wo` and
bandwidth `bw` from an analog low-pass filter prototype with unity
cutoff frequency, in transfer function ('ba') representation.
"""
a, b = map(atleast_1d, (a, b))
D = len(a) - 1
N = len(b) - 1
artype = mintypecode((a, b))
M = max([N, D])
Np = M + M
Dp = M + M
bprime = numpy.zeros(Np + 1, artype)
aprime = numpy.zeros(Dp + 1, artype)
wosq = wo * wo
for j in range(Np + 1):
val = 0.0
for i in range(0, N + 1):
for k in range(0, M - i + 1):
if i + 2 * k == j:
val += (comb(M - i, k) * b[N - i] *
(wosq) ** (M - i - k) * bw ** i)
bprime[Np - j] = val
for j in range(Dp + 1):
val = 0.0
for i in range(0, D + 1):
for k in range(0, M - i + 1):
if i + 2 * k == j:
val += (comb(M - i, k) * a[D - i] *
(wosq) ** (M - i - k) * bw ** i)
aprime[Dp - j] = val
return normalize(bprime, aprime)
def bilinear(b, a, fs=1.0):
"""Return a digital filter from an analog one using a bilinear transform.
The bilinear transform substitutes ``(z-1) / (z+1)`` for ``s``.
"""
fs = float(fs)
a, b = map(atleast_1d, (a, b))
D = len(a) - 1
N = len(b) - 1
artype = float
M = max([N, D])
Np = M
Dp = M
bprime = numpy.zeros(Np + 1, artype)
aprime = numpy.zeros(Dp + 1, artype)
for j in range(Np + 1):
val = 0.0
for i in range(N + 1):
for k in range(i + 1):
for l in range(M - i + 1):
if k + l == j:
val += (comb(i, k) * comb(M - i, l) * b[N - i] *
pow(2 * fs, i) * (-1) ** k)
bprime[j] = real(val)
for j in range(Dp + 1):
val = 0.0
for i in range(D + 1):
for k in range(i + 1):
for l in range(M - i + 1):
if k + l == j:
val += (comb(i, k) * comb(M - i, l) * a[D - i] *
pow(2 * fs, i) * (-1) ** k)
aprime[j] = real(val)
return normalize(bprime, aprime)
def iirdesign(wp, ws, gpass, gstop, analog=False, ftype='ellip', output='ba'):
"""Complete IIR digital and analog filter design.
Given passband and stopband frequencies and gains, construct an analog or
digital IIR filter of minimum order for a given basic type. Return the
output in numerator, denominator ('ba'), pole-zero ('zpk') or second order
sections ('sos') form.
Parameters
----------
wp, ws : float
Passband and stopband edge frequencies.
For digital filters, these are normalized from 0 to 1, where 1 is the
Nyquist frequency, pi radians/sample. (`wp` and `ws` are thus in
half-cycles / sample.) For example:
- Lowpass: wp = 0.2, ws = 0.3
- Highpass: wp = 0.3, ws = 0.2
- Bandpass: wp = [0.2, 0.5], ws = [0.1, 0.6]
- Bandstop: wp = [0.1, 0.6], ws = [0.2, 0.5]
For analog filters, `wp` and `ws` are angular frequencies (e.g. rad/s).
gpass : float
The maximum loss in the passband (dB).
gstop : float
The minimum attenuation in the stopband (dB).
analog : bool, optional
When True, return an analog filter, otherwise a digital filter is
returned.
ftype : str, optional
The type of IIR filter to design:
- Butterworth : 'butter'
- Chebyshev I : 'cheby1'
- Chebyshev II : 'cheby2'
- Cauer/elliptic: 'ellip'
- Bessel/Thomson: 'bessel'
output : {'ba', 'zpk', 'sos'}, optional
Type of output: numerator/denominator ('ba'), pole-zero ('zpk'), or
second-order sections ('sos'). Default is 'ba'.
Returns
-------
b, a : ndarray, ndarray
Numerator (`b`) and denominator (`a`) polynomials of the IIR filter.
Only returned if ``output='ba'``.
z, p, k : ndarray, ndarray, float
Zeros, poles, and system gain of the IIR filter transfer
function. Only returned if ``output='zpk'``.
sos : ndarray
Second-order sections representation of the IIR filter.
Only returned if ``output=='sos'``.
See Also
--------
butter : Filter design using order and critical points
cheby1, cheby2, ellip, bessel
buttord : Find order and critical points from passband and stopband spec
cheb1ord, cheb2ord, ellipord
iirfilter : General filter design using order and critical frequencies
Notes
-----
The ``'sos'`` output parameter was added in 0.16.0.
"""
try:
ordfunc = filter_dict[ftype][1]
except KeyError:
raise ValueError("Invalid IIR filter type: %s" % ftype)
except IndexError:
raise ValueError(("%s does not have order selection. Use "
"iirfilter function.") % ftype)
wp = atleast_1d(wp)
ws = | atleast_1d(ws) | numpy.atleast_1d |
"""
Copyright (c) 2010-2018 CNRS / Centre de Recherche Astrophysique de Lyon
Copyright (c) 2015-2019 <NAME> <<EMAIL>>
Copyright (c) 2015-2016 <NAME> <<EMAIL>>
Copyright (c) 2016 <NAME> <<EMAIL>>
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors
may be used to endorse or promote products derived from this software
without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
"""
import logging
import numpy as np
import warnings
from astropy import units as u
from astropy.io import fits
from datetime import datetime
from numpy import ma
from .coords import WCS, WaveCoord, determine_refframe
from .objs import UnitMaskedArray, UnitArray, is_int
from ..tools import (MpdafUnitsWarning, fix_unit_read, is_valid_fits_file,
copy_header, read_slice_from_fits)
__all__ = ('DataArray', )
class LazyData:
def __init__(self, label):
self.label = label
def read_data(self, obj):
obj_dict = obj.__dict__
data, mask = read_slice_from_fits(
obj.filename, ext=obj._data_ext, mask_ext=obj._dq_ext,
dtype=obj.dtype, convert_float64=obj._convert_float64)
if mask is None:
mask = ~(np.isfinite(data))
obj_dict['_data'] = data
obj_dict['_mask'] = mask
obj._loaded_data = True
return mask if self.label == '_mask' else data
def __get__(self, obj, owner=None):
try:
return obj.__dict__[self.label]
except KeyError:
if obj.filename is None:
return
if self.label in ('_data', '_mask'):
val = self.read_data(obj)
if self.label == '_var':
if obj._var_ext is None:
return None
# Make sure that data is read because the mask may be needed
if not obj._loaded_data:
self.read_data(obj)
val, _ = read_slice_from_fits(
obj.filename, ext=obj._var_ext, dtype=obj._var_dtype,
convert_float64=obj._convert_float64)
obj.__dict__[self.label] = val
return val
def __set__(self, obj, val):
label = self.label
if label == '_data':
obj._loaded_data = True
elif (val is not None and val is not np.ma.nomask and
obj.shape is not None and
not np.array_equal(val.shape, obj.shape)):
raise ValueError("Can't set %s with a different shape" % label)
obj.__dict__[label] = val
class DataArray:
"""Parent class for `~mpdaf.obj.Cube`, `~mpdaf.obj.Image` and
`~mpdaf.obj.Spectrum`.
Its primary purpose is to store pixel values and, optionally, also
variances in masked Numpy arrays. For Cube objects these are 3D arrays
indexed in the order ``[wavelength, image_y, image_x]``. For Image objects
they are 2D arrays indexed in the order ``[image_y, image_x]``. For
Spectrum objects they are 1D arrays.
Image arrays hold flat 2D map-projections of the sky. The X and Y axes of
the image arrays are orthogonal on the sky at the tangent point of the
projection. When the rotation angle of the projection on the sky is zero,
the Y axis of the image arrays is along the declination axis, and the
X axis is perpendicular to this, with the positive X axis pointing east.
Given a DataArray object ``obj``, the data and variance arrays are
accessible via the properties ``obj.data`` and ``obj.var``. These two
masked arrays share a single array of boolean masking elements, which is
also accessible as a simple boolean array via the ``obj.mask property``.
The shared mask can be modified through any of the three properties::
obj.data[20:22] = numpy.ma.masked
Is equivalent to::
obj.var[20:22] = numpy.ma.masked
And is also equivalent to::
obj.mask[20:22] = True
All three of the above statements mask pixels 20 and 21 of the data and
variance arrays, without changing their values.
Similarly, if one performs an operation on either ``obj.data`` or
``obj.var`` that modifies the mask, this is reflected in the shared mask of
all three properties. For example, the following statement multiplies
elements 20 and 21 of the data by 2.0, while changing the shared mask of
these pixels to True. In this way the data and the variances of these
pixels are consistently masked::
obj.data[20:22] *= numpy.ma.array([2.0,2.0], mask=[True,True])
The data and variance arrays can be completely replaced by assigning new
arrays to the ``obj.data`` and ``obj.var`` properties, but these must have
the same shape as before (ie. obj.shape). New arrays that are assigned to
``obj.data`` or ``obj.var`` can be simple numpy arrays, or a numpy masked
arrays.
When a normal numpy array is assigned to ``obj.data``, the ``obj.mask``
array is also assigned a mask array, whose elements are True wherever NaN
or Inf values are found in the data array. An exception to this rule is if
the mask has previously been disabled by assigning ``numpy.ma.nomask`` to
``obj.mask``. In this case a mask array is not constructed.
When a numpy masked array is assigned to ``obj.data``, then its mask is
also assigned, unchanged, to ``obj.mask``.
Assigning a normal numpy array to the ``obj.var`` attribute, has no effect
on the contents of ``obj.mask``. On the other hand, when a numpy masked
array is assigned to ``obj.var`` the ``obj.mask`` array becomes the union
of its current value and the mask of the provided array.
The ability to record variances for each element is optional. When no
variances are stored, ``obj.var`` has the value None. To discard an
unwanted variance array, None can be subsequently assigned to ``obj.var``.
For cubes and spectra, the wavelengths of the spectral pixels are specified
in the ``.wave`` member. For cubes and images, the world-coordinates of the
image pixels are specified in the ``.wcs`` member.
When a DataArray object is constructed from a FITS file, the name of the
file and the file's primary header are recorded. If the data are read from
a FITS extension, the header of this extension is also recorded.
Alternatively, the primary header and data header can be passed to the
DataArray constructor. Where FITS headers are neither provided, nor
available in a provided FITS file, generic headers are substituted.
Methods are provided for masking and unmasking pixels, and performing basic
arithmetic operations on pixels. Operations that are specific to cubes or
spectra or images are provided elsewhere by derived classes.
Parameters
----------
filename : str
FITS file name, default to None.
hdulist : `astropy.fits.HDUList`
HDUList object, can be used instead of ``filename`` to avoid opening
the FITS file multiple times.
data : array_like
Data array, passed to `numpy.ma.MaskedArray`.
mask : bool or numpy.ma.nomask or numpy.ndarray
Mask used for the creation of the ``.data`` MaskedArray. If mask is
False (default value), a mask array of the same size of the data array
is created. To avoid creating an array, it is possible to use
numpy.ma.nomask, but in this case several methods will break if
they use the mask.
var : array_like
Variance array, passed to `numpy.ma.MaskedArray`.
ext : int or tuple of int or str or tuple of str
Number/name of the data extension, or numbers/names of the data,
variance, and optionally mask extensions.
unit : `astropy.units.Unit`
Physical units of the data values, default to u.dimensionless_unscaled.
copy : bool
If True (default), then the data and variance arrays are copied.
Passed to `numpy.ma.MaskedArray`.
dtype : numpy.dtype
Type of the data. Passed to `numpy.ma.MaskedArray`.
primary_header : `astropy.io.fits.Header`
FITS primary header instance.
data_header : `astropy.io.fits.Header`
FITS data header instance.
fits_kwargs : dict
Additional arguments that can be passed to `astropy.io.fits.open`.
convert_float64 : bool
By default input arrays or FITS data are converted to float64, in
order to increase precision to the detriment of memory usage.
Attributes
----------
filename : str
FITS filename.
primary_header : `astropy.io.fits.Header`
FITS primary header instance.
data_header : `astropy.io.fits.Header`
FITS data header instance.
wcs : `mpdaf.obj.WCS`
World coordinates.
wave : `mpdaf.obj.WaveCoord`
Wavelength coordinates
ndim : int
Number of dimensions.
shape : sequence
Lengths of the data axes (python notation (nz,ny,nx)).
data : numpy.ma.MaskedArray
Masked array containing the cube of pixel values.
var : numpy.ma.MaskedArray
Masked array containing the variance.
mask : numpy.ndarray
Array containing the mask.
unit : `astropy.units.Unit`
Physical units of the data values.
dtype : numpy.dtype
Type of the data (int, float, ...).
"""
_ndim_required = None
_has_wcs = False
_has_wave = False
_data = LazyData('_data')
_mask = LazyData('_mask')
_var = LazyData('_var')
def __init__(self, filename=None, hdulist=None, data=None, mask=False,
var=None, ext=None, unit=u.dimensionless_unscaled, copy=True,
dtype=None, primary_header=None, data_header=None,
convert_float64=True, **kwargs):
self._logger = logging.getLogger(__name__)
self._loaded_data = False
self._data_ext = None
self._var_ext = None
self._dq_ext = None
self._convert_float64 = convert_float64
self.filename = filename
self.wcs = None
self.wave = None
self._dtype = dtype
self._var_dtype = np.float64 if convert_float64 else None
self.unit = u.Unit(unit)
self.data_header = data_header or fits.Header()
self.primary_header = primary_header or fits.Header()
if (filename is not None or hdulist is not None) and data is None:
# Read the data from a FITS file
if not hdulist and not is_valid_fits_file(filename):
raise IOError('Invalid file: %s' % filename)
if hdulist is None:
fits_kwargs = kwargs.pop('fits_kwargs', {})
hdulist = fits.open(filename, **fits_kwargs)
close_hdu = True
else:
if filename is None:
self.filename = hdulist.filename()
close_hdu = False
# Find the hdu of the data. This is either the primary HDU (if the
# number of extension is 1) or a DATA or SCI extension. Also see if
# there is an extension that contains variances. This is either
# a STAT extension, or the second of a tuple of extensions passed
# via the ext[] parameter.
if len(hdulist) == 1:
self._data_ext = 0
elif ext is None:
if 'DATA' in hdulist:
self._data_ext = 'DATA'
elif 'SCI' in hdulist:
self._data_ext = 'SCI'
else:
raise IOError('No DATA or SCI extension found.\n'
'Please use the `ext` parameter to specify '
'which extension must be loaded.')
if 'STAT' in hdulist:
self._var_ext = 'STAT'
if 'DQ' in hdulist:
self._dq_ext = 'DQ'
elif isinstance(ext, (list, tuple, np.ndarray)):
if len(ext) == 2:
self._data_ext, self._var_ext = ext
elif len(ext) == 3:
self._data_ext, self._var_ext, self._dq_ext = ext
elif isinstance(ext, (int, str)):
self._data_ext = ext
self.primary_header = hdulist[0].header
self.data_header = hdr = hdulist[self._data_ext].header
if (self._ndim_required is not None and
self._ndim_required != self.data_header['NAXIS']):
raise ValueError('{} class cannot manage data with {} axes'
.format(self.__class__.__name__,
self.data_header['NAXIS']))
try:
self.unit = u.Unit(fix_unit_read(hdr['BUNIT']))
except KeyError:
warnings.warn('No physical unit in the FITS header: missing '
'BUNIT keyword.', MpdafUnitsWarning)
except Exception as e:
warnings.warn('Error parsing the BUNIT: ' + str(e),
MpdafUnitsWarning)
if 'FSCALE' in hdr:
self.unit *= u.Unit(hdr['FSCALE'])
self._compute_wcs_from_header()
if close_hdu:
hdulist.close()
else:
if mask is ma.nomask:
self._mask = mask
# Use a specified numpy data array?
if data is not None:
# Force data to be in double instead of float
if (self._dtype is None and data.dtype.type == np.float32 and
convert_float64):
self._dtype = np.float64
if isinstance(data, ma.MaskedArray):
self._data = np.array(data.data, dtype=self.dtype,
copy=copy)
if data.mask is ma.nomask:
self._mask = data.mask
else:
self._mask = np.array(data.mask, dtype=bool, copy=copy)
else:
self._data = np.array(data, dtype=self.dtype, copy=copy)
if mask is None or mask is False:
self._mask = ~(np.isfinite(data))
elif mask is True:
self._mask = np.ones(shape=data.shape, dtype=bool)
elif mask is not ma.nomask:
self._mask = np.array(mask, dtype=bool, copy=copy)
# Use a specified variance array?
if var is not None:
if isinstance(var, ma.MaskedArray):
self._var = np.array(var.data, dtype=self._var_dtype,
copy=copy)
self._mask |= var.mask
else:
self._var = np.array(var, dtype=self._var_dtype, copy=copy)
# Where WCS and/or wavelength objects are specified as optional
# parameters, install them.
self.set_wcs(wcs=kwargs.pop('wcs', None),
wave=kwargs.pop('wave', None))
def __getstate__(self):
state = self.__dict__.copy()
# remove un-pickable objects
state['_logger'] = None
state['wcs'] = None
state['wave'] = None
if '_spflims' in state and state['_spflims'] is not None:
state['_spflims'] = None
# Image.plot stores the matplotlib axes on the object, but it is not
# pickable. Delete it!
if '_ax' in state:
del state['_ax']
# Try to determine if the object has some wcs/wave information but not
# available in the FITS header. In this case we add the wcs info in the
# data header.
if ((self._has_wcs and self.wcs is not None) or
(self._has_wave and self.wave is not None)):
hdu = self.get_data_hdu(convert_float32=False)
state['data_header'] = hdu.header
return state
def __setstate__(self, state):
# set attributes on the object, making sure that _data, _mask and _var
# are set last as these are descriptors and need the other attributes.
# Also these attributes may bot exists yet if the data is not loaded.
for slot, value in state.items():
if slot not in ('_data', '_mask', '_var'):
setattr(self, slot, value)
for slot in ('_data', '_mask', '_var'):
if slot in state:
setattr(self, slot, state[slot])
self._logger = logging.getLogger(__name__)
# Recreate the wcs/wave objects from the fits headers
self._compute_wcs_from_header()
# and to get the naxis1/naxis2 right
self.set_wcs(wcs=self.wcs, wave=self.wave)
def _compute_wcs_from_header(self):
frame, equinox = determine_refframe(self.primary_header)
hdr = self.data_header
# Is this a derived class like Cube/Image that require WCS information?
if self._has_wcs:
try:
self.wcs = WCS(hdr, frame=frame, equinox=equinox)
except fits.VerifyError as e:
# Workaround for
# https://github.com/astropy/astropy/issues/887
self._logger.warning(e)
if 'IRAF-B/P' in hdr:
hdr.remove('IRAF-B/P')
self.wcs = WCS(hdr, frame=frame, equinox=equinox)
# Get the wavelength coordinates.
wave_ext = 1 if self._ndim_required == 1 else 3
crpix = 'CRPIX{}'.format(wave_ext)
crval = 'CRVAL{}'.format(wave_ext)
if self._has_wave and crpix in hdr and crval in hdr:
self.wave = WaveCoord(hdr)
@classmethod
def new_from_obj(cls, obj, data=None, var=None, copy=False, unit=None):
"""Create a new object from another one, copying its attributes.
Parameters
----------
obj : `mpdaf.obj.DataArray`
The object to use as the template for the new object. This
should be an object based on DataArray, such as an Image,
Cube or Spectrum.
data : array-like, optional
An optional data array, or None to indicate that
``obj.data`` should be used. The default is None.
var : array-like, optional
An optional variance array, or None to indicate that
``obj.var`` should be used, or False to indicate that the
new object should not have any variances. The default
is None.
copy : bool
Copy the data and variance arrays if True (default False).
"""
data = obj.data if data is None else data
if var is None:
var = obj._var
elif var is False:
var = None
if unit is None:
unit = obj.unit
kwargs = dict(filename=obj.filename, data=data, unit=unit, var=var,
ext=(obj._data_ext, obj._var_ext, obj._dq_ext),
copy=copy, data_header=obj.data_header.copy(),
primary_header=obj.primary_header.copy())
if cls._has_wcs:
kwargs['wcs'] = obj.wcs
if cls._has_wave:
kwargs['wave'] = obj.wave
return cls(**kwargs)
@property
def ndim(self):
""" The number of dimensions in the data and variance arrays : int """
if self._loaded_data:
return self._data.ndim
try:
return self.data_header['NAXIS']
except KeyError:
return None
@property
def shape(self):
"""The lengths of each of the data axes."""
if self._loaded_data:
return self._data.shape
try:
return tuple(self.data_header['NAXIS%d' % i]
for i in range(self.ndim, 0, -1))
except (KeyError, TypeError):
return None
@property
def dtype(self):
"""The type of the data."""
if self._loaded_data:
return self._data.dtype
else:
return self._dtype
@property
def data(self):
"""Return data as a `numpy.ma.MaskedArray`.
The DataArray constructor postpones reading data from FITS files until
they are first used. Read the data array here if not already read.
Changes can be made to individual elements of the data property. When
simple numeric values or Numpy array elements are assigned to elements
of the data property, the values of these elements are updated and
become unmasked.
When masked Numpy values or masked-array elements are assigned to
elements of the data property, then these change both the values of the
data property and the shared mask of the data and var properties.
Completely new arrays can also be assigned to the data property,
provided that they have the same shape as before.
"""
res = ma.MaskedArray(self._data, mask=self._mask, copy=False)
res._sharedmask = False
return res
@data.setter
def data(self, value):
# Handle this case specifically for .data, since it is already done for
# ._var and ._mask, but ._data can be used to change the shape
if self.shape is not None and \
not np.array_equal(value.shape, self.shape):
raise ValueError('try to set data with an array with a different '
'shape')
if isinstance(value, ma.MaskedArray):
self._data = value.data
self._mask = value.mask
else:
self._data = value
self._mask = ~(np.isfinite(value))
@property
def var(self):
"""Return variance as a `numpy.ma.MaskedArray`.
If variances have been provided for each data pixel, then this property
can be used to record those variances. Normally this is a masked array
which shares the mask of the data property. However if no variances
have been provided, then this property is None.
Variances are typically provided along with the data values in the
originating FITS file. Alternatively a variance array can be assigned
to this property after the data have been read.
Note that any function that modifies the contents of the data array may
need to update the array of variances accordingly. For example, after
scaling pixel values by a constant factor c, the variances should be
scaled by c**2.
When masked-array values are assigned to elements of the var property,
the mask of the new values is assigned to the shared mask of the data
and variance properties.
Completely new arrays can also be assigned to the var property. When
a masked array is assigned to the var property, its mask is combined
with the existing shared mask, rather than replacing it.
"""
if self._var is None:
return None
else:
res = ma.MaskedArray(self._var, mask=self._mask, copy=False)
res._sharedmask = False
return res
@var.setter
def var(self, value):
if value is not None:
if isinstance(value, ma.MaskedArray):
self._var = value.data
self._mask |= value.mask
else:
self._var = np.asarray(value)
else:
self._var_ext = None
self._var = value
@property
def mask(self):
"""The shared masking array of the data and variance arrays.
This is a bool array which has the same shape as the data and variance
arrays. Setting an element of this array to True, flags the
corresponding pixels of the data and variance arrays, so that they
don't take part in subsequent calculations. Reverting this element to
False, unmasks the pixel again.
This array can be modified either directly by assignments to elements
of this property or by modifying the masks of the .data and .var
arrays. An entirely new mask array can also be assigned to this
property, provided that it has the same shape as the data array.
"""
return self._mask
@mask.setter
def mask(self, value):
# By default, if mask=False create a mask array with False values.
# numpy.ma does it but with a np.resize/np.concatenate which cause a
# huge memory peak, so a workaround is to create the mask here.
# Also we force the creation of a mask array because currently many
# method in MPDAF expect that the mask is an array and will not work
# with np.ma.nomask. But nomask can still be used explicitly for
# specific cases.
if value is ma.nomask:
self._mask = value
else:
self._mask = np.asarray(value, dtype=bool)
def copy(self):
"""Return a copy of the object."""
return self.__class__.new_from_obj(self, copy=True)
def clone(self, data_init=None, var_init=None):
"""Return a shallow copy with the same header and coordinates.
Optionally fill the cloned array using values returned by provided
functions.
Parameters
----------
data_init : callable, optional
An optional function to use to create the data array
(it takes the shape as parameter). For example ``np.zeros``
or ``np.empty`` can be used. It defaults to None, which results
in the data attribute being None.
var_init : callable, optional
An optional function to use to create the variance array,
with the same specifics as data_init. This default to None,
which results in the var attribute being assigned None.
"""
# Create a new data_header with correct NAXIS keywords because an
# object without data relies on this to get the shape
hdr = copy_header(self.data_header, self.get_wcs_header(),
exclude=('CD*', 'PC*', 'CDELT*', 'CRPIX*', 'CRVAL*',
'CSYER*', 'CTYPE*', 'CUNIT*', 'NAXIS*',
'RADESYS', 'LATPOLE', 'LONPOLE'),
unit=self.unit)
hdr['NAXIS'] = self.ndim
for i in range(1, self.ndim + 1):
hdr['NAXIS%d' % i] = self.shape[-i]
return self.__class__(
unit=self.unit, dtype=None, copy=False,
data=None if data_init is None else data_init(self.shape,
dtype=self.dtype),
var=None if var_init is None else var_init(self.shape,
dtype=self.dtype),
wcs=None if self.wcs is None else self.wcs,
wave=None if self.wave is None else self.wave,
data_header=hdr,
primary_header=self.primary_header.copy()
)
def __repr__(self):
fmt = """<{}(shape={}, unit='{}', dtype='{}')>"""
return fmt.format(self.__class__.__name__, self.shape,
self.unit.to_string(), self.dtype)
def info(self):
"""Print information."""
log = self._logger.info
shape_str = (' x '.join(str(x) for x in self.shape)
if self.shape is not None else 'no shape')
log('%s %s (%s)', shape_str, self.__class__.__name__,
self.filename or 'no name')
data = ('no data' if self._data is None and self._data_ext is None
else '.data({})'.format(shape_str))
noise = ('no noise' if self._var is None and self._var_ext is None
else '.var({})'.format(shape_str))
unit = str(self.unit) or 'no unit'
log('%s (%s), %s', data, unit, noise)
if self._has_wcs:
if self.wcs is None:
log('no world coordinates for spatial direction')
else:
self.wcs.info()
if self._has_wave:
if self.wave is None:
log('no world coordinates for spectral direction')
else:
self.wave.info()
def __le__(self, item):
"""Mask data elements whose values are greater than a
given value (<=).
Parameters
----------
item : float
minimum value.
Returns
-------
`~mpdaf.obj.DataArray`
"""
result = self.copy()
result.data = np.ma.masked_greater(self.data, item)
return result
def __lt__(self, item):
"""Mask data elements whose values are greater than or equal
to a given value (<).
Parameters
----------
item : float
minimum value.
Returns
-------
`~mpdaf.obj.DataArray`
"""
result = self.copy()
result.data = | np.ma.masked_greater_equal(self.data, item) | numpy.ma.masked_greater_equal |
"""
The :mod:`ezaero.vlm.steady` module includes a Vortex Lattice Method
implementation for lifting surfaces.
References
----------
.. [1] <NAME>., *Low-Speed Aerodynamics*, 2nd ed, Cambridge University
Press, 2001: Chapter 12
"""
import numpy as np
class WingParams:
"""
Container for the geometric parameters of the analyzed wing.
Attributes
----------
cr : float
Chord at root of the wing.
ct : float
Chord at tip of the wing.
bp : float
Wingspan of the planform.
theta : float
Sweep angle of the 1/4 chord line, expressed in radians.
delta : float
Dihedral angle, expressed in radians.
"""
def __init__(self, cr, ct, bp, theta, delta):
self.cr = cr
self.ct = ct
self.bp = bp
self.theta = theta
self.delta = delta
class MeshParams:
"""
Container for the wing mesh parameters.
Attributes
----------
m : int
Number of chordwise panels.
n : int
Number of spanwise panels.
"""
def __init__(self, m, n):
self.m = m
self.n = n
class FlightConditions:
"""
Container for the flight conditions.
Attributes
----------
ui : float
Free-stream flow velocity.
alpha : float
Angle of attack of the wing, expressed in radians.
rho : float
Free-stream flow density.
"""
def __init__(self, ui, alpha, rho):
self.ui = ui
self.alpha = alpha
self.rho = rho
def get_quarter_chord_x(y, cr, theta):
# slope of the quarter chord line
p = np.tan(theta)
return cr / 4 + p * abs(y)
def get_chord_at_section(y, cr, ct, bp):
c = cr + (ct - cr) * abs(2 * y / bp)
return c
def build_panel(wing, mesh, i, j):
"""
Construct a wing panel indexed by its chord and spanwise indices.
Parameters
----------
wing : WingParams
Wing geometry specification.
mesh : MeshParams
Mesh geometry specification.
i : int
Panel chordwise index.
j : int
Panel spanwise index.
Returns
-------
panel : np.ndarray, shape (4, 3)
Array containing the (x,y,z) coordinates of the (`i`, `j`)-th panel's
vertices (sorted A-B-D-C).
pc : np.ndarray, shape (3, )
(x,y,z) coordinates of the (`i`, `j`)-th panel's collocation point.
"""
dy = wing.bp / mesh.n
y_A = - wing.bp / 2 + j * dy
y_B = y_A + dy
y_C, y_D = y_A, y_B
y_pc = y_A + dy / 2
# chord law evaluation
c_AC = get_chord_at_section(y_A, cr=wing.cr, ct=wing.ct, bp=wing.bp)
c_BD = get_chord_at_section(y_B, cr=wing.cr, ct=wing.ct, bp=wing.bp)
c_pc = get_chord_at_section(y_pc, cr=wing.cr, ct=wing.ct, bp=wing.bp)
# division of the chord in m equal panels
dx_AC = c_AC / mesh.m
dx_BD = c_BD / mesh.m
dx_pc = c_pc / mesh.m
# r,s,q are the X coordinates of the quarter chord line at spanwise
# locations: y_A, y_B and y_pc respectively
r = get_quarter_chord_x(y_A, cr=wing.cr, theta=wing.theta)
s = get_quarter_chord_x(y_B, cr=wing.cr, theta=wing.theta)
q = get_quarter_chord_x(y_pc, cr=wing.cr, theta=wing.theta)
x_A = (r - c_AC / 4) + i * dx_AC
x_B = (s - c_BD / 4) + i * dx_BD
x_C = x_A + dx_AC
x_D = x_B + dx_BD
x_pc = (q - c_pc / 4) + (i + 3 / 4) * dx_pc
x = np.array([x_A, x_B, x_D, x_C])
y = np.array([y_A, y_B, y_D, y_C])
z = np.tan(wing.delta) * np.abs(y)
panel = np.stack((x, y, z), axis=-1)
z_pc = np.tan(wing.delta) * np.abs(y_pc)
pc = np.array([x_pc, y_pc, z_pc])
return panel, pc
def build_wing_panels(wing, mesh):
"""
Construct wing panels and collocation points given the definition of
the geometry of the wing and mesh.
Parameters
----------
wing : WingParams
Wing geometry specification.
mesh : MeshParams
Mesh geometry specification.
Returns
-------
wing_panels : np.ndarray, shape (m, n, 4, 3)
Array containing the (x,y,z) coordinates of all wing panel vertices.
cpoints : np.ndarray, shape (m, n, 3)
Array containing the (x,y,z) coordinates of all collocation points.
"""
m, n = mesh.m, mesh.n
wing_panels = np.empty((m, n, 4, 3))
cpoints = | np.empty((m, n, 3)) | numpy.empty |
'''
Author: <NAME>
Functions for perfect phylogeny and incomplete phylogeny algorithms
'''
import numpy as np
import copy
import string
import subprocess
from mgraph import MGraph
def get_duplicates(items):
'''
returns the indices of all duplicates in a list
@param items a 1D list
'''
locs = []
for i in range(len(items)):
loc_tmp = [i]
item = items[i]
start_at = i+1
while True:
try:
loc = items.index(item,start_at+1)
except ValueError:
break
else:
loc_tmp.append(loc)
start_at = loc
if len(loc_tmp)>1:
locs.append(loc_tmp)
return(locs)
def remove_duplicates(m_prime, c_prime):
'''
remove any duplicate columns and merge associated features
@param m_prime M' matrix
@param c_prime features list corresponding to columns of M'
'''
m_prime_tmp = map(lambda x: '.'.join(map(str,x)),np.rot90(m_prime)[::-1])
dups = get_duplicates(m_prime_tmp)
n_dup = len(dups)
to_del = []
if n_dup > 0:
for idx,dup in enumerate(dups):
to_del.extend(dup[1:])
c_prime[dup[0]] = '_'.join(c_prime[dup])
m_prime = np.delete(m_prime,to_del,axis=1)
c_prime = np.delete(c_prime,to_del)
return(m_prime, c_prime)
def remove_zero_entry_cols(m3,c3):
'''
remove any columns that have no 0 entries
@param m3 the M matrix
@param c3 column features corresponding to the M matrix
'''
mi = np.empty(0,dtype='int')
ncol = len(m3[0])
idxs_to_delete = [i for i in range(ncol) if not np.any(m3[:,i]==0)]
m3 = np.delete(m3,idxs_to_delete,axis=1)
c3 = np.delete(c3,idxs_to_delete)
return(m3,c3)
def get_m_prime(m,c):
'''
Construct M' matrix
Obtain binary encoding for each feature, sort by binary value,
then rotate and reverse the resulting matrix
@param nshared nxm matrix of samples (cols) and
@param svrot is true, the matrix is of form rows = svs, cols = samples
'''
m_prime, c_prime = remove_zero_entry_cols(m,c)
m_prime, c_prime = remove_duplicates(m_prime, c_prime)
m_prime = np.rot90(m_prime)
# count binary score of columns
binary_strings = []
for col in m_prime:
col = np.array([ci if ci>0 else 0 for ci in col])
col_string = '0b'+''.join(map(str,col))
binary_strings.append(int(col_string,2))
# sort by binary score
order = np.argsort(binary_strings)[::-1]
m_prime = m_prime[order]
m_prime = np.rot90(m_prime)[::-1] #rotate again
c_order = (len(c_prime) - 1) - order #translate order of rotated matrix to order of columns
c_prime = c_prime[c_order]
return(m_prime,c_prime)
def get_k1_matrix(m_prime,features):
'''
Generate k1 from m' matrix
Allows for checking of perfect phylogeny
@param mp the m prime matrix
@param nodes corresponding to the matrix
'''
ncol = len(m_prime[0])
k = np.empty( [0,ncol], dtype='|S15' )
for m in m_prime:
row_feats = features[m!=0] #features in the row
mrow = np.zeros(ncol,dtype='|S15')
mrow.fill('0')
for idx,feature in enumerate(row_feats):
mrow[idx] = feature
n_feat = len(row_feats)
if n_feat < ncol:
mrow[n_feat]='#'
k = np.append(k,[mrow],axis=0)
return(k)
def perfect_phylogeny_exists(k1,features):
'''
Determine whether perfect phylogeny exists from a k1 matrix
@param k1 the k1 matrix (output from get_k1_matrix)
@param features the column features
'''
locations = []
for feature in features:
present_at = set([])
for k_i in k1:
[ present_at.add(loc_list) for loc_list in list(np.where(k_i==feature)[0]) ]
locations.append(present_at)
loc_test = np.array([len(loc_list)>1 for loc_list in locations])
if np.any(loc_test):
print('No phylogeny found!')
return(False)
else:
print('Success! Found phylogeny!\nK1 matrix:')
print(k1)
return(True)
def get_k(k,q,m_graph):
'''
return the first K vector with E[K] >= 1
@param k holds the connection vector, initialise with set()
@param q chain of connected vertices
@param m_graph graph object containing matrix connections
'''
if not q:
return(k)
else:
q1 = q.pop()
k.add(q1)
pairs = m_graph.get_pairs_containing(q1)
pairs = set([node for pair in pairs for node in pair]) #flatten set of elements
for node in pairs:
if node not in k:
q.add(node)
return(get_k(k,q,m_graph))
def solve_incomplete_phylogeny(m,s,c):
'''
implement Pe'er incomplete phylogeny algorithm
@param m M matrix
@param s samples/species (rows)
@param c features (columns)
'''
m3, c3 = get_m_prime(m,c)
m_graph = MGraph()
m_graph.build_graph(m3,s,c3)
m_pairs = m_graph.get_edge_pairs()
q = set(m_pairs[0]) #pick the first elements as k
k = get_k(set(),q,m_graph)
t = [set(s)] #initialise a tree
while len(m_pairs) > 1:
while len(k) < 3: #
for n in k:
m_graph.delNode(n)
m_pairs = m_graph.get_edge_pairs()
if len(m_pairs) > 1:
q = set(m_pairs[0])
k = get_k(set(),q,m_graph)
else:
break
s_prime = set(s).intersection(k)
s_indexes = np.array([np.where(s_i==s)[0][0] for s_i in s_prime])
m_tmp = m3.copy()[s_indexes]
print('k:')
print(k)
print("S':")
print(s_prime)
u = []
c_in_k = set(c).intersection(k)
for c_i in c_in_k:
c_index = np.where(c_i==c3)[0]
m_col = m_tmp[:,c_index:c_index+1]
if np.all(m_col!=0):
cm = np.where(c_i==c3)[0]
u.append(c_i)
if not u:
break
else:
print('u:')
print(u)
t.append(s_prime)
for n in u:
m_graph.delNode(n)
m_pairs = m_graph.get_edge_pairs()
k = get_k(set(),set(m_pairs[0]),m_graph)
print('Tree:')
print(t)
m_new = m3.copy()
c_indexes = [np.where(c3==x)[0][0] for x in u]
for s_set in t[1:]:
s_prime = set(s).intersection(s_set)
s_indexes = np.array([np.where(s_i==s)[0][0] for s_i in s_prime])
m_tmp = m3.copy()[s_indexes]
for c_i in c3:
c_idx = np.where(c_i==c3)[0]
m_col = m_tmp[:,c_index:c_index+1]
if np.all(m_col!=0) and np.any(m_col==-1):
cm = | np.where(c_i==c3) | numpy.where |
"""
The utilities module is a collection of classes and functions used across the eolearn package, such as checking whether
two objects are deeply equal, padding of an image, etc.
"""
import logging
from collections import OrderedDict
import numpy as np
from .constants import FeatureType
LOGGER = logging.getLogger(__name__)
class FeatureParser:
""" Takes a collection of features structured in a various ways and parses them into one way. It can parse features
straight away or it can parse them only if they exist in a given `EOPatch`. If input format is not recognized or
feature don't exist in a given `EOPatch` it raises an error. The class is a generator therefore parsed features
can be obtained by iterating over an instance of the class. An `EOPatch` is given as a parameter of the generator.
General guidelines:
- Almost all `EOTask`s have take as a parameter some information about features. The purpose of this class is
to unite and generalize parsing of such parameter over entire eo-learn package
- The idea for this class is that it should support more or less any logical way how to describe a collection
of features.
- Parameter `...` is used as a contextual clue. In the supported formats it is used to describe the most obvious
way how to specify certain parts of feature collection.
- Supports formats defined with lists, tuples, sets and dictionaries.
Supported input formats:
- `...` - Anything that exists in a given `EOPatch`
- A feature type describing all features of that type. E.g. `FeatureType.DATA` or `FeatureType.BBOX`
- A single feature as a tuple. E.g. (FeatureType.DATA, 'BANDS')
- A single feature as a tuple with new name. E.g. (FeatureType.DATA, 'BANDS', 'NEW_BANDS')
- A list of features (new names or not).
E.g. [(FeatureType.DATA, 'BANDS'), (FeatureType.MASK, 'CLOUD_MASK', 'NEW_CLOUD_MASK')]
- A dictionary with feature types as keys and lists, sets, single feature or `...` of feature names as values.
E.g. {
FeatureType.DATA: ['S2-BANDS', 'L8-BANDS'],
FeatureType.MASK: {'IS_VALID', 'IS_DATA'},
FeatureType.MASK_TIMELESS: 'LULC',
FeatureType.TIMESTAMP: ...
}
- A dictionary with feature types as keys and dictionaries, where feature names are mapped into new names, as
values.
E.g. {
FeatureType.DATA: {
'S2-BANDS': 'INTERPOLATED_S2_BANDS',
'L8-BANDS': 'INTERPOLATED_L8_BANDS',
'NDVI': ...
},
}
Note: Therese are most general input formats, but even more are supported or might be supported in the future.
Outputs of the generator:
- tuples in form of (feature type, feature name) if parameter `new_names=False`
- tuples in form of (feature type, feature name, new feature name) if parameter `new_names=True`
"""
def __init__(self, features, new_names=False, rename_function=None, default_feature_type=None,
allowed_feature_types=None):
"""
:param features: A collection of features in one of the supported formats
:type features: object
:param new_names: If `False` the generator will only return tuples with in form of
(feature type, feature name). If `True` it will return tuples
(feature type, feature name, new feature name) which can be used for renaming
features or creating new features out of old ones.
:type new_names: bool
:param rename_function: A function which transforms feature name into a new feature name, default is identity
function. This parameter is only applied if `new_names` is set to `True`.
:type rename_function: function or None
:param default_feature_type: If feature type of any given feature is not set, this will be used. By default this
is set to `None`. In this case if feature type of any feature is not given the following will happen:
- if iterated over `EOPatch` - It will try to find a feature with matching name in EOPatch. If such
features exist, it will return any of them. Otherwise it will raise an error.
- if iterated without `EOPatch` - It will return `...` instead of a feature type.
:type default_feature_type: FeatureType or None
:param allowed_feature_types: Makes sure that only features of these feature types will be returned, otherwise
an error is raised
:type: set(FeatureType) or None
:raises: ValueError
"""
self.feature_collection = self._parse_features(features, new_names)
self.new_names = new_names
self.rename_function = rename_function
self.default_feature_type = default_feature_type
self.allowed_feature_types = FeatureType if allowed_feature_types is None else set(allowed_feature_types)
if rename_function is None:
self.rename_function = self._identity_rename_function # <- didn't use lambda function - it can't be pickled
if allowed_feature_types is not None:
self._check_feature_types()
def __call__(self, eopatch=None):
return self._get_features(eopatch)
def __iter__(self):
return self._get_features()
@staticmethod
def _parse_features(features, new_names):
"""Takes a collection of features structured in a various ways and parses them into one way.
If input format is not recognized it raises an error.
:return: A collection of features
:rtype: collections.OrderedDict(FeatureType: collections.OrderedDict(str: str or Ellipsis) or Ellipsis)
:raises: ValueError
"""
if isinstance(features, dict):
return FeatureParser._parse_dict(features, new_names)
if isinstance(features, list):
return FeatureParser._parse_list(features, new_names)
if isinstance(features, tuple):
return FeatureParser._parse_tuple(features, new_names)
if features is ...:
return OrderedDict([(feature_type, ...) for feature_type in FeatureType])
if isinstance(features, FeatureType):
return OrderedDict([(features, ...)])
if isinstance(features, str):
return OrderedDict([(None, OrderedDict([(features, ...)]))])
raise ValueError('Unknown format of input features: {}'.format(features))
@staticmethod
def _parse_dict(features, new_names):
"""Helping function of `_parse_features` that parses a list."""
feature_collection = OrderedDict()
for feature_type, feature_names in features.items():
try:
feature_type = FeatureType(feature_type)
except ValueError:
ValueError('Failed to parse {}, keys of the dictionary have to be instances '
'of {}'.format(features, FeatureType.__name__))
feature_collection[feature_type] = feature_collection.get(feature_type, OrderedDict())
if feature_names is ...:
feature_collection[feature_type] = ...
if feature_type.has_dict() and feature_collection[feature_type] is not ...:
feature_collection[feature_type].update(FeatureParser._parse_feature_names(feature_names, new_names))
return feature_collection
@staticmethod
def _parse_list(features, new_names):
"""Helping function of `_parse_features` that parses a list."""
feature_collection = OrderedDict()
for feature in features:
if isinstance(feature, FeatureType):
feature_collection[feature] = ...
elif isinstance(feature, (tuple, list)):
for feature_type, feature_dict in FeatureParser._parse_tuple(feature, new_names).items():
feature_collection[feature_type] = feature_collection.get(feature_type, OrderedDict())
if feature_dict is ...:
feature_collection[feature_type] = ...
if feature_collection[feature_type] is not ...:
feature_collection[feature_type].update(feature_dict)
else:
raise ValueError('Failed to parse {}, expected a tuple'.format(feature))
return feature_collection
@staticmethod
def _parse_tuple(features, new_names):
"""Helping function of `_parse_features` that parses a tuple."""
name_idx = 1
try:
feature_type = FeatureType(features[0])
except ValueError:
feature_type = None
name_idx = 0
if feature_type and not feature_type.has_dict():
return OrderedDict([(feature_type, ...)])
return OrderedDict([(feature_type, FeatureParser._parse_names_tuple(features[name_idx:], new_names))])
@staticmethod
def _parse_feature_names(feature_names, new_names):
"""Helping function of `_parse_features` that parses a collection of feature names."""
if isinstance(feature_names, set):
return FeatureParser._parse_names_set(feature_names)
if isinstance(feature_names, dict):
return FeatureParser._parse_names_dict(feature_names)
if isinstance(feature_names, (tuple, list)):
return FeatureParser._parse_names_tuple(feature_names, new_names)
raise ValueError('Failed to parse {}, expected dictionary, set or tuple'.format(feature_names))
@staticmethod
def _parse_names_set(feature_names):
"""Helping function of `_parse_feature_names` that parses a set of feature names."""
feature_collection = OrderedDict()
for feature_name in feature_names:
if isinstance(feature_name, str):
feature_collection[feature_name] = ...
else:
raise ValueError('Failed to parse {}, expected string'.format(feature_name))
return feature_collection
@staticmethod
def _parse_names_dict(feature_names):
"""Helping function of `_parse_feature_names` that parses a dictionary of feature names."""
feature_collection = OrderedDict()
for feature_name, new_feature_name in feature_names.items():
if isinstance(feature_name, str) and (isinstance(new_feature_name, str) or
new_feature_name is ...):
feature_collection[feature_name] = new_feature_name
else:
if not isinstance(feature_name, str):
raise ValueError('Failed to parse {}, expected string'.format(feature_name))
raise ValueError('Failed to parse {}, expected string or Ellipsis'.format(new_feature_name))
return feature_collection
@staticmethod
def _parse_names_tuple(feature_names, new_names):
"""Helping function of `_parse_feature_names` that parses a tuple or a list of feature names."""
for feature in feature_names:
if not isinstance(feature, str) and feature is not ...:
raise ValueError('Failed to parse {}, expected a string'.format(feature))
if feature_names[0] is ...:
return ...
if new_names:
if len(feature_names) == 1:
return OrderedDict([(feature_names[0], ...)])
if len(feature_names) == 2:
return OrderedDict([(feature_names[0], feature_names[1])])
raise ValueError("Failed to parse {}, it should contain at most two strings".format(feature_names))
if ... in feature_names:
return ...
return OrderedDict([(feature_name, ...) for feature_name in feature_names])
def _check_feature_types(self):
""" Checks that feature types are a subset of allowed feature types. (`None` is handled
:raises: ValueError
"""
if self.default_feature_type is not None and self.default_feature_type not in self.allowed_feature_types:
raise ValueError('Default feature type parameter must be one of the allowed feature types')
for feature_type in self.feature_collection:
if feature_type is not None and feature_type not in self.allowed_feature_types:
raise ValueError('Feature type has to be one of {}, but {} found'.format(self.allowed_feature_types,
feature_type))
def _get_features(self, eopatch=None):
"""A generator of parsed features.
:param eopatch: A given EOPatch
:type eopatch: EOPatch or None
:return: One by one feature
:rtype: tuple(FeatureType, str) or tuple(FeatureType, str, str)
"""
for feature_type, feature_dict in self.feature_collection.items():
if feature_type is None and self.default_feature_type is not None:
feature_type = self.default_feature_type
if feature_type is None:
for feature_name, new_feature_name in feature_dict.items():
if eopatch is None:
yield self._return_feature(..., feature_name, new_feature_name)
else:
found_feature_type = self._find_feature_type(feature_name, eopatch)
if found_feature_type:
yield self._return_feature(found_feature_type, feature_name, new_feature_name)
else:
raise ValueError("Feature with name '{}' does not exist among features of allowed feature"
" types in given EOPatch. Allowed feature types are "
"{}".format(feature_name, self.allowed_feature_types))
elif feature_dict is ...:
if not feature_type.has_dict() or eopatch is None:
yield self._return_feature(feature_type, ...)
else:
for feature_name in eopatch[feature_type]:
yield self._return_feature(feature_type, feature_name)
else:
for feature_name, new_feature_name in feature_dict.items():
if eopatch is not None and feature_name not in eopatch[feature_type]:
raise ValueError('Feature {} of type {} was not found in EOPatch'.format(feature_name,
feature_type))
yield self._return_feature(feature_type, feature_name, new_feature_name)
def _find_feature_type(self, feature_name, eopatch):
""" Iterates over allowed feature types of given EOPatch and tries to find a feature type for which there
exists a feature with given name
:return: A feature type or `None` if such feature type does not exist
:rtype: FeatureType or None
"""
for feature_type in self.allowed_feature_types:
if feature_type.has_dict() and feature_name in eopatch[feature_type]:
return feature_type
return None
def _return_feature(self, feature_type, feature_name, new_feature_name=...):
""" Helping function of `get_features`
"""
if self.new_names:
return feature_type, feature_name, (self.rename_function(feature_name) if new_feature_name is ... else
new_feature_name)
return feature_type, feature_name
@staticmethod
def _identity_rename_function(name):
return name
def get_common_timestamps(source, target):
"""Return indices of timestamps from source that are also found in target.
:param source: timestamps from source
:type source: list of datetime objects
:param target: timestamps from target
:type target: list of datetime objects
:return: indices of timestamps from source that are also found in target
:rtype: list of ints
"""
remove_from_source = set(source).difference(target)
remove_from_source_idxs = [source.index(rm_date) for rm_date in remove_from_source]
return [idx for idx, _ in enumerate(source) if idx not in remove_from_source_idxs]
def deep_eq(fst_obj, snd_obj):
"""Compares whether fst_obj and snd_obj are deeply equal.
In case when both fst_obj and snd_obj are of type np.ndarray or either np.memmap, they are compared using
np.array_equal(fst_obj, snd_obj). Otherwise, when they are lists or tuples, they are compared for length and then
deep_eq is applied component-wise. When they are dict, they are compared for key set equality, and then deep_eq is
applied value-wise. For all other data types that are not list, tuple, dict, or np.ndarray, the method falls back
to the __eq__ method.
Because np.ndarray is not a hashable object, it is impossible to form a set of numpy arrays, hence deep_eq works
correctly.
:param fst_obj: First object compared
:param snd_obj: Second object compared
:return: `True` if objects are deeply equal, `False` otherwise
"""
# pylint: disable=too-many-return-statements
if isinstance(fst_obj, (np.ndarray, np.memmap)):
if not isinstance(snd_obj, (np.ndarray, np.memmap)):
return False
if fst_obj.dtype != snd_obj.dtype:
return False
fst_nan_mask = np.isnan(fst_obj)
snd_nan_mask = np.isnan(snd_obj)
return np.array_equal(fst_obj[~fst_nan_mask], snd_obj[~snd_nan_mask]) and \
np.array_equal(fst_nan_mask, snd_nan_mask)
if not isinstance(fst_obj, type(snd_obj)):
return False
if isinstance(fst_obj, np.ndarray):
if fst_obj.dtype != snd_obj.dtype:
return False
fst_nan_mask = np.isnan(fst_obj)
snd_nan_mask = np.isnan(snd_obj)
return np.array_equal(fst_obj[~fst_nan_mask], snd_obj[~snd_nan_mask]) and \
| np.array_equal(fst_nan_mask, snd_nan_mask) | numpy.array_equal |
import numpy as np
from envs.FiniteMDP import FiniteMDP
class WideNarrow(FiniteMDP):
def __init__(self, n=1, w=6, gamma=0.999, horizon=1000):
# WideNarrow parameters
self.N, self.W = n, w
self.mu_l, self.sig_l = 0., 1.
self.mu_h, self.sig_h = 0.5, 1.
self.mu_n, self.sig_n = 0, 1
P, R = self.get_dynamics_and_rewards_distributions()
p, r = self.get_mean_P_and_R()
mu = np.zeros(self.N * 2 + 1)
mu[0] = 1.
super(WideNarrow, self).__init__(p, r, mu, gamma, horizon)
def get_dynamics_and_rewards_distributions(self):
'''
Implementation of the corresponding method from TabularEnvironment
'''
# Dict for transitions, P_probs[(s, a)] = [(s1, ...), (p1, ...)]
P_probs = {}
for n in range(self.N):
for a in range(self.W):
# Wide part transitions
P_probs[(2 * n, a)] = [(2 * n + 1,), (1.00,)]
P_probs[(2 * n + 1, 0)] = [(2 * n + 2,), (1.00,)]
# Last state transitions to first state
P_probs[(2 * self.N, 0)] = [(0,), (1.00,)]
self.P_probs = P_probs
def P(s, a):
# Next states and transition probabilities
s_, p = P_probs[(s, a)]
# Sample s_ according to the transition probabilities
s_ = np.random.choice(s_, p=p)
return s_
def R(s, a, s_):
# Booleans for current and next state
even_s, odd_s_ = s % 2 == 0, s_ % 2 == 1
# Zero reward for transition from last to first state
if s == 2 * self.N and s_ == 0:
return 0.
# High reward for correct action from odd state
elif even_s and odd_s_ and (a == 0):
return self.mu_h + self.sig_h * np.random.normal()
# Low reward for incorrect action from odd state
elif even_s and odd_s_:
return self.mu_l + self.sig_l * np.random.normal()
# Reward from even state
else:
return self.mu_n + self.sig_n * np.random.normal()
return P, R
def get_name(self):
return 'WideNarrow-N-{}_W-{}'.format(self.N, self.W)
def get_mean_P_and_R(self):
P = np.zeros((2 * self.N + 1, self.W, 2 * self.N + 1))
R = | np.zeros((2 * self.N + 1, self.W, 2 * self.N + 1)) | numpy.zeros |
"""
Showcases *CIE 1994* chromatic adaptation model computations.
"""
import numpy as np
import colour
from colour.utilities import message_box
message_box('"CIE 1994" Chromatic Adaptation Model Computations')
XYZ_1 = np.array([0.2800, 0.2126, 0.0527])
xy_o1 = | np.array([0.4476, 0.4074]) | numpy.array |
import pytest
import unittest.mock as mock
import open_cp.sepp_base as sepp_base
import open_cp.data
import open_cp.predictors
import numpy as np
import datetime
class OurModel(sepp_base.ModelBase):
def background(self, points):
assert len(points.shape) == 2
assert points.shape[0] == 3
return points[0] * np.exp(-(points[1]**2 + points[2]**2))
def trigger(self, pt, dpts):
assert pt.shape == (3,)
assert len(dpts.shape) == 2
assert dpts.shape[0] == 3
w = np.sum(np.abs(pt))
return dpts[0] * np.exp(-(dpts[1]**2 + dpts[2]**2) / w)
def slow_p_matrix(model, points):
assert points.shape[0] == 3
d = points.shape[1]
p = np.zeros((d,d))
for i in range(d):
pt = points[:,i]
p[i,i] = model.background(pt[:,None])
for j in range(i):
dp = pt - points[:,j]
if dp[0] <= 0:
p[j,i] = 0
else:
p[j,i] = model.trigger(pt, dp[:,None])
for i in range(d):
p[:,i] /= np.sum(p[:,i])
return p
def test_p_matrix():
model = OurModel()
for _ in range(10):
points = np.random.random((3,20))
points[0].sort()
expected = slow_p_matrix(model, points)
got = sepp_base.p_matrix(model, points)
np.testing.assert_allclose(got, expected)
class OurModel1(OurModel):
def trigger(self, pt, dpts):
super().trigger(pt, dpts)
w = np.sum(np.abs(pt))
return (1 + dpts[0]) * np.exp(-(dpts[1]**2 + dpts[2]**2) / w)
def test_p_matrix_with_time_repeats():
model = OurModel1()
for _ in range(10):
points = np.random.random((3,20))
points[0].sort()
points[0][1] = points[0][0]
points[0][15] = points[0][14]
expected = slow_p_matrix(model, points)
got = sepp_base.p_matrix(model, points)
np.testing.assert_allclose(got, expected)
@pytest.fixture
def p_matrix_mock():
with mock.patch("open_cp.sepp_base.p_matrix") as m:
m.return_value = [[1, 0.5, 0.1, 0.2],
[0, 0.5, 0.6, 0.4],
[0, 0, 0.3, 0.3],
[0, 0, 0, 0.1]]
yield m
@pytest.fixture
def model():
return OurModel()
@pytest.fixture
def points():
return np.asarray([ [0,1,2,3], [1,4,7,9], [8,6,4,2] ])
@pytest.fixture
def optimiser(p_matrix_mock, model, points):
yield sepp_base.Optimiser(model, points)
def test_Optimiser_p_diag(optimiser):
assert optimiser.p.shape == (4,4)
np.testing.assert_allclose(optimiser.p_diag, [1, 0.5, 0.3, 0.1])
assert optimiser.p_diag_sum == pytest.approx(1.9)
def test_Optimiser_p_upper_tri_sum(optimiser):
assert optimiser.p_upper_tri_sum == pytest.approx(0.5 + 0.7 + 0.9)
def test_Optimiser_upper_tri_col(optimiser):
optimiser.upper_tri_col(0) == np.asarray([])
optimiser.upper_tri_col(1) == np.asarray([0.5])
optimiser.upper_tri_col(2) == np.asarray([0.1, 0.6])
optimiser.upper_tri_col(3) == np.asarray([0.2, 0.4, 0.3])
optimiser.diff_col_times(0) == np.asarray([])
optimiser.diff_col_times(1) == np.asarray([1])
optimiser.diff_col_times(2) == np.asarray([2,1])
optimiser.diff_col_times(3) == np.asarray([3,2,1])
optimiser.diff_col_points(0) == np.asarray([])
optimiser.diff_col_points(1) == np.asarray([[3], [-2]])
optimiser.diff_col_points(1) == np.asarray([[6,3], [4,2]])
optimiser.diff_col_points(1) == np.asarray([[8,5,2], [6,4,2]])
def test_Optimiser(optimiser):
assert optimiser.num_points == 4
def test_Trainer_constructs():
tr = sepp_base.Trainer()
assert tr.time_unit / np.timedelta64(1, "h") == pytest.approx(24)
tr.time_unit = datetime.timedelta(seconds = 6 * 60)
assert tr.time_unit / np.timedelta64(1, "m") == pytest.approx(6)
class OurTrainer(sepp_base.Trainer):
def __init__(self):
super().__init__()
self._testing_fixed = mock.Mock()
self._testing_im = mock.Mock()
self._opt_class_mock = mock.Mock()
def make_fixed(self, times):
self._make_fixed_times = times
return self._testing_fixed
def initial_model(self, fixed, data):
self._initial_model_params = (fixed, data)
return self._testing_im
@property
def _optimiser(self):
return self._opt_class_mock
@pytest.fixture
def trainer():
sepp = OurTrainer()
t = [np.datetime64("2017-05-01T00:00"), np.datetime64("2017-05-02T00:00"),
np.datetime64("2017-05-04T00:00"), np.datetime64("2017-05-10T23:45")]
x = [1,2,3,4]
y = [5,6,7,8]
sepp.data = open_cp.data.TimedPoints.from_coords(t, x, y)
return sepp
def test_Trainer_make_data(trainer):
sepp = trainer
fixed, data = sepp.make_data()
assert fixed is sepp._testing_fixed
offset = 15 / 60 / 24
np.testing.assert_allclose(sepp._make_fixed_times, [10, 9, 7, offset])
np.testing.assert_allclose(data[0], [0, 1, 3, 10 - offset])
np.testing.assert_allclose(data[1], [1,2,3,4])
np.testing.assert_allclose(data[2], [5,6,7,8])
fixed, data = sepp.make_data(predict_time = datetime.datetime(2017,5,10,23,45))
assert fixed is sepp._testing_fixed
np.testing.assert_allclose(sepp._make_fixed_times, [10 - offset, 9 - offset,
7 - offset, 0])
np.testing.assert_allclose(data[0], [0, 1, 3, 10 - offset])
np.testing.assert_allclose(data[1], [1,2,3,4])
np.testing.assert_allclose(data[2], [5,6,7,8])
def test_Trainer_make_initial_model(trainer):
fixed, data = trainer.make_data()
im = trainer.initial_model(fixed, data)
assert im is trainer._testing_im
assert trainer._initial_model_params[0] is fixed
assert trainer._initial_model_params[1] is data
offset = 15 / 60 / 24
np.testing.assert_allclose(trainer._make_fixed_times, [10, 9, 7, offset])
def test_Trainer_optimise(trainer):
model = trainer.train()
opt = trainer._opt_class_mock.return_value
assert model == opt.iterate.return_value
assert len(trainer._opt_class_mock.call_args_list) == 1
call = trainer._opt_class_mock.call_args_list[0]
assert call[0][0] is trainer._testing_im
def test_Trainer_optimise_predict_time(trainer):
model = trainer.train(predict_time = datetime.datetime(2017,5,10,23,45))
opt = trainer._opt_class_mock.return_value
assert model == opt.iterate.return_value
offset = 15 / 60 / 24
np.testing.assert_allclose(trainer._make_fixed_times, [10 - offset, 9 - offset,
7 - offset, 0])
assert len(trainer._opt_class_mock.call_args_list) == 1
call = trainer._opt_class_mock.call_args_list[0]
assert call[0][0] is trainer._testing_im
def test_Trainer_optimise2(trainer):
model = trainer.train(iterations=2)
opt = trainer._opt_class_mock.return_value
assert model == opt.iterate.return_value
assert len(trainer._opt_class_mock.call_args_list) == 2
call = trainer._opt_class_mock.call_args_list[0]
assert call[0][0] is trainer._testing_im
call = trainer._opt_class_mock.call_args_list[1]
assert call[0][0] is model
def test_PredictorBase():
class Model():
def background(self, points):
return points[0]
def trigger(self, pt, dp):
return pt[0] * (dp[1] + dp[2])**2
pts = [[0,1,2,3], [4,7,2,3], [4,5,6,1]]
model = Model()
pred = sepp_base.PredictorBase(model, pts)
assert pred.model is model
np.testing.assert_allclose(pred.points, pts)
assert pred.point_predict(1, [2,3]) == pytest.approx(10)
assert pred.point_predict(0.5, [2,3]) == pytest.approx(5)
assert pred.point_predict(1, [4,4]) == pytest.approx(1)
assert pred.point_predict(1, [4,5]) == pytest.approx(2)
np.testing.assert_allclose(pred.point_predict(1, [[2,4,4], [3,4,5]]), [10,1,2])
assert pred.point_predict(2, [2,3]) == pytest.approx(2 + 18 + 2*49)
expected = sum(t*10 for t in np.linspace(0,1,20))
assert pred.range_predict(0, 1, [2,3]) == pytest.approx(expected / 20)
assert pred.background_predict(1, [2,3]) == pytest.approx(1)
assert pred.background_predict(2, [4,7]) == pytest.approx(2)
def test_Predictor(trainer):
mask = np.asarray([[False, True, False], [False]*3])
grid = open_cp.data.MaskedGrid(xsize=10, ysize=15, xoffset=2, yoffset=3, mask=mask)
model = OurModel()
pred = sepp_base.Predictor(grid, model)
pred.data = trainer.data
gp = pred.predict(np.datetime64("2017-05-04T00:00"))
np.testing.assert_allclose(gp.intensity_matrix.mask, mask)
assert (gp.xsize, gp.ysize) == (grid.xsize, grid.ysize)
gp = pred.predict(np.datetime64("2017-05-04T00:00"), end_time=np.datetime64("2017-05-05T00:00"))
np.testing.assert_allclose(gp.intensity_matrix.mask, mask)
assert (gp.xsize, gp.ysize) == (grid.xsize, grid.ysize)
gp = pred.background_predict(np.datetime64("2017-05-04T00:00"))
np.testing.assert_allclose(gp.intensity_matrix.mask, mask)
assert (gp.xsize, gp.ysize) == (grid.xsize, grid.ysize)
def test_clamp_p():
p = [[1, 0, 0, 0], [0.6, 0.4, 0, 0], [0.99, 0.01, 0, 0], [0.2, 0.05, 0.7, 0.05]]
p = np.asarray(p).T
pc = np.asarray(p)
pp = sepp_base.clamp_p(p, 99)
np.testing.assert_allclose(p, pc) # Don't mutate p
np.testing.assert_allclose(pp[:,0], [1,0,0,0])
np.testing.assert_allclose(pp[:,1], [0.6,0.4,0,0])
np.testing.assert_allclose(pp[:,2], [0.99,0,0,0])
np.testing.assert_allclose(pp[:,3], [0.2,0.05,0.7,0.05])
pp = sepp_base.clamp_p(p, 49)
np.testing.assert_allclose(pp[:,0], [1,0,0,0])
np.testing.assert_allclose(pp[:,1], [0.6,0,0,0])
np.testing.assert_allclose(pp[:,2], [0.99,0,0,0])
np.testing.assert_allclose(pp[:,3], [0,0,0.7,0])
def test_Optimiser_sample():
model = sepp_base.ModelBase()
model.background = lambda pts : [1]*pts.shape[-1]
model.trigger = lambda tp, pts : [1]*pts.shape[-1]
opt = sepp_base.Optimiser(model, np.random.random((3,4)))
p = [[1,0,0,0], [0,1,0,0], [1,0,0,0], [0,0,1,0]]
opt._p = | np.asarray(p) | numpy.asarray |
import cv2
import numpy as np
import random
import glob
from src.utils import im2single, getWH, hsv_transform
from src.label import Label
from src.projection_utils import perspective_transform, find_T_matrix, getRectPts
#
# Use UseBG if you want to pad distorted images with bakcground data
#
UseBG = True
bgimages = []
dim0 = 208
BGDataset = 'bgimages\\' # directory with background images using to pad images in data augmentation
#
# Creates list with BG images
#
if UseBG:
imglist = glob.glob(BGDataset + '*.jpg')
for im in imglist:
img = cv2.imread(im)
factor = max(1, dim0/min(img.shape[0:2]))
img = cv2.resize(img, (0,0), fx = factor, fy = factor).astype('float32')/255
bgimages.append(img)
def random_crop(img, width, height):
#
# generates random crop of img with desired size
#
or_height = img.shape[0]
or_width = img.shape[1]
top = int(np.random.rand(1)*(or_height - height))
bottom = int(np.random.rand(1)*(or_width - width))
crop = img[top:(top+height), bottom:(bottom+width),:]
return crop
def GetCentroid(pts):
#
# Gets centroids of a quadrilateral
#
return np.mean(pts, 1);
def ShrinkQuadrilateral(pts, alpha=0.75):
#
# Shribks quadtrilateral by a factor alpha
#
centroid = GetCentroid(pts)
temp = centroid + alpha * (pts.T - centroid)
return temp.T
def LinePolygonEdges(pts):
#
# Finds the line equations of the polygon edges (given the verices in clockwise order)
#
lines = []
for i in range(4):
x1 = np.hstack((pts[:, i], 1))
x2 = np.hstack((pts[:, (i + 1) % 4], 1))
lines.append(np.cross(x1, x2))
return lines
def insidePolygon(pt, lines):
#
# Checks is a point pt is inisde quadrilateral given by pts. Must be all negative??
#
pth = np.hstack((pt, 1))
allsigns = []
output = True
#
# Scans all edges
#
for i in range(len(lines)):
sig = np.dot(pth, lines[i])
allsigns.append(sig)
if sig < 0:
output = False
break
return output
def labels2output_map(labelist, lpptslist, dim, stride, alfa=0.75):
#
# Generates outpmut map with binary (classification) labels and quadrilateral corners (regression)
# label is the bounding box of the quadrilateral, and its locations are given in a list of plates
# lpptslist
#
dim0 = 208 # used to define the range of LP scales in the training procedure
#
# Aveage LP side in output layer (with spatial dimension outsize)
#
side = ((float(dim0) + 40.) / 2.) / stride # 7.75 when dim = 208 and stride = 16
outsize = int(dim / stride)
#
# Prepares GT map with 9 channels
#
Y = np.zeros((outsize, outsize, 2 * 4 + 1), dtype='float32')
MN = np.array([outsize, outsize])
WH = np.array([dim, dim], dtype=float)
#
# Scans all annotated LPs in the image
#
for i in range(0, len(labelist)):
#
# Gets corners and labels (labels igored at the moment)
#
lppts = lpptslist[i]
label = labelist[i]
#
# Gets location of bounding box of LP resized to output resolution
#
tlx, tly = np.floor(np.maximum(label.tl(), 0.) * MN).astype(int).tolist()
brx, bry = np.ceil(np.minimum(label.br(), 1.) * MN).astype(int).tolist()
#
# Finds location of quadrilateral in the output resolution
#
p_WH = lppts * WH.reshape((2, 1))
p_MN = p_WH / stride
#
# Finds line equations of shrunk quadrilaterals
#
pts2 = (ShrinkQuadrilateral(lppts, alfa).T * MN).T;
lines = LinePolygonEdges(pts2);
#
# Scans LP bounding box and triggers a classification label if point is inside
# shrunk LP
#
for x in range(tlx, brx):
for y in range(tly, bry):
mn = np.array([float(x) + .5, float(y) + .5])
#
# Tests if current point is inside shrunk LP
#
if insidePolygon(mn, lines):
#
# Translates LP points to the cell center
#
p_MN_center_mn = p_MN - mn.reshape((2, 1))
#
# Re-scales according to avergate LP side
#
p_side = p_MN_center_mn / side
#
# Defines classification label and re-scaled LP locations to be regressed
#
Y[y, x, 0] = 1.
Y[y, x, 1:] = p_side.T.flatten()
#
# Always set a true label at centroid if not fake LP (first test)
#
if (max(lppts[0,]) - min(lppts[0,]) > .01 and max(lppts[1,]) - min(lppts[1,]) > .01):
cc = np.array(np.round(GetCentroid(lppts) * MN - 0.5), np.int8)
#
# Centroid of LP in output resolution (round to smallest integer )
#
cc = np.array(np.round(GetCentroid(p_MN) - 0.5), np.int8)
#
# Ensures that it is in a valid location of the output map
#
x = max(0, min(cc[0], outsize - 1))
y = max(0, min(cc[1], outsize - 1))
mn = np.array([float(x) + .5, float(y) + .5])
p_MN_center_mn = p_MN - mn.reshape((2, 1))
#
# Defines classification label and re-scaled LP locations to be regressed
#
p_side = p_MN_center_mn / side
Y[y, x, 0] = 1.
Y[y, x, 1:] = p_side.T.flatten()
return Y
def pts2ptsh(pts):
#
# Gets homogeneous coordinates
#
return np.matrix(np.concatenate((pts, np.ones((1, pts.shape[1]))), 0))
def project(I, T, pts, dim):
#
# Projects image I and points pts according to matrix T
#
ptsh = np.matrix(np.concatenate((pts, np.ones((1, 4))), 0))
ptsh = np.matmul(T, ptsh)
ptsh = ptsh / ptsh[2]
ptsret = ptsh[:2]
ptsret = ptsret / dim
Iroi = cv2.warpPerspective(I, T, (dim, dim), borderValue=.0, flags = cv2.INTER_CUBIC)
return Iroi, ptsret
def project_all(I, T, ptslist, dim, bgimages = bgimages):
#
# Warps image I to desired dimensions using matrix T. if bgimage is not empty,
# completes with background
# Also projects LP coordinates given in ptslist to keep coherence
#
#
outptslist = []
#
# Scans annotated LPs and warps them
#
for pts in ptslist:
ptsh = np.matrix(np.concatenate((pts, np.ones((1, 4))), 0))
ptsh = np.matmul(T, ptsh)
ptsh = ptsh / ptsh[2]
ptsret = ptsh[:2]
ptsret = ptsret / dim
outptslist.append(np.array(ptsret))
#
# Warps input image (possibly padding with BG images)
#
Iroi = cv2.warpPerspective(I, T, (dim, dim), borderValue=(.5,.5,.5), flags=cv2.INTER_CUBIC)
if len(bgimages) > 0:
bgimage = bgimages[int(np.random.rand()*len(bgimages))]
bgimage = random_crop(bgimage, dim, dim)
bw = np.ones(I.shape)
bw = cv2.warpPerspective(bw, T, (dim, dim), borderValue= (0, 0, 0), flags=cv2.INTER_LINEAR)
Iroi[bw == 0] = bgimage[bw == 0]
return Iroi, outptslist
def randomblur(img):
#
# Applies random blur to image
#
maxblur = np.min(img.shape)/10
sig = abs(np.random.normal(0, .1))*maxblur
ksize = 2*int(0.5 + 2*sig) + 1
out = cv2.GaussianBlur(img, (ksize, ksize), sig)
return out
def flip_image_and_ptslist(I, ptslist):
#
# Applies random flip to image and labels
#
I = cv2.flip(I, 1)
for i in range(len(ptslist)):
pts = ptslist[i]
pts[0] = 1. - pts[0]
idx = [1, 0, 3, 2]
pts = pts[..., idx]
ptslist[i] = pts
return I, ptslist
def flip_image_and_pts(I, pts):
I = cv2.flip(I, 1)
pts[0] = 1. - pts[0]
idx = [1, 0, 3, 2]
pts = pts[..., idx]
return I, pts
def augment_sample(I, shapelist, dim, maxangle = 2 * np.array([65.,65.,55.]), maxsum = 140):
#
# Main augmentation function. Generates an augmented version
# of input image I and the corresponding LP corners given in shapelist
#
#
# Input is image I, list of shape elements (shape), and input dim
#
#
# Gets first LP corners and label
#
pts = shapelist[0].pts
vtype = shapelist[0].text
ptslist = []
#
# List of ROI corners
#
for entry in shapelist:
ptslist.append(entry.pts)
#
# maximum 3D rotation angles
#
angles = (np.random.rand(3) - 0.5) * maxangle
if sum(np.abs(angles)) > maxsum:
angles = (angles/angles.sum())*(maxangle/maxangle.sum())
#
# Normalizes intensities to [0,1]
#
I = im2single(I)
#
# Possible negative of the image
#
if np.random.uniform(0,1) < 0.05:
I = 1 - I;
#
# Possible blur
#
if np.random.rand() < 0.15:
I = randomblur(I)
#
# Gets image dimensions
#
iwh = getWH(I.shape)
#
# Checks is annotation is a real or fake plate
#
if (pts[0][1] - pts[0][0] > .002): ## if not fake plate
for i in range(len(ptslist)):
#
# LP region from relative to absolute coordinates
#
ptslist[i] = ptslist[i] * iwh.reshape((2, 1))
#
# Target aspect ratio of the LP (bike or car)
#
if vtype == 'bike':
whratio = random.uniform(1.25, 2.5)
else:
whratio = random.uniform(2.5, 4.5)
#
# Width of LP in training image
#
dim0 = 208 # augments data w.r.t. a fixed resolution
#
# Defines range of LP widths w.r.t to baseline resolution dim0 = 208
#
wsiz = random.uniform(dim0*0.2, dim0*1.0)
#
# Defines height based on width and aspect ratio
#
hsiz = wsiz/whratio
#
# Defines horizontal and vertical offsets
#
dx = random.uniform(0.,dim - wsiz)
dy = random.uniform(0.,dim - hsiz)
#
# Warps annotated plate to a rectified rectangle - frontal view
#
pph = getRectPts(dx, dy, dx+wsiz, dy+hsiz)
pts = pts*iwh.reshape((2,1))
T = find_T_matrix(pts2ptsh(pts), pph)
#
# Finds 3D rotation matrix based on angles
#
H = perspective_transform((dim,dim), angles=angles)
#
# Applies 3D rotation to rectification transform
#
H = | np.matmul(H,T) | numpy.matmul |
#!/usr/bin/env python
#
# Copyright 2019 DFKI GmbH.
#
# Permission is hereby granted, free of charge, to any person obtaining a
# copy of this software and associated documentation files (the
# "Software"), to deal in the Software without restriction, including
# without limitation the rights to use, copy, modify, merge, publish,
# distribute, sublicense, and/or sell copies of the Software, and to permit
# persons to whom the Software is furnished to do so, subject to the
# following conditions:
#
# The above copyright notice and this permission notice shall be included
# in all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
# NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
# DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
# OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
# USE OR OTHER DEALINGS IN THE SOFTWARE.
# -*- coding: utf-8 -*-
#===============================================================================
# author: <NAME> (DFKI GmbH, FB: Agenten und Simulierte Realität)
# last update: 3.1.2014
#orbiting camera based on http://www.glprogramming.com/red/chapter03.html
#Horizontal Movement implementation based on
#http://www.youtube.com/watch?v=RInkwoCgIps
#http://www.youtube.com/watch?v=H20stuPG-To
#===============================================================================
import numpy as np
import numpy.linalg as la
import math
import transformations as trans
from ..graphics import utils
UP = np.array([0,1,0])
FORWARD = np.array([0,0,-1])
class BoundigBox(object):
def __init__(self):
self.min_v = np.zeros(3)
self.max_v = np.zeros(3)
self.min_v[:] = np.inf
self.max_v[:] = -np.inf
def update(self, p):
for d in range(3):
if p[d] < self.min_v [d]:
self.min_v[d] = p[d]
elif p[d] > self.max_v[d]:
self.max_v[d] = p[d]
def inside(self, p):
inside = True
for d in range(3):
if p[d] < self.min_v[d]:
inside = False
break
elif p[d] > self.max_v[d]:
inside = False
break
return inside
class Camera(object):
def __init__(self):
self.viewMatrix = np.eye(4)
self.projectionMatrix = np.eye(4)
self.orthographMatrix = np.eye(4)
self.aspect = 0
self.near = 0
self.far = 0
self.fov = 0
def get_transform(self):
""" Copied from ThinMatrix shadow tutorial
src: https://www.youtube.com/watch?v=o6zDfDkOFIc
https://www.dropbox.com/sh/g9vnfiubdglojuh/AACpq1KDpdmB8ZInYxhsKj2Ma/shadows
"""
yaw = math.radians(self.yaw)
pitch = math.radians(self.pitch)
rot_y = trans.quaternion_about_axis(-yaw, np.array([0, 1, 0]))
rot_y = trans.quaternion_matrix(rot_y)
rot_x = trans.quaternion_about_axis(-pitch, np.array([1, 0, 0]))
rot_x = trans.quaternion_matrix(rot_x)
transform = np.dot(rot_y, rot_x)
transform[3, :3] = -self.get_world_position()
return transform
def get_frustrum_vertices(self):
""" src:https://github.com/pyth/sgltk P_Camera class
"""
ndc = [[-1,-1,-1, 1],
[1, -1, -1, 1],
[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_m = self.get_projection_matrix().T
v_m = self.get_view_matrix().T
rm = np.dot(p_m, v_m)
m = np.linalg.inv(rm)
ret = np.zeros((8,3))
for idx in range(8):
v = np.dot(m, ndc[idx])
ret[idx] = v[:3]/ v[3]
return ret
def get_frustrum_bounding_box(self):
v = self.get_frustrum_vertices()
v_m = self.get_view_matrix().T
_p = np.zeros(4)
bb = BoundigBox()
for p in v:
_p[0] = p[0]
_p[1] = p[1]
_p[2] = p[2]
_p[3] = 1
_p = np.dot(v_m, _p)
bb.update(_p[:3])
return bb
class OrbitingCamera(Camera):
""" orbiting camera based on http://www.glprogramming.com/red/chapter03.html
"""
def __init__(self):
super().__init__()
self.position = np.array([0.0,-10.0,0.0])
self.zoom = -5.0
self.view_dir = np.array([0.0,0.0,-1.0,1.0])
self.rotation_matrix = | np.eye(4) | numpy.eye |
'''
25 2D-Gaussian Simulation
Compare different Sampling methods and DRE methods
1. DRE method
1.1. By NN
DR models: MLP
Loss functions: uLISF, DSKL, BARR, SP (ours)
lambda for SP is selected by maximizing average denstity ratio on validation set
1.2. GAN property
2. Data Generation:
(1). Target Distribution p_r: A mixture of 25 2-D Gaussian
25 means which are combinations of any two points in [-2, -1, 0, 1, 2]
Each Gaussian has a covariance matrix sigma*diag(2), sigma=0.05
(2). Proposal Distribution p_g: GAN
NTRAIN = 50000, NVALID=50000, NTEST=10000
3. Sampling from GAN by None/RS/MH/SIR
4. Evaluation on a held-out test set
Prop. of good samples (within 4 sd) and Prop. of recovered modes
'''
wd = './Simulation'
import os
os.chdir(wd)
import timeit
import torch
import torchvision
import torchvision.transforms as transforms
import numpy as np
import torch.nn as nn
import torch.backends.cudnn as cudnn
from torch.nn import functional as F
import random
import matplotlib.pyplot as plt
import matplotlib as mpl
from torch import autograd
from torchvision.utils import save_image
from tqdm import tqdm
import gc
from itertools import groupby
import argparse
from sklearn.linear_model import LogisticRegression
import multiprocessing
from scipy.stats import multivariate_normal
from scipy.stats import ks_2samp
import pickle
import csv
from sklearn.model_selection import GridSearchCV
from sklearn import mixture
from utils import *
from models import *
from Train_DRE import train_DRE_GAN
from Train_GAN import *
#######################################################################################
''' Settings '''
#######################################################################################
parser = argparse.ArgumentParser(description='Simulation')
'''Overall Settings'''
parser.add_argument('--NSIM', type=int, default=1,
help = "How many times does this experiment need to be repeated?")
parser.add_argument('--DIM', type=int, default=2,
help = "Dimension of the Euclidean space of our interest")
parser.add_argument('--n_comp_tar', type=int, default=25,
help = "Number of mixture components in the target distribution")
parser.add_argument('--DRE', type=str, default='DRE_SP',
choices=['None', 'GT', 'DRE_uLSIF', 'DRE_DSKL', 'DRE_BARR', 'DRE_SP', 'disc', 'disc_MHcal', 'disc_KeepTrain'], #GT is ground truth
help='Density ratio estimation method; None means randomly sample from the proposal distribution or the trained GAN')
parser.add_argument('--Sampling', type=str, default='RS',
help='Sampling method; Candidiate: None, RS, MH, SIR') #RS: rejection sampling, MH: Metropolis-Hastings; SIR: Sampling-Importance Resampling
parser.add_argument('--seed', type=int, default=2019, metavar='S',
help='random seed (default: 2019)')
parser.add_argument('--show_reference', action='store_true', default=False,
help='Assign 1 as density ratios to all samples and compute errors')
parser.add_argument('--show_visualization', action='store_true', default=False,
help='Plot fake samples in 2D coordinate')
''' Data Generation '''
parser.add_argument('--NTRAIN', type=int, default=50000)
parser.add_argument('--NTEST', type=int, default=10000)
''' GAN settings '''
parser.add_argument('--epoch_gan', type=int, default=50) #default 50
parser.add_argument('--lr_gan', type=float, default=1e-3,
help='learning rate')
parser.add_argument('--dim_gan', type=int, default=2,
help='Latent dimension of GAN')
parser.add_argument('--batch_size_gan', type=int, default=512, metavar='N',
help='input batch size for training GAN')
parser.add_argument('--resumeTrain_gan', type=int, default=0)
parser.add_argument('--compute_disc_err', action='store_true', default=False,
help='Compute the distance between the discriminator and its optimality')
'''DRE Settings'''
parser.add_argument('--DR_Net', type=str, default='MLP5',
choices=['MLP3', 'MLP5', 'MLP7', 'MLP9',
'CNN5'],
help='DR Model') # DR models
parser.add_argument('--epoch_DRE', type=int, default=200)
parser.add_argument('--base_lr_DRE', type=float, default=1e-5,
help='learning rate')
parser.add_argument('--decay_lr_DRE', action='store_true', default=False,
help='decay learning rate')
parser.add_argument('--lr_decay_epochs_DRE', type=int, default=400)
parser.add_argument('--batch_size_DRE', type=int, default=512, metavar='N',
help='input batch size for training DRE')
parser.add_argument('--lambda_DRE', type=float, default=0.0, #BARR: lambda=10
help='penalty in DRE')
parser.add_argument('--weightdecay_DRE', type=float, default=0.0,
help='weight decay in DRE')
parser.add_argument('--resumeTrain_DRE', type=int, default=0)
parser.add_argument('--DR_final_ActFn', type=str, default='ReLU',
help='Final layer of the Density-ratio model; Candidiate: Softplus or ReLU')
parser.add_argument('--TrainPreNetDRE', action='store_true', default=False,
help='Pre-trained MLP for DRE in Feature Space')
parser.add_argument('--DRE_save_at_epoch', nargs='+', type=int)
parser.add_argument('--epoch_KeepTrain', type=int, default=20)
parser.add_argument('--compute_dre_err', action='store_true', default=False,
help='Compare the DRE method with the ground truth')
''' Mixture Gaussian (for density estimation) Settings '''
parser.add_argument('--gmm_nfake', type=int, default=100000)
# parser.add_argument('--gmm_ncomp', type=int, default=0) #gmm_ncomp is non-positive, then we do ncomp selection
parser.add_argument('--gmm_ncomp_nsim', nargs='+', type=int) #A list of ncomp for NSIM rounds. If gmm_ncomp is None, then we do ncomp selection
parser.add_argument('--gmm_ncomp_grid', nargs='+', type=int)
parser.add_argument('--gmm_ncomp_grid_lb', type=int, default=1)
parser.add_argument('--gmm_ncomp_grid_ub', type=int, default=100)
parser.add_argument('--gmm_ncomp_grid_step', type=int, default=1)
args = parser.parse_args()
#--------------------------------
# system
assert torch.cuda.is_available()
NGPU = torch.cuda.device_count()
device = torch.device("cuda" if NGPU>0 else "cpu")
cores= multiprocessing.cpu_count()
#--------------------------------
# Extra Data Generation Settings
n_comp_tar = args.n_comp_tar
n_features = args.DIM
mean_grid_tar = [-2, -1, 0, 1, 2]
sigma_tar = 0.05
n_classes = n_comp_tar
quality_threshold = sigma_tar*4 #good samples are within 4 standard deviation
#--------------------------------
# GAN Settings
epoch_GAN = args.epoch_gan
lr_GAN = args.lr_gan
batch_size_GAN = args.batch_size_gan
dim_GAN = args.dim_gan
plot_in_train = True
gan_Adam_beta1 = 0.5
gan_Adam_beta2 = 0.999
#--------------------------------
# Extra DRE Settings
DRE_Adam_beta1 = 0.5
DRE_Adam_beta2 = 0.999
comp_ratio_bs = 1000 #batch size for computing density ratios
base_lr_PreNetDRE = 1e-1
epoch_PreNetDRE = 100
DRE_save_at_epoch = args.DRE_save_at_epoch # save checkpoints at these epochs
# DRE_save_at_epoch = [20, 50, 100, 150, 200, 300, 400, 500, 800]
epoch_KeepTrain = args.epoch_KeepTrain #keep training for DRS
ckp_epoch_KeepTrain = [i for i in range(100) if i%5==0]
#--------------------------------
# Mixture Gaussian Setting
gmm_nfake = args.gmm_nfake
# gmm_ncomp = args.gmm_ncomp
gmm_ncomp_nsim = args.gmm_ncomp_nsim
# if gmm_ncomp_nsim is not None:
# assert len(gmm_ncomp_nsim) == args.NSIM
if args.gmm_ncomp_grid is not None:
gmm_ncomp_grid = args.gmm_ncomp_grid
else:
gmm_ncomp_grid = np.arange(args.gmm_ncomp_grid_lb, args.gmm_ncomp_grid_ub+args.gmm_ncomp_grid_step, args.gmm_ncomp_grid_step)
#--------------------------------
# Extra Sampling Settings
NFAKE = args.NTEST
samp_batch_size = 10000
MH_K = 100
MH_mute = True #do not print sampling progress
#-------------------------------
# seeds
random.seed(args.seed)
torch.manual_seed(args.seed)
torch.backends.cudnn.deterministic = True
| np.random.seed(args.seed) | numpy.random.seed |
import numpy as np
class SECS:
"""Spherical Elementary Current System (SECS).
The algorithm is implemented directly in spherical coordinates
from the equations of the 1999 Amm & Viljanen paper [1]_.
Parameters
----------
sec_df_loc : ndarray (nsec x 3 [lat, lon, r])
The latitude, longiutde, and radius of the divergence free (df) SEC locations.
sec_cf_loc : ndarray (nsec x 3 [lat, lon, r])
The latitude, longiutde, and radius of the curl free (cf) SEC locations.
References
----------
.. [1] <NAME>., and <NAME>. "Ionospheric disturbance magnetic field continuation
from the ground to the ionosphere using spherical elementary current systems."
Earth, Planets and Space 51.6 (1999): 431-440. doi:10.1186/BF03352247
"""
def __init__(self, sec_df_loc=None, sec_cf_loc=None):
if sec_df_loc is None and sec_cf_loc is None:
raise ValueError("Must initialize the object with SEC locations")
self.sec_df_loc = sec_df_loc
self.sec_cf_loc = sec_cf_loc
if self.sec_df_loc is not None:
self.sec_df_loc = np.asarray(sec_df_loc)
if self.sec_df_loc.shape[-1] != 3:
raise ValueError("SEC DF locations must have 3 columns (lat, lon, r)")
if self.sec_df_loc.ndim == 1:
# Add an empty dimension if only one SEC location is passed in
self.sec_df_loc = self.sec_df_loc[np.newaxis, ...]
if self.sec_cf_loc is not None:
self.sec_cf_loc = np.asarray(sec_cf_loc)
if self.sec_cf_loc.shape[-1] != 3:
raise ValueError("SEC CF locations must have 3 columns (lat, lon, r)")
if self.sec_cf_loc.ndim == 1:
# Add an empty dimension if only one SEC location is passed in
self.sec_cf_loc = self.sec_cf_loc[np.newaxis, ...]
# Storage of the scaling factors
self.sec_amps = None
self.sec_amps_var = None
@property
def has_df(self):
"""Whether this system has any divergence free currents."""
return self.sec_df_loc is not None
@property
def has_cf(self):
"""Whether this system has any curl free currents."""
return self.sec_cf_loc is not None
@property
def nsec(self):
"""The number of elementary currents in this system."""
nsec = 0
if self.has_df:
nsec += len(self.sec_df_loc)
if self.has_cf:
nsec += len(self.sec_cf_loc)
return nsec
def fit(self, obs_loc, obs_B, obs_std=None, epsilon=0.05):
"""Fits the SECS to the given observations.
Given a number of observation locations and measurements,
this function fits the SEC system to them. It uses singular
value decomposition (SVD) to fit the SEC amplitudes with the
`epsilon` parameter used to regularize the solution.
Parameters
----------
obs_locs : ndarray (nobs x 3 [lat, lon, r])
Contains latitude, longitude, and radius of the observation locations
(place where the measurements are made)
obs_B: ndarray (ntimes x nobs x 3 [Bx, By, Bz])
An array containing the measured/observed B-fields.
obs_std : ndarray (ntimes x nobs x 3 [varX, varY, varZ]), optional
Standard error of vector components at each observation location.
This can be used to weight different observations more/less heavily.
An infinite value eliminates the observation from the fit.
Default: ones(nobs x 3) equal weights
epsilon : float
Value used to regularize/smooth the SECS amplitudes. Multiplied by the
largest singular value obtained from SVD.
Default: 0.05
"""
if obs_loc.shape[-1] != 3:
raise ValueError("Observation locations must have 3 columns (lat, lon, r)")
if obs_B.ndim == 2:
# Just a single snapshot given, so expand the dimensionality
obs_B = obs_B[np.newaxis, ...]
# Assume unit standard error of all measurements
if obs_std is None:
obs_std = np.ones(obs_B.shape)
ntimes = len(obs_B)
# Calculate the transfer functions
T_obs = self._calc_T(obs_loc)
# Store the fit sec_amps in the object
self.sec_amps = np.empty((ntimes, self.nsec))
self.sec_amps_var = np.empty((ntimes, self.nsec))
# Calculate the singular value decomposition (SVD)
# NOTE: T_obs has shape (nobs, 3, nsec), we reshape it
# to (nobs*3, nsec); obs_std has shape (ntimes, nobs, 3),
# we reshape it to (ntimes, nobs*3), then loop over ntimes
# to solve using (potentially) time-dependent observation
# standard errors to weight the observations
for i in range(ntimes):
# Only (re-)calculate SVD when necessary
if i == 0 or not np.all(obs_std[i] == obs_std[i-1]):
# Weight T_obs with obs_std
svd_in = (T_obs.reshape(-1, self.nsec) /
obs_std[i].ravel()[:, np.newaxis])
# Find singular value decompostion
U, S, Vh = np.linalg.svd(svd_in, full_matrices=False)
# Eliminate singular values less than epsilon by setting their
# reciprocal to zero (setting S to infinity firsts avoids
# divide-by-zero warings)
S[S < epsilon * S.max()] = np.inf
W = 1./S
# Update VWU if obs_std changed
VWU = Vh.T @ (np.diag(W) @ U.T)
# Solve for SEC amplitudes and error variances
# shape: ntimes x nsec
self.sec_amps[i, :] = (VWU @ (obs_B[i] / obs_std[i]).reshape(-1).T).T
# Maybe we want the variance of the predictions sometime later...?
# shape: ntimes x nsec
valid = np.isfinite(obs_std[i].reshape(-1))
self.sec_amps_var[i, :] = np.sum(
(VWU[:,valid] * obs_std[i].reshape(-1)[valid])**2,
axis=1)
return self
def fit_unit_currents(self):
"""Sets all SECs to a unit current amplitude."""
self.sec_amps = np.ones((1, self.nsec))
return self
def predict(self, pred_loc, J=False):
"""Calculate the predicted magnetic field or currents.
After a set of observations has been fit to this system we can
predict the magnetic fields or currents at any other location. This
function uses those fit amplitudes to predict at the requested locations.
Parameters
----------
pred_loc: ndarray (npred x 3 [lat, lon, r])
An array containing the locations where the predictions are desired.
J: boolean
Whether to predict currents (J=True) or magnetic fields (J=False)
Default: False (magnetic field prediction)
Returns
-------
ndarray (ntimes x npred x 3 [lat, lon, r])
The predicted values calculated from the current amplitudes that were
fit to this system.
"""
if pred_loc.shape[-1] != 3:
raise ValueError("Prediction locations must have 3 columns (lat, lon, r)")
if self.sec_amps is None:
raise ValueError("There are no currents associated with the SECs," +
"you need to call .fit() first to fit to some observations.")
# T_pred shape=(npred x 3 x nsec)
# sec_amps shape=(nsec x ntimes)
if J:
# Predicting currents
T_pred = self._calc_J(pred_loc)
else:
# Predicting magnetic fields
T_pred = self._calc_T(pred_loc)
# NOTE: dot product is slow on multi-dimensional arrays (i.e. > 2 dimensions)
# Therefore this is implemented as tensordot, and the arguments are
# arranged to eliminate needs of transposing things later.
# The dot product is done over the SEC locations, so the final output
# is of shape: (ntimes x npred x 3)
return np.squeeze(np.tensordot(self.sec_amps, T_pred, (1, 2)))
def predict_B(self, pred_loc):
"""Calculate the predicted magnetic fields.
After a set of observations has been fit to this system we can
predict the magnetic fields or currents at any other location. This
function uses those fit amplitudes to predict at the requested locations.
Parameters
----------
pred_loc: ndarray (npred x 3 [lat, lon, r])
An array containing the locations where the predictions are desired.
Returns
-------
ndarray (ntimes x npred x 3 [lat, lon, r])
The predicted values calculated from the current amplitudes that were
fit to this system.
"""
return self.predict(pred_loc)
def predict_J(self, pred_loc):
"""Calculate the predicted currents.
After a set of observations has been fit to this system we can
predict the magnetic fields or currents at any other location. This
function uses those fit amplitudes to predict at the requested locations.
Parameters
----------
pred_loc: ndarray (npred x 3 [lat, lon, r])
An array containing the locations where the predictions are desired.
Returns
-------
ndarray (ntimes x npred x 3 [lat, lon, r])
The predicted values calculated from the current amplitudes that were
fit to this system.
"""
return self.predict(pred_loc, J=True)
def _calc_T(self, obs_loc):
"""Calculates the T transfer matrix.
The magnetic field transfer matrix to go from SEC locations to observation
locations. It assumes unit current amplitudes that will then be
scaled with the proper amplitudes later.
"""
if self.has_df:
T = T_df(obs_loc=obs_loc, sec_loc=self.sec_df_loc)
if self.has_cf:
T1 = T_cf(obs_loc=obs_loc, sec_loc=self.sec_cf_loc)
# df is already present in T
if self.has_df:
T = np.concatenate([T, T1], axis=2)
else:
T = T1
return T
def _calc_J(self, obs_loc):
"""Calculates the J transfer matrix.
The current transfer matrix to go from SEC locations to observation
locations. It assumes unit current amplitudes that will then be
scaled with the proper amplitudes later.
"""
if self.has_df:
J = J_df(obs_loc=obs_loc, sec_loc=self.sec_df_loc)
if self.has_cf:
J1 = J_cf(obs_loc=obs_loc, sec_loc=self.sec_cf_loc)
# df is already present in T
if self.has_df:
J = np.concatenate([J, J1], axis=2)
else:
J = J1
return J
def T_df(obs_loc, sec_loc):
"""Calculates the divergence free magnetic field transfer function.
The transfer function goes from SEC location to observation location
and assumes unit current SECs at the given locations.
Parameters
----------
obs_loc : ndarray (nobs, 3 [lat, lon, r])
The locations of the observation points.
sec_loc : ndarray (nsec, 3 [lat, lon, r])
The locations of the SEC points.
Returns
-------
ndarray (nobs, 3, nsec)
The T transfer matrix.
"""
nobs = len(obs_loc)
nsec = len(sec_loc)
obs_r = obs_loc[:, 2][:, np.newaxis]
sec_r = sec_loc[:, 2][np.newaxis, :]
theta = calc_angular_distance(obs_loc[:, :2], sec_loc[:, :2])
alpha = calc_bearing(obs_loc[:, :2], sec_loc[:, :2])
# magnetic permeability
mu0 = 4*np.pi*1e-7
# simplify calculations by storing this ratio
x = obs_r/sec_r
sin_theta = np.sin(theta)
cos_theta = np.cos(theta)
factor = 1./np.sqrt(1 - 2*x*cos_theta + x**2)
# Amm & Viljanen: Equation 9
Br = mu0/(4*np.pi*obs_r) * (factor - 1)
# Amm & Viljanen: Equation 10 (transformed to try and eliminate trig operations and
# divide by zeros)
Btheta = -mu0/(4*np.pi*obs_r) * (factor*(x - cos_theta) + cos_theta)
# If sin(theta) == 0: Btheta = 0
# There is a possible 0/0 in the expansion when sec_loc == obs_loc
Btheta = np.divide(Btheta, sin_theta, out=np.zeros_like(sin_theta),
where=sin_theta != 0)
# When observation points radii are outside of the sec locations
under_locs = sec_r < obs_r
# NOTE: If any SECs are below observations the math will be done on all points.
# This could be updated to only work on the locations where this condition
# occurs, but would make the code messier, with minimal performance gain
# except for very large matrices.
if np.any(under_locs):
# Flipped from previous case
x = sec_r/obs_r
# Amm & Viljanen: Equation A.7
Br2 = mu0*x/(4*np.pi*obs_r) * (1./np.sqrt(1 - 2*x*cos_theta + x**2) - 1)
# Amm & Viljanen: Equation A.8
Btheta2 = - mu0 / (4*np.pi*obs_r) * ((obs_r-sec_r*cos_theta) /
np.sqrt(obs_r**2 -
2*obs_r*sec_r*cos_theta +
sec_r**2) - 1)
Btheta2 = np.divide(Btheta2, sin_theta, out=np.zeros_like(sin_theta),
where=sin_theta != 0)
# Update only the locations where secs are under observations
Btheta[under_locs] = Btheta2[under_locs]
Br[under_locs] = Br2[under_locs]
# Transform back to Bx, By, Bz at each local point
T = np.empty((nobs, 3, nsec))
# alpha == angle (from cartesian x-axis (By), going towards y-axis (Bx))
T[:, 0, :] = -Btheta*np.sin(alpha)
T[:, 1, :] = -Btheta*np.cos(alpha)
T[:, 2, :] = -Br
return T
def T_cf(obs_loc, sec_loc):
"""Calculates the curl free magnetic field transfer function.
The transfer function goes from SEC location to observation location
and assumes unit current SECs at the given locations.
Parameters
----------
obs_loc : ndarray (nobs, 3 [lat, lon, r])
The locations of the observation points.
sec_loc : ndarray (nsec, 3 [lat, lon, r])
The locations of the SEC points.
Returns
-------
ndarray (nobs, 3, nsec)
The T transfer matrix.
"""
raise NotImplementedError("Curl Free Magnetic Field Transfers are not implemented yet.")
def J_df(obs_loc, sec_loc):
"""Calculates the divergence free current density transfer function.
The transfer function goes from SEC location to observation location
and assumes unit current SECs at the given locations.
Parameters
----------
obs_loc : ndarray (nobs, 3 [lat, lon, r])
The locations of the observation points.
sec_loc : ndarray (nsec, 3 [lat, lon, r])
The locations of the SEC points.
Returns
-------
ndarray (nobs, 3, nsec)
The J transfer matrix.
"""
nobs = len(obs_loc)
nsec = len(sec_loc)
obs_r = obs_loc[:, 2][:, np.newaxis]
sec_r = sec_loc[:, 2][np.newaxis, :]
# Input to the distance calculations is degrees, output is in radians
theta = calc_angular_distance(obs_loc[:, :2], sec_loc[:, :2])
alpha = calc_bearing(obs_loc[:, :2], sec_loc[:, :2])
# Amm & Viljanen: Equation 6
tan_theta2 = np.tan(theta/2.)
J_phi = 1./(4*np.pi*sec_r)
J_phi = np.divide(J_phi, tan_theta2, out=np.ones_like(tan_theta2)*np.inf,
where=tan_theta2 != 0.)
# Only valid on the SEC shell
J_phi[sec_r != obs_r] = 0.
# Transform back to Bx, By, Bz at each local point
J = | np.empty((nobs, 3, nsec)) | numpy.empty |
import cv2
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import numpy as np
from dataclasses import dataclass, field
from typing import List
from camera_distortion import load_camera_precalculated_coefficients, correct_camera_distortion
from threshold import get_binary_image
from perspective import warp_image
from utility import get_input_path, get_output_folder_path
def transform_image(image, show_process=False):
camera_matrix, distortion_coeff = load_camera_precalculated_coefficients()
undistort_image = correct_camera_distortion(image, camera_matrix, distortion_coeff)
binary_image = get_binary_image(undistort_image)
binary_warped, M = warp_image(binary_image)
if show_process:
fig, ax = plt.subplots(3)
ax[0].imshow(undistort_image)
ax[1].imshow(binary_image, cmap="gray")
ax[2].imshow(binary_warped, cmap="gray")
plt.show()
return M, binary_warped
@dataclass
class LanePolynominal:
current_fit: List[float] = None
last_best_fit: List[float] = None
previous_fits: List[List[float]] = field(default_factory=list)
detected: bool = False
def fit_polynominal(self, lanex, laney, side):
try:
self.current_fit = np.polyfit(laney, lanex, 2)
self.previous_fits.append(self.current_fit)
self.detected = True
self.last_best_fit = np.mean(self.previous_fits[-4:], axis=0)
except Exception:
if len(self.previous_fits) == 1:
self.previous_fits = []
self.detected = False
return self.last_best_fit
class LaneDetector:
LEFT_LANE = "left"
RIGHT_LANE = "right"
def __init__(self):
self.left_lane = LanePolynominal()
self.right_lane = LanePolynominal()
# Set Hyperparamaters
self.nwindows = 30
# Set the width of the windows +/- margin
self.margin = 100
# Set minimum number of pixels found to recenter window
self.minpix = 50
# Set height of windows - based on nwindows above and image shape
def _get_lane_centers(self, binary_warped, draw_windows=False):
histogram = np.sum(binary_warped[binary_warped.shape[0] // 2 :, :], axis=0)
if draw_windows:
plt.figure()
plt.plot(histogram)
# Find the peak of the left and right halves of the histogram
# These will be the starting point for the left and right lines
midpoint = np.int(histogram.shape[0] // 2)
leftx_base = np.argmax(histogram[:midpoint])
rightx_base = np.argmax(histogram[midpoint:]) + midpoint
return leftx_base, rightx_base
def get_lanes(self, binary_warped, draw=False):
# left_fit = self.left_fits[-1] if self.left_fits is not [] and self.left_fits[-1] != None else None
# right_fit = self.right_fits[-1] if self.right_fits is not [] and self.right_fits[-1] != None else None
if self.left_lane.detected is True and self.right_lane.detected is True:
left_fitx, right_fitx, ploty = self._search_around_prior_poly(binary_warped, draw)
self.window_height = np.int(binary_warped.shape[0] // self.nwindows)
self.left_lane_tracker = True
self.right_lane_tracker = True
windows_img = np.dstack((binary_warped, binary_warped, binary_warped))
width, height = height, width = binary_warped.shape[:2]
# Identify the x and y positions of all nonzero pixels in the image
nonzero = binary_warped.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
# Current positions to be updated later for each window in nwindows
leftx_base, rightx_base = self._get_lane_centers(binary_warped)
# Create empty lists to receive left and right lane pixel indices
left_lane_inds = []
right_lane_inds = []
leftx_current = leftx_base
rightx_current = rightx_base
counter = 0
for window in range(self.nwindows):
if self.left_lane_tracker:
good_left_inds, leftx_current = self._sliding_window(
window,
leftx_current,
nonzerox,
nonzeroy,
height,
width,
"left",
windows_img,
counter,
draw_windows=draw,
)
left_lane_inds.append(good_left_inds)
if self.right_lane_tracker:
good_right_inds, rightx_current = self._sliding_window(
window,
rightx_current,
nonzerox,
nonzeroy,
height,
width,
"right",
windows_img,
counter,
draw_windows=draw,
)
right_lane_inds.append(good_right_inds)
if self.left_lane_tracker and self.right_lane_tracker:
counter += 1
if not self.left_lane_tracker and not self.right_lane_tracker:
break
left_lane_inds = np.concatenate(left_lane_inds)
right_lane_inds = np.concatenate(right_lane_inds)
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds]
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds]
if draw:
fig = plt.figure()
fig.suptitle("Windows")
plt.imshow(windows_img)
left_fitx, right_fitx, ploty = self._get_polynominals(binary_warped, leftx, lefty, rightx, righty)
out_img = np.dstack((binary_warped, binary_warped, binary_warped))
out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [0, 0, 255]
return left_fitx, right_fitx, ploty, out_img
def _sliding_window(
self, window, lanex_current, nonzerox, nonzeroy, height, width, side, out_img, counter, draw_windows=False
):
win_y_low = height - (window + 1) * self.window_height
win_y_high = height - window * self.window_height
win_xlane_low = lanex_current - self.margin
win_xlane_high = lanex_current + self.margin
if draw_windows:
cv2.rectangle(out_img, (win_xlane_low, win_y_low), (win_xlane_high, win_y_high), (0, 255, 0), 2)
good_lane_inds = (
(nonzeroy >= win_y_low)
& (nonzeroy < win_y_high)
& (nonzerox >= win_xlane_low)
& (nonzerox < win_xlane_high)
).nonzero()[0]
if (win_xlane_high > width or win_xlane_low < 0) and counter >= 5:
if side == self.LEFT_LANE:
self.left_lane_tracker = False
elif side == self.RIGHT_LANE:
self.right_lane_tracker = False
### f you found > minpix pixels, recenter next window ###
### (`right` or `leftx_current`) on their mean position ###
if len(good_lane_inds) > self.minpix:
lanex_current = np.int(np.mean(nonzerox[good_lane_inds]))
return good_lane_inds, lanex_current
def _search_around_prior_poly(self, binary_warped, draw_windows=False):
# Take last polynominals
left_fit = self.left_lane.previous_fits[-1]
right_fit = self.right_lane.previous_fits[-1]
# Grab activated pixels
nonzero = binary_warped.nonzero()
nonzeroy = | np.array(nonzero[0]) | numpy.array |
# -*- coding: utf-8 -*-
"""
Created on Tues at some point in time
@author: bokorn with some code pulled from https://github.com/yuxng/PoseCNN/blob/master/lib/datasets/lov.py
"""
import os
import cv2
import torch
import numpy as np
import scipy.io as sio
import time
import sys
from se3_distributions.datasets.image_dataset import PoseImageDataset
from se3_distributions.datasets.ycb_data_processing import preprocessPoseCNNMetaData
from se3_distributions.utils import SingularArray
import se3_distributions.utils.transformations as tf_trans
from se3_distributions.utils.pose_processing import viewpoint2Pose
from se3_distributions.utils.image_preprocessing import cropAndPad
from transforms3d.quaternions import quat2mat, mat2quat
def ycbRenderTransform(q):
trans_quat = q.copy()
trans_quat = tf_trans.quaternion_multiply(trans_quat, tf_trans.quaternion_about_axis(-np.pi/2, [1,0,0]))
return viewpoint2Pose(trans_quat)
def setYCBCamera(renderer, width=640, height=480):
fx = 1066.778
fy = 1067.487
px = 312.9869
py = 241.3109
renderer.setCameraMatrix(fx, fy, px, py, width, height)
def getYCBSymmeties(obj):
if(obj == 13):
return [[0,0,1]], [[np.inf]]
elif(obj == 16):
return [[0.9789,-0.2045,0.], [0.,0.,1.]], [[0.,np.pi], [0.,np.pi/2,np.pi,3*np.pi/2]]
elif(obj == 19):
return [[-0.14142136, 0.98994949,0]], [[0.,np.pi]]
elif(obj == 20):
return [[0.9931506 , 0.11684125,0]], [[0.,np.pi]]
elif(obj == 21):
return [[0.,0.,1.]], [[0.,np.pi]]
else:
return [],[]
class YCBDataset(PoseImageDataset):
def __init__(self, data_dir, image_set,
obj = None, use_syn_data = False,
use_posecnn_masks = False,
*args, **kwargs):
super(YCBDataset, self).__init__(*args, **kwargs)
self.use_syn_data = use_syn_data
self.data_dir = data_dir
#self.classes = ('__background__', '002_master_chef_can', '003_cracker_box', '004_sugar_box', '005_tomato_soup_can', '006_mustard_bottle', \
# '007_tuna_fish_can', '008_pudding_box', '009_gelatin_box', '010_potted_meat_can', '011_banana', '019_pitcher_base', \
# '021_bleach_cleanser', '024_bowl', '025_mug', '035_power_drill', '036_wood_block', '037_scissors', '040_large_marker', \
# '051_large_clamp', '052_extra_large_clamp', '061_foam_brick')
self.classes = ['__background__']
with open(os.path.join(self.data_dir, 'image_sets', 'classes.txt')) as f:
self.classes.extend([x.rstrip('\n') for x in f.readlines()])
self.num_classes = len(self.classes)
self.model_filenames = {}
for j in range(1, self.num_classes):
self.model_filenames[j] = os.path.join(self.data_dir, 'models', self.classes[j], 'textured.obj')
self.symmetry = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1])
self.image_set = image_set
self.append_rendered = False
self.use_posecnn_masks = use_posecnn_masks
#self.data_filenames = self.loadImageSet()
if(obj is not None):
self.setObject(obj)
#self.points, self.points_all = self.load_object_points()
def getSymmetry(self):
return getYCBSymmeties(self.obj)
def loadObjectPoints(self):
points = [[] for _ in xrange(len(self.classes))]
num = np.inf
for i in xrange(1, len(self.classes)):
point_file = os.path.join(self.data_dir, 'models', self.classes[i], 'points.xyz')
#print point_file
assert os.path.exists(point_file), 'Path does not exist: {}'.format(point_file)
points[i] = | np.loadtxt(point_file) | numpy.loadtxt |
#==============================================================================
# WELCOME
#==============================================================================
# Welcome to RainyDay, a framework for coupling remote sensing precipitation
# fields with Stochastic Storm Transposition for assessment of rainfall-driven hazards.
# Copyright (C) 2017 <NAME> (<EMAIL>)
#
#Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
#The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
#THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.#
#==============================================================================
# THIS DOCUMENT CONTAINS VARIOUS FUNCTIONS NEEDED TO RUN RainyDay
#==============================================================================
import os
import sys
import numpy as np
import scipy as sp
import glob
import math
from datetime import datetime, date, time, timedelta
import time
from copy import deepcopy
from mpl_toolkits.basemap import Basemap, addcyclic
from matplotlib.patches import Polygon
from scipy import stats
from netCDF4 import Dataset, num2date, date2num
#import gdal
import rasterio
import pandas as pd
from numba import prange,jit
import shapely
import geopandas as gp
from scipy.stats import norm
from scipy.stats import lognorm
# plotting stuff, really only needed for diagnostic plots
import matplotlib.pyplot as plt
import matplotlib
from matplotlib.colors import LogNorm
import subprocess
try:
os.environ.pop('PYTHONIOENCODING')
except KeyError:
pass
import warnings
warnings.filterwarnings("ignore")
from numba.types import int32,int64,float32,uint32
import linecache
GEOG="+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs"
# =============================================================================
# Smoother that is compatible with nan values. Adapted from https://stackoverflow.com/questions/18697532/gaussian-filtering-a-image-with-nan-in-python
# =============================================================================
def mysmoother(inarray,sigma=[3,3]):
if len(sigma)!=len(inarray.shape):
sys.exit("there seems to be a mismatch between the sigma dimension and the dimension of the array you are trying to smooth")
V=inarray.copy()
V[np.isnan(inarray)]=0.
VV=sp.ndimage.gaussian_filter(V,sigma=sigma)
W=0.*inarray.copy()+1.
W[np.isnan(inarray)]=0.
WW=sp.ndimage.gaussian_filter(W,sigma=sigma)
outarray=VV/WW
outarray[np.isnan(inarray)]=np.nan
return outarray
def my_kde_bandwidth(obj, fac=1): # this 1.5 choice is completely subjective :(
#We use Scott's Rule, multiplied by a constant factor
return np.power(obj.n, -1./(obj.d+4)) * fac
def convert_3D_2D(geometry):
'''
Takes a GeoSeries of 3D Multi/Polygons (has_z) and returns a list of 2D Multi/Polygons
'''
new_geo = []
for p in geometry:
if p.has_z:
if p.geom_type == 'Polygon':
lines = [xy[:2] for xy in list(p.exterior.coords)]
new_p = shapely.geometry.Polygon(lines)
new_geo.append(new_p)
elif p.geom_type == 'MultiPolygon':
new_multi_p = []
for ap in p:
lines = [xy[:2] for xy in list(ap.exterior.coords)]
new_p = shapely.geometry.Polygon(lines)
new_multi_p.append(new_p)
new_geo.append(shapely.geometry.MultiPolygon(new_multi_p))
return new_geo
#==============================================================================
# LOOP TO DO SPATIAL SEARCHING FOR MAXIMUM RAINFALL LOCATION AT EACH TIME STEP
# THIS IS THE CORE OF THE STORM CATALOG CREATION TECHNIQUE
#==============================================================================
#def catalogweave(temparray,trimmask,xlen,ylen,maskheight,maskwidth,rainsum):
# rainsum[:]=0.
# code= """
# #include <stdio.h>
# int i,j,x,y;
# for (x=0;x<xlen;x++) {
# for (y=0;y<ylen;y++) {
# for (j=0;j<maskheight;j++) {
# for (i=0;i<maskwidth;i++) {
# rainsum(y,x)=rainsum(y,x)+temparray(y+j,x+i)*trimmask(j,i);
# }
# }
# }
# }
# """
# vars=['temparray','trimmask','xlen','ylen','maskheight','maskwidth','rainsum']
# sp.weave.inline(code,vars,type_converters=converters.blitz,compiler='gcc')
# rmax=np.nanmax(rainsum)
# wheremax=np.where(rainsum==rmax)
# return rmax, wheremax[0][0], wheremax[1][0]
#
def catalogAlt(temparray,trimmask,xlen,ylen,maskheight,maskwidth,rainsum,domainmask):
rainsum[:]=0.
for i in range(0,(ylen)*(xlen)):
y=i//xlen
x=i-y*xlen
#print x,
rainsum[y,x]=np.nansum(np.multiply(temparray[(y):(y+maskheight),(x):(x+maskwidth)],trimmask))
#wheremax=np.argmax(rainsum)
rmax=np.nanmax(rainsum)
wheremax=np.where(rainsum==rmax)
return rmax, wheremax[0][0], wheremax[1][0]
def catalogAlt_irregular(temparray,trimmask,xlen,ylen,maskheight,maskwidth,rainsum,domainmask):
rainsum[:]=0.
for i in range(0,(ylen)*(xlen)):
y=i//xlen
x=i-y*xlen
#print x,y
if np.any(np.equal(domainmask[y+maskheight/2,x:x+maskwidth],1.)) and np.any(np.equal(domainmask[y:y+maskheight,x+maskwidth/2],1.)):
rainsum[y,x]=np.nansum(np.multiply(temparray[(y):(y+maskheight),(x):(x+maskwidth)],trimmask))
else:
rainsum[y,x]=0.
#wheremax=np.argmax(rainsum)
rmax=np.nanmax(rainsum)
wheremax=np.where(rainsum==rmax)
return rmax, wheremax[0][0], wheremax[1][0]
@jit(nopython=True,fastmath=True)
def catalogNumba_irregular(temparray,trimmask,xlen,ylen,maskheight,maskwidth,rainsum,domainmask):
rainsum[:]=0.
halfheight=int32(np.ceil(maskheight/2))
halfwidth=int32(np.ceil(maskwidth/2))
for i in range(0,ylen*xlen):
y=i//xlen
x=i-y*xlen
#print x,y
if np.any(np.equal(domainmask[y+halfheight,x:x+maskwidth],1.)) and np.any(np.equal(domainmask[y:y+maskheight,x+halfwidth],1.)):
rainsum[y,x]=np.nansum(np.multiply(temparray[y:(y+maskheight),x:(x+maskwidth)],trimmask))
else:
rainsum[y,x]=0.
#wheremax=np.argmax(rainsum)
rmax=np.nanmax(rainsum)
wheremax=np.where(np.equal(rainsum,rmax))
return rmax, wheremax[0][0], wheremax[1][0]
@jit(nopython=True)
def catalogNumba(temparray,trimmask,xlen,ylen,maskheight,maskwidth,rainsum):
rainsum[:]=0.
for i in range(0,(ylen)*(xlen)):
y=i//xlen
x=i-y*xlen
#print x,y
rainsum[y,x]=np.nansum(np.multiply(temparray[(y):(y+maskheight),(x):(x+maskwidth)],trimmask))
#wheremax=np.argmax(rainsum)
rmax=np.nanmax(rainsum)
wheremax=np.where(np.equal(rainsum,rmax))
return rmax, wheremax[0][0], wheremax[1][0]
@jit(nopython=True)
def DistributionBuilder(intenserain,tempmax,xlen,ylen,checksep):
for y in np.arange(0,ylen):
for x in np.arange(0,xlen):
if np.any(checksep[:,y,x]):
#fixind=np.where(checksep[:,y,x]==True)
for i in np.arange(0,checksep.shape[0]):
if checksep[i,y,x]==True:
fixind=i
break
if tempmax[y,x]>intenserain[fixind,y,x]:
intenserain[fixind,y,x]=tempmax[y,x]
checksep[:,y,x]=False
checksep[fixind,y,x]=True
else:
checksep[fixind,y,x]=False
elif tempmax[y,x]>np.min(intenserain[:,y,x]):
fixind=np.argmin(intenserain[:,y,x])
intenserain[fixind,y,x]=tempmax[y,x]
checksep[fixind,y,x]=True
return intenserain,checksep
# slightly faster numpy-based version of above
def DistributionBuilderFast(intenserain,tempmax,xlen,ylen,checksep):
minrain=np.min(intenserain,axis=0)
if np.any(checksep):
flatsep=np.any(checksep,axis=0)
minsep=np.argmax(checksep[:,flatsep],axis=0)
islarger=np.greater(tempmax[flatsep],intenserain[minsep,flatsep])
if np.any(islarger):
intenserain[minsep,flatsep][islarger]=tempmax[flatsep][islarger]
checksep[:]=False
checksep[minsep,flatsep]=True
else:
checksep[minsep,flatsep]=False
elif np.any(np.greater(tempmax,minrain)):
#else:
fixind=np.greater(tempmax,minrain)
minrainind=np.argmin(intenserain,axis=0)
intenserain[minrainind[fixind],fixind]=tempmax[fixind]
checksep[minrainind[fixind],fixind]=True
return intenserain,checksep
#def SSTalt(passrain,sstx,ssty,trimmask,maskheight,maskwidth,intense_data=False):
# rainsum=np.zeros((len(sstx)),dtype='float32')
# nreals=len(rainsum)
#
# for i in range(0,nreals):
# rainsum[i]=np.nansum(np.multiply(passrain[(ssty[i]) : (ssty[i]+maskheight) , (sstx[i]) : (sstx[i]+maskwidth)],trimmask))
# return rainsum
@jit(fastmath=True)
def SSTalt(passrain,sstx,ssty,trimmask,maskheight,maskwidth,intensemean=None,intensestd=None,intensecorr=None,homemean=None,homestd=None,durcheck=False):
maxmultiplier=1.5
rainsum=np.zeros((len(sstx)),dtype='float32')
whichstep=np.zeros((len(sstx)),dtype='int32')
nreals=len(rainsum)
nsteps=passrain.shape[0]
multiout=np.empty_like(rainsum)
if (intensemean is not None) and (homemean is not None):
domean=True
else:
domean=False
if (intensestd is not None) and (intensecorr is not None) and (homestd is not None):
#rquant=np.random.random_integers(5,high=95,size=nreals)/100.
rquant=np.random.random_sample(size=nreals)
doall=True
else:
doall=False
rquant=np.nan
if durcheck==False:
exprain=np.expand_dims(passrain,0)
else:
exprain=passrain
for k in range(0,nreals):
y=int(ssty[k])
x=int(sstx[k])
if np.all(np.less(exprain[:,y:y+maskheight,x:x+maskwidth],0.5)):
rainsum[k]=0.
multiout[k]=-999.
else:
if domean:
#sys.exit('need to fix short duration part')
muR=homemean-intensemean[y,x]
if doall:
stdR=np.sqrt(np.power(homestd,2)+np.power(intensestd[y,x],2)-2.*intensecorr[y,x]*homestd*intensestd[y,x])
# multiplier=sp.stats.lognorm.ppf(rquant[k],stdR,loc=0,scale=np.exp(muR))
#multiplier=10.
#while multiplier>maxmultiplier: # who knows what the right number is to use here...
inverrf=sp.special.erfinv(2.*rquant-1.)
multiplier=np.exp(muR+np.sqrt(2.*np.power(stdR,2))*inverrf[k])
#multiplier=np.random.lognormal(muR,stdR)
if multiplier>maxmultiplier:
multiplier=1.
else:
multiplier=np.exp(muR)
if multiplier>maxmultiplier:
multiplier=1.
else:
multiplier=1.
# print("still going!")
if multiplier>maxmultiplier:
sys.exit("Something seems to be going horribly wrong in the multiplier scheme!")
else:
multiout[k]=multiplier
if durcheck==True:
storesum=0.
storestep=0
for kk in range(0,nsteps):
#tempsum=numba_multimask_calc(passrain[kk,:],rsum,train,trimmask,ssty[k],maskheight,sstx[k],maskwidth)*multiplier
tempsum=numba_multimask_calc(passrain[kk,:],trimmask,y,x,maskheight,maskwidth)*multiplier
if tempsum>storesum:
storesum=tempsum
storestep=kk
rainsum[k]=storesum
whichstep[k]=storestep
else:
rainsum[k]=numba_multimask_calc(passrain,trimmask,y,x,maskheight,maskwidth)*multiplier
if domean:
return rainsum,multiout,whichstep
else:
return rainsum,whichstep
#@jit(nopython=True,fastmath=True,parallel=True)
@jit(nopython=True,fastmath=True)
def numba_multimask_calc(passrain,trimmask,ssty,sstx,maskheight,maskwidth):
train=np.multiply(passrain[ssty : ssty+maskheight , sstx : sstx+maskwidth],trimmask)
rainsum=np.sum(train)
return rainsum
@jit(fastmath=True)
def SSTalt_singlecell(passrain,sstx,ssty,trimmask,maskheight,maskwidth,intensemean=None,intensestd=None,intensecorr=None,homemean=None,homestd=None,durcheck=False):
rainsum=np.zeros((len(sstx)),dtype='float32')
whichstep=np.zeros((len(sstx)),dtype='int32')
nreals=len(rainsum)
nsteps=passrain.shape[0]
multiout=np.empty_like(rainsum)
# do we do deterministic or dimensionless rescaling?
if (intensemean is not None) and (homemean is not None):
domean=True
else:
domean=False
# do we do stochastic rescaling?
if (intensestd is not None) and (intensecorr is not None) and (homestd is not None):
rquant=np.random.random_sample(size=nreals)
inverrf=sp.special.erfinv(2.*rquant-1.)
doall=True
else:
doall=False
#rquant=np.nan
if durcheck==False:
passrain=np.expand_dims(passrain,0)
# deterministic or dimensionless:
if domean and doall==False:
rain,multi,step=killerloop_singlecell(passrain,rainsum,whichstep,nreals,ssty,sstx,nsteps,durcheck=durcheck,intensemean=intensemean,homemean=homemean,multiout=multiout)
return rain,multi,step
# stochastic:
elif doall:
rain,multi,step=killerloop_singlecell(passrain,rainsum,whichstep,nreals,ssty,sstx,nsteps,durcheck=durcheck,intensemean=intensemean,intensestd=intensestd,intensecorr=intensecorr,homemean=homemean,homestd=homestd,multiout=multiout,inverrf=inverrf)
return rain,multi,step
# no rescaling:
else:
rain,_,step=killerloop_singlecell(passrain,rainsum,whichstep,nreals,ssty,sstx,nsteps,durcheck=durcheck,multiout=multiout)
return rain,step
#@jit(nopython=True,fastmath=True,parallel=True)
@jit(nopython=True,fastmath=True)
def killerloop_singlecell(passrain,rainsum,whichstep,nreals,ssty,sstx,nsteps,durcheck=False,intensemean=None,homemean=None,homestd=None,multiout=None,rquant=None,intensestd=None,intensecorr=None,inverrf=None):
maxmultiplier=1.5 # who knows what the right number is to use here...
for k in prange(nreals):
y=int(ssty[k])
x=int(sstx[k])
# deterministic or dimensionless:
if (intensemean is not None) and (homemean is not None) and (homestd is None):
if np.less(homemean,0.001) or np.less(intensemean[y,x],0.001):
multiplier=1. # or maybe this should be zero
else:
multiplier=np.exp(homemean-intensemean[y,x])
if multiplier>maxmultiplier:
multiplier=1. # or maybe this should be zero
# stochastic:
elif (intensemean is not None) and (homemean is not None) and (homestd is not None):
if np.less(homemean,0.001) or np.less(intensemean[y,x],0.001):
multiplier=1. # or maybe this should be zero
else:
muR=homemean-intensemean[y,x]
stdR=np.sqrt(np.power(homestd,2)+np.power(intensestd[y,x],2)-2*intensecorr[y,x]*homestd*intensestd[y,x])
multiplier=np.exp(muR+np.sqrt(2.*np.power(stdR,2))*inverrf[k])
if multiplier>maxmultiplier:
multiplier=1. # or maybe this should be zero
# no rescaling:
else:
multiplier=1.
if durcheck==False:
rainsum[k]=np.nansum(passrain[:,y, x])
else:
storesum=0.
storestep=0
for kk in range(nsteps):
tempsum=passrain[kk,y,x]
if tempsum>storesum:
storesum=tempsum
storestep=kk
rainsum[k]=storesum*multiplier
multiout[k]=multiplier
whichstep[k]=storestep
return rainsum,multiout,whichstep
#@jit(nopython=True,fastmath=True,parallel=True)
#def killerloop(passrain,rainsum,nreals,ssty,sstx,maskheight,maskwidth,trimmask,nsteps,durcheck):
# for k in prange(nreals):
# spanx=int64(sstx[k]+maskwidth)
# spany=int64(ssty[k]+maskheight)
# if np.all(np.less(passrain[:,ssty[k]:spany,sstx[k]:spanx],0.5)):
# rainsum[k]=0.
# else:
# if durcheck==False:
# rainsum[k]=np.nansum(np.multiply(passrain[ssty[k] : spany , sstx[k] : spanx],trimmask))
# else:
# storesum=float32(0.)
# for kk in range(nsteps):
# tempsum=np.nansum(np.multiply(passrain[kk,ssty[k]:spany,sstx[k]:spanx],trimmask))
# if tempsum>storesum:
# storesum=tempsum
# rainsum[k]=storesum
# return rainsum
#whichstep[k]=storestep
#return rainsum,whichstep
# this function below never worked for some unknown Numba problem-error messages indicated that it wasn't my fault!!! Some problem in tempsum
#@jit(nopython=True,fastmath=True,parallel=True)
#def killerloop(passrain,rainsum,nreals,ssty,sstx,maskheight,maskwidth,masktile,nsteps,durcheck):
# for k in prange(nreals):
# spanx=sstx[k]+maskwidth
# spany=ssty[k]+maskheight
# if np.all(np.less(passrain[:,ssty[k]:spany,sstx[k]:spanx],0.5)):
# rainsum[k]=0.
# else:
# if durcheck==False:
# #tempstep=np.multiply(passrain[:,ssty[k] : spany , sstx[k] : spanx],trimmask)
# #xnum=int64(sstx[k])
# #ynum=int64(ssty[k])
# #rainsum[k]=np.nansum(passrain[:,ssty[k], sstx[k]])
# rainsum[k]=np.nansum(np.multiply(passrain[:,ssty[k] : spany , sstx[k] : spanx],masktile))
# else:
# storesum=float32(0.)
# for kk in range(nsteps):
# #tempsum=0.
# #tempsum=np.multiply(passrain[kk,ssty[k]:spany,sstx[k]:spanx],masktile[0,:,:])
# tempsum=np.nansum(np.multiply(passrain[kk,ssty[k]:spany,sstx[k]:spanx],masktile[0,:,:]))
# return rainsum
#==============================================================================
# THIS VARIANT IS SIMPLER AND UNLIKE SSTWRITE, IT ACTUALLY WORKS RELIABLY!
#==============================================================================
#def SSTwriteAlt(catrain,rlzx,rlzy,rlzstm,trimmask,xmin,xmax,ymin,ymax,maskheight,maskwidth):
# nyrs=np.int(rlzx.shape[0])
# raindur=np.int(catrain.shape[1])
# outrain=np.zeros((nyrs,raindur,maskheight,maskwidth),dtype='float32')
# unqstm,unqind,unqcnts=np.unique(rlzstm,return_inverse=True,return_counts=True)
# #ctr=0
# for i in range(0,len(unqstm)):
# unqwhere=np.where(unqstm[i]==rlzstm)[0]
# for j in unqwhere:
# #ctr=ctr+1
# #print ctr
# outrain[j,:]=np.multiply(catrain[unqstm[i],:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)],trimmask)
# return outrain
#==============================================================================
# THIS VARIANT IS SAME AS ABOVE, BUT HAS A MORE INTERESTING RAINFALL PREPENDING PROCEDURE
#==============================================================================
#def SSTwriteAltPreCat(catrain,rlzx,rlzy,rlzstm,trimmask,xmin,xmax,ymin,ymax,maskheight,maskwidth,precat,ptime):
# catyears=ptime.astype('datetime64[Y]').astype(int)+1970
# ptime=ptime.astype('datetime64[M]').astype(int)-(catyears-1970)*12+1
# nyrs=np.int(rlzx.shape[0])
# raindur=np.int(catrain.shape[1]+precat.shape[1])
# outrain=np.zeros((nyrs,raindur,maskheight,maskwidth),dtype='float32')
# unqstm,unqind,unqcnts=np.unique(rlzstm,return_inverse=True,return_counts=True)
#
# for i in range(0,len(unqstm)):
# unqwhere=np.where(unqstm[i]==rlzstm)[0]
# unqmonth=ptime[unqstm[i]]
# pretimeind=np.where(np.logical_and(ptime>unqmonth-2,ptime<unqmonth+2))[0]
# for j in unqwhere:
# temprain=np.concatenate((np.squeeze(precat[np.random.choice(pretimeind, 1),:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)],axis=0),catrain[unqstm[i],:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)]),axis=0)
# outrain[j,:]=np.multiply(temprain,trimmask)
# return outrain
#
#==============================================================================
# SAME AS ABOVE, BUT HANDLES STORM ROTATION
#==============================================================================
#def SSTwriteAltPreCatRotation(catrain,rlzx,rlzy,rlzstm,trimmask,xmin,xmax,ymin,ymax,maskheight,maskwidth,precat,ptime,delarray,rlzanglebin,rainprop):
##def SSTwriteAltPreCatRotation(catrain,rlzx,rlzy,rlzstm,trimmask,xmin,xmax,ymin,ymax,maskheight,maskwidth,precat,ptime,delarray,rlzanglebin):
# catyears=ptime.astype('datetime64[Y]').astype(int)+1970
# ptime=ptime.astype('datetime64[M]').astype(int)-(catyears-1970)*12+1
# nyrs=np.int(rlzx.shape[0])
# raindur=np.int(catrain.shape[1]+precat.shape[1])
# outrain=np.zeros((nyrs,raindur,maskheight,maskwidth),dtype='float32')
# unqstm,unqind,unqcnts=np.unique(rlzstm,return_inverse=True,return_counts=True) # unqstm is the storm number
#
# for i in range(0,len(unqstm)):
# unqwhere=np.where(unqstm[i]==rlzstm)[0]
# unqmonth=ptime[unqstm[i]]
# pretimeind=np.where(np.logical_and(ptime>unqmonth-2,ptime<unqmonth+2))[0]
# for j in unqwhere:
# inrain=catrain[unqstm[i],:].copy()
#
# xctr=rlzx[j]+maskwidth/2.
# yctr=rlzy[j]+maskheight/2.
# xlinsp=np.linspace(-xctr,rainprop.subdimensions[1]-xctr,rainprop.subdimensions[1])
# ylinsp=np.linspace(-yctr,rainprop.subdimensions[0]-yctr,rainprop.subdimensions[0])
#
# ingridx,ingridy=np.meshgrid(xlinsp,ylinsp)
# ingridx=ingridx.flatten()
# ingridy=ingridy.flatten()
# outgrid=np.column_stack((ingridx,ingridy))
#
# for k in range(0,inrain.shape[0]):
# interp=sp.interpolate.LinearNDInterpolator(delarray[unqstm[i]][rlzanglebin[j]-1],inrain[k,:].flatten(),fill_value=0.)
# inrain[k,:]=np.reshape(interp(outgrid),rainprop.subdimensions)
# #inrain[k,:]=temprain
#
# temprain=np.concatenate((np.squeeze(precat[np.random.choice(pretimeind, 1),:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)],axis=0),inrain[:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)]),axis=0)
#
# outrain[j,:]=np.multiply(temprain,trimmask)
# return outrain
@jit(fastmath=True)
def SSTspin_write_v2(catrain,rlzx,rlzy,rlzstm,trimmask,maskheight,maskwidth,precat,ptime,rainprop,rlzanglebin=None,delarray=None,spin=False,flexspin=True,samptype='uniform',cumkernel=None,rotation=False,domaintype='rectangular'):
catyears=ptime.astype('datetime64[Y]').astype(int)+1970
ptime=ptime.astype('datetime64[M]').astype(int)-(catyears-1970)*12+1
nyrs=np.int(rlzx.shape[0])
raindur=np.int(catrain.shape[1]+precat.shape[1])
outrain=np.zeros((nyrs,raindur,maskheight,maskwidth),dtype='float32')
unqstm,unqind,unqcnts=np.unique(rlzstm,return_inverse=True,return_counts=True) # unqstm is the storm number
for i in range(0,len(unqstm)):
unqwhere=np.where(unqstm[i]==rlzstm)[0]
unqmonth=ptime[unqstm[i]]
pretimeind=np.where(np.logical_and(ptime>unqmonth-1,ptime<unqmonth+1))[0]
# flexspin allows you to use spinup rainfall from anywhere in transposition domain, rather than just storm locations, but it doesn't seem to be very useful based on initial testing
if spin==True and flexspin==True:
if samptype=='kernel' or domaintype=='irregular':
rndloc=np.random.random_sample(len(unqwhere))
shiftprex,shiftprey=numbakernel(rndloc,cumkernel)
else:
shiftprex=np.random.random_integers(0,np.int(rainprop.subdimensions[1])-maskwidth-1,len(unqwhere))
shiftprey=np.random.random_integers(0,np.int(rainprop.subdimensions[0])-maskheight-1,len(unqwhere))
ctr=0
for j in unqwhere:
inrain=catrain[unqstm[i],:].copy()
# this doesn't rotate the prepended rainfall
if rotation==True:
xctr=rlzx[j]+maskwidth/2.
yctr=rlzy[j]+maskheight/2.
xlinsp=np.linspace(-xctr,rainprop.subdimensions[1]-xctr,rainprop.subdimensions[1])
ylinsp=np.linspace(-yctr,rainprop.subdimensions[0]-yctr,rainprop.subdimensions[0])
ingridx,ingridy=np.meshgrid(xlinsp,ylinsp)
ingridx=ingridx.flatten()
ingridy=ingridy.flatten()
outgrid=np.column_stack((ingridx,ingridy))
for k in range(0,inrain.shape[0]):
interp=sp.interpolate.LinearNDInterpolator(delarray[unqstm[i]][rlzanglebin[j]-1],inrain[k,:].flatten(),fill_value=0.)
inrain[k,:]=np.reshape(interp(outgrid),rainprop.subdimensions)
if spin==True and flexspin==True:
temprain=np.concatenate((np.squeeze(precat[np.random.choice(pretimeind, 1),:,(shiftprey[ctr]) : (shiftprey[ctr]+maskheight) , (shiftprex[ctr]) : (shiftprex[ctr]+maskwidth)],axis=0),inrain[:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)]),axis=0)
elif spin==True and flexspin==False:
temprain=np.concatenate((np.squeeze(precat[np.random.choice(pretimeind, 1),:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)],axis=0),inrain[:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)]),axis=0)
elif spin==False:
temprain=inrain[:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)]
else:
sys.exit("what else is there?")
ctr=ctr+1
outrain[j,:]=np.multiply(temprain,trimmask)
return outrain
##==============================================================================
## SAME AS ABOVE, BUT A BIT MORE DYNAMIC IN TERMS OF SPINUP
##==============================================================================
#def SSTspin_write_v2(catrain,rlzx,rlzy,rlzstm,trimmask,xmin,xmax,ymin,ymax,maskheight,maskwidth,precat,ptime,rainprop,rlzanglebin=None,delarray=None,spin=False,flexspin=True,samptype='uniform',cumkernel=None,rotation=False,domaintype='rectangular',intense_data=False):
# catyears=ptime.astype('datetime64[Y]').astype(int)+1970
# ptime=ptime.astype('datetime64[M]').astype(int)-(catyears-1970)*12+1
# nyrs=np.int(rlzx.shape[0])
# raindur=np.int(catrain.shape[1]+precat.shape[1])
# outrain=np.zeros((nyrs,raindur,maskheight,maskwidth),dtype='float32')
# unqstm,unqind,unqcnts=np.unique(rlzstm,return_inverse=True,return_counts=True) # unqstm is the storm number
#
# if intense_data!=False:
# sys.exit("Scenario writing for intensity-based resampling not tested!")
# intquant=intense_data[0]
# fullmu=intense_data[1]
# fullstd=intense_data[2]
# muorig=intense_data[3]
# stdorig=intense_data[4]
#
# for i in range(0,len(unqstm)):
# unqwhere=np.where(unqstm[i]==rlzstm)[0]
# unqmonth=ptime[unqstm[i]]
# pretimeind=np.where(np.logical_and(ptime>unqmonth-1,ptime<unqmonth+1))[0]
#
# if transpotype=='intensity':
# origmu=np.multiply(murain[caty[i]:caty[i]+maskheight,catx[i]:catx[i]+maskwidth],trimmask)
# origstd=np.multiply(stdrain[caty[i]:caty[i]+maskheight,catx[i]:catx[i]+maskwidth],trimmask)
# #intense_dat=[intquant[],murain,stdrain,origmu,origstd]
#
# # flexspin allows you to use spinup rainfall from anywhere in transposition domain, rather than just storm locations, but it doesn't seem to be very useful based on initial testing
# if spin==True and flexspin==True:
# if samptype=='kernel' or domaintype=='irregular':
# rndloc=np.random.random_sample(len(unqwhere))
# shiftprex,shiftprey=numbakernel(rndloc,cumkernel)
# else:
# shiftprex=np.random.random_integers(0,np.int(rainprop.subdimensions[1])-maskwidth-1,len(unqwhere))
# shiftprey=np.random.random_integers(0,np.int(rainprop.subdimensions[0])-maskheight-1,len(unqwhere))
#
# ctr=0
# for j in unqwhere:
# inrain=catrain[unqstm[i],:].copy()
#
# if intense_data!=False:
# transmu=np.multiply(fullmu[(rlzy[i]) : (rlzy[i]+maskheight) , (rlzx[i]) : (rlzx[i]+maskwidth)],trimmask)
# transtd=np.multiply(fullstd[(rlzy[i]) : (rlzy[i]+maskheight) , (rlzx[i]) : (rlzx[i]+maskwidth)],trimmask)
# mu_multi=transmu/muorig
# std_multi=np.abs(transtd-stdorig)/stdorig
# multipliermask=norm.ppf(intquant[i],loc=mu_multi,scale=std_multi)
# multipliermask[multipliermask<0.]=0.
# multipliermask[np.isnan(multipliermask)]=0.
#
# # this doesn't rotate the prepended rainfall
# if rotation==True:
# xctr=rlzx[j]+maskwidth/2.
# yctr=rlzy[j]+maskheight/2.
# xlinsp=np.linspace(-xctr,rainprop.subdimensions[1]-xctr,rainprop.subdimensions[1])
# ylinsp=np.linspace(-yctr,rainprop.subdimensions[0]-yctr,rainprop.subdimensions[0])
#
# ingridx,ingridy=np.meshgrid(xlinsp,ylinsp)
# ingridx=ingridx.flatten()
# ingridy=ingridy.flatten()
# outgrid=np.column_stack((ingridx,ingridy))
#
# for k in range(0,inrain.shape[0]):
# interp=sp.interpolate.LinearNDInterpolator(delarray[unqstm[i]][rlzanglebin[j]-1],inrain[k,:].flatten(),fill_value=0.)
# inrain[k,:]=np.reshape(interp(outgrid),rainprop.subdimensions)
#
# if spin==True and flexspin==True:
# temprain=np.concatenate((np.squeeze(precat[np.random.choice(pretimeind, 1),:,(shiftprey[ctr]) : (shiftprey[ctr]+maskheight) , (shiftprex[ctr]) : (shiftprex[ctr]+maskwidth)],axis=0),inrain[:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)]),axis=0)
# elif spin==True and flexspin==False:
# temprain=np.concatenate((np.squeeze(precat[np.random.choice(pretimeind, 1),:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)],axis=0),inrain[:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)]),axis=0)
# elif spin==False:
# temprain=inrain[:,(rlzy[j]) : (rlzy[j]+maskheight) , (rlzx[j]) : (rlzx[j]+maskwidth)]
# else:
# sys.exit("what else is there?")
# ctr=ctr+1
# if intense_data!=False:
# outrain[j,:]=np.multiply(temprain,multipliermask)
# else:
# outrain[j,:]=np.multiply(temprain,trimmask)
# return outrain
#==============================================================================
# LOOP FOR KERNEL BASED STORM TRANSPOSITION
# THIS FINDS THE TRANSPOSITION LOCATION FOR EACH REALIZATION IF YOU ARE USING THE KERNEL-BASED RESAMPLER
# IF I CONFIGURE THE SCRIPT SO THE USER CAN PROVIDE A CUSTOM RESAMPLING SCHEME, THIS WOULD PROBABLY WORK FOR THAT AS WELL
#==============================================================================
#def weavekernel(rndloc,cumkernel):
# nlocs=len(rndloc)
# nrows=cumkernel.shape[0]
# ncols=cumkernel.shape[1]
# tempx=np.empty((len(rndloc)),dtype="int32")
# tempy=np.empty((len(rndloc)),dtype="int32")
# code= """
# #include <stdio.h>
# int i,x,y,brklp;
# double prevprob;
# for (i=0;i<nlocs;i++) {
# prevprob=0.0;
# brklp=0;
# for (y=0; y<nrows; y++) {
# for (x=0; x<ncols; x++) {
# if ( (rndloc(i)<=cumkernel(y,x)) && (rndloc(i)>prevprob) ) {
# tempx(i)=x;
# tempy(i)=y;
# prevprob=cumkernel(y,x);
# brklp=1;
# break;
# }
# }
# if (brklp==1) {
# break;
# }
# }
# }
# """
# vars=['rndloc','cumkernel','nlocs','nrows','ncols','tempx','tempy']
# sp.weave.inline(code,vars,type_converters=converters.blitz,compiler='gcc')
# return tempx,tempy
def pykernel(rndloc,cumkernel):
nlocs=len(rndloc)
ncols=cumkernel.shape[1]
tempx=np.empty((len(rndloc)),dtype="int32")
tempy=np.empty((len(rndloc)),dtype="int32")
flatkern=np.append(0.,cumkernel.flatten())
for i in range(0,nlocs):
x=rndloc[i]-flatkern
x[np.less(x,0.)]=1000.
whereind = np.argmin(x)
y=whereind//ncols
x=whereind-y*ncols
tempx[i]=x
tempy[i]=y
return tempx,tempy
@jit
def numbakernel(rndloc,cumkernel,tempx,tempy,ncols):
nlocs=len(rndloc)
#ncols=xdim
flatkern=np.append(0.,cumkernel.flatten())
#x=np.zeros_like(rndloc,dtype='float64')
for i in np.arange(0,nlocs):
x=rndloc[i]-flatkern
x[np.less(x,0.)]=10.
whereind=np.argmin(x)
y=whereind//ncols
x=whereind-y*ncols
tempx[i]=x
tempy[i]=y
return tempx,tempy
@jit
def numbakernel_fast(rndloc,cumkernel,tempx,tempy,ncols):
nlocs=int32(len(rndloc))
ncols=int32(cumkernel.shape[1])
flatkern=np.append(0.,cumkernel.flatten())
return kernelloop(nlocs,rndloc,flatkern,ncols,tempx,tempy)
#@jit(nopython=True,fastmath=True,parallel=True)
@jit(nopython=True,fastmath=True)
def kernelloop(nlocs,rndloc,flatkern,ncols,tempx,tempy):
for i in prange(nlocs):
diff=rndloc[i]-flatkern
diff[np.less(diff,0.)]=10.
whereind=np.argmin(diff)
y=whereind//ncols
x=whereind-y*ncols
tempx[i]=x
tempy[i]=y
return tempx,tempy
#==============================================================================
# FIND THE BOUNDARY INDICIES AND COORDINATES FOR THE USER-DEFINED SUBAREA
# NOTE THAT subind ARE THE MATRIX INDICIES OF THE SUBBOX, STARTING FROM UPPER LEFT CORNER OF DOMAIN AS (0,0)
# NOTE THAT subcoord ARE THE COORDINATES OF THE OUTSIDE BORDER OF THE SUBBOX
# THEREFORE THE DISTANCE FROM THE WESTERN (SOUTHERN) BOUNDARY TO THE EASTERN (NORTHERN) BOUNDARY IS NCOLS (NROWS) +1 TIMES THE EAST-WEST (NORTH-SOUTH) RESOLUTION
#==============================================================================
def findsubbox(inarea,rainprop):
outind=np.empty([4],dtype='int')
outextent=np.empty([4])
outdim=np.empty([2])
inbox=deepcopy(inarea)
rangex=np.arange(rainprop.bndbox[0],rainprop.bndbox[1]-rainprop.spatialres[0]/1000,rainprop.spatialres[0])
rangey=np.arange(rainprop.bndbox[3],rainprop.bndbox[2]+rainprop.spatialres[1]/1000,-rainprop.spatialres[1])
if rangex.shape[0]<rainprop.dimensions[1]:
rangex=np.append(rangex,rangex[-1])
if rangey.shape[0]<rainprop.dimensions[0]:
rangey=np.append(rangey,rangey[-1])
if rangex.shape[0]>rainprop.dimensions[1]:
rangex=rangex[0:-1]
if rangey.shape[0]>rainprop.dimensions[0]:
rangey=rangey[0:-1]
outextent=inbox
# "SNAP" output extent to grid
outind[0]=np.abs(rangex-outextent[0]).argmin()
outind[1]=np.abs(rangex-outextent[1]).argmin()-1
outind[2]=np.abs(rangey-outextent[2]).argmin()-1
outind[3]=np.abs(rangey-outextent[3]).argmin()
outextent[0]=rangex[outind[0]]
outextent[1]=rangex[outind[1]+1]
outextent[2]=rangey[outind[2]+1]
outextent[3]=rangey[outind[3]]
outdim[1]=np.shape(np.arange(outind[0],outind[1]+1))[0]
outdim[0]=np.shape(np.arange(outind[3],outind[2]+1))[0]
outdim=np.array(outdim,dtype='int32')
return outextent,outind,outdim
#==============================================================================
# THIS RETURNS A LOGICAL GRID THAT CAN THEN BE APPLIED TO THE GLOBAL GRID TO EXTRACT
# A USEER-DEFINED SUBGRID
# THIS HELPS TO KEEP ARRAY SIZES SMALL
#==============================================================================
def creategrids(rainprop):
globrangex=np.arange(0,rainprop.dimensions[1],1)
globrangey=np.arange(0,rainprop.dimensions[0],1)
subrangex=np.arange(rainprop.subind[0],rainprop.subind[1]+1,1)
subrangey=np.arange(rainprop.subind[3],rainprop.subind[2]+1,1)
subindx=np.logical_and(globrangex>=subrangex[0],globrangex<=subrangex[-1])
subindy=np.logical_and(globrangey>=subrangey[0],globrangey<=subrangey[-1])
gx,gy=np.meshgrid(subindx,subindy)
outgrid=np.logical_and(gx==True,gy==True)
return outgrid,subindx,subindy
#==============================================================================
# FUNCTION TO CREATE A MASK ACCORDING TO A USER-DEFINED POLYGON SHAPEFILE AND PROJECTION
# THIS USES GDAL COMMANDS FROM THE OS TO RASTERIZE
#==============================================================================
def rastermaskGDAL(shpname,shpproj,rainprop,masktype,fullpath,gdalpath=False):
bndbox=np.array(rainprop.subind)
bndcoords=np.array(rainprop.subextent)
if rainprop.projection==GEOG:
xdim=np.shape(np.linspace(bndcoords[0],bndcoords[1],rainprop.subind[1]-rainprop.subind[0]+1))[0]
ydim=np.shape(np.linspace(bndcoords[2],bndcoords[3],rainprop.subind[2]-rainprop.subind[3]+1))[0]
else:
sys.exit("unrecognized projection!")
rastertemplate=np.zeros((ydim,xdim),dtype='float32')
if masktype=='simple':
print('creating simple mask (0s and 1s)')
#os.system('gdal_rasterize -at -burn 1.0 -te '+str(rainprop.subextent[0])+' '+str(rainprop.subextent[2])+' '+str(rainprop.subextent[1])+' '+str(rainprop.subextent[3])+' -tr '+str(rainprop.spatialres[0])+' '+str(rainprop.spatialres[1])+' -ts '+str(np.int(rainprop.subdimensions[1]))+' '+str(np.int(rainprop.subdimensions[0]))+' -ot Float32 '+shpname+' '+fullpath+'/temp.tiff');
if gdalpath!=False:
rasterizecmd=gdalpath+'/gdal_rasterize -at -burn 1.0 -te '+"%.9f"%(rainprop.subextent[0])+' '+"%.9f"%(rainprop.subextent[2])+' '+"%.9f"%(rainprop.subextent[1])+' '+"%.9f"%(rainprop.subextent[3])+' -tr '+"%.9f"%(rainprop.spatialres[0])+' '+"%.9f"%(rainprop.spatialres[1])+' -ts '+"%.9f"%(np.int(rainprop.subdimensions[1]))+' '+"%.9f"%(np.int(rainprop.subdimensions[0]))+' -ot Float32 '+shpname+' '+fullpath+'/temp.tiff'
else:
rasterizecmd='gdal_rasterize -at -burn 1.0 -te '+"%.9f"%(rainprop.subextent[0])+' '+"%.9f"%(rainprop.subextent[2])+' '+"%.9f"%(rainprop.subextent[1])+' '+"%.9f"%(rainprop.subextent[3])+' -tr '+"%.9f"%(rainprop.spatialres[0])+' '+"%.9f"%(rainprop.spatialres[1])+' -ts '+"%.9f"%(np.int(rainprop.subdimensions[1]))+' '+"%.9f"%(np.int(rainprop.subdimensions[0]))+' -ot Float32 '+shpname+' '+fullpath+'/temp.tiff'
os.system(rasterizecmd)
ds=rasterio.open(fullpath+'/temp.tiff')
rastertemplate=ds.read(1)
os.system('rm '+fullpath+'/temp.tiff')
elif masktype=="fraction":
print('creating fractional mask (range from 0.0-1.0)')
#os.system('gdal_rasterize -at -burn 1.0 -te '+str(rainprop.subextent[0])+' '+str(rainprop.subextent[2])+' '+str(rainprop.subextent[1])+' '+str(rainprop.subextent[3])+' -tr '+str(rainprop.spatialres[0]/10.)+' '+str(rainprop.spatialres[1]/10.)+' -ts '+str(np.int(rainprop.subdimensions[1])*10)+' '+str(np.int(rainprop.subdimensions[0])*10)+' -ot Float32 '+shpname+' '+fullpath+'/temp.tiff');
#os.system('gdalwarp -r average -te '+str(rainprop.subextent[0])+' '+str(rainprop.subextent[2])+' '+str(rainprop.subextent[1])+' '+str(rainprop.subextent[3])+' -ts '+str(np.int(rainprop.subdimensions[1]))+' '+str(np.int(rainprop.subdimensions[0]))+' -overwrite '+fullpath+'/temp.tiff '+fullpath+'/tempAGG.tiff');
if gdalpath!=False:
rasterizecmd=gdalpath+'/gdal_rasterize -at -burn 1.0 -te '+"%.9f"%(rainprop.subextent[0])+' '+"%.9f"%(rainprop.subextent[2])+' '+"%.9f"%(rainprop.subextent[1])+' '+"%.9f"%(rainprop.subextent[3])+' -tr '+"%.9f"%(rainprop.spatialres[0]/10.)+' '+"%.9f"%(rainprop.spatialres[1]/10.)+' -ts '+"%.9f"%(np.int(rainprop.subdimensions[1])*10)+' '+"%.9f"%(np.int(rainprop.subdimensions[0])*10)+' -ot Float32 '+shpname+' '+fullpath+'/temp.tiff'
else:
rasterizecmd='gdal_rasterize -at -burn 1.0 -te '+"%.9f"%(rainprop.subextent[0])+' '+"%.9f"%(rainprop.subextent[2])+' '+"%.9f"%(rainprop.subextent[1])+' '+"%.9f"%(rainprop.subextent[3])+' -tr '+"%.9f"%(rainprop.spatialres[0]/10.)+' '+"%.9f"%(rainprop.spatialres[1]/10.)+' -ts '+"%.9f"%(np.int(rainprop.subdimensions[1])*10)+' '+"%.9f"%( | np.int(rainprop.subdimensions[0]) | numpy.int |
"""
Collection of math utility functions used by > 1 modules.
"""
from typing import Tuple
import numpy as np
def euler_coord_to_homogeneous_coord(Xe: np.array) -> np.array:
"""Convert Euler coordinates to homogeneous coordinates."""
no_points = | np.shape(Xe) | numpy.shape |
import random
import math
from functools import partial
import json
import pysndfx
import librosa
import numpy as np
import torch
from ops.audio import (
read_audio, compute_stft, trim_audio, mix_audio_and_labels,
shuffle_audio, cutout
)
SAMPLE_RATE = 44100
class Augmentation:
"""A base class for data augmentation transforms"""
pass
class MapLabels:
def __init__(self, class_map, drop_raw=True):
self.class_map = class_map
def __call__(self, dataset, **inputs):
labels = np.zeros(len(self.class_map), dtype=np.float32)
for c in inputs["raw_labels"]:
labels[self.class_map[c]] = 1.0
transformed = dict(inputs)
transformed["labels"] = labels
transformed.pop("raw_labels")
return transformed
class MixUp(Augmentation):
def __init__(self, p):
self.p = p
def __call__(self, dataset, **inputs):
transformed = dict(inputs)
if | np.random.uniform() | numpy.random.uniform |
# -*- coding: utf-8 -*-
"""
Copyright Netherlands eScience Center
Function : Forecast Lorenz 84 model - Train BayesConvLSTM model
Author : <NAME>
First Built : 2020.03.09
Last Update : 2020.04.12
Library : Pytorth, Numpy, NetCDF4, os, iris, cartopy, dlacs, matplotlib
Description : This notebook serves to predict the Lorenz 84 model using deep learning. The Bayesian Convolutional
Long Short Time Memory neural network is used to deal with this spatial-temporal sequence problem.
We use Pytorch as the deep learning framework.
Return Values : pkl model and figures
"""
import sys
import warnings
import numbers
import logging
import time as tttt
# for data loading
import os
from netCDF4 import Dataset
# for pre-processing and machine learning
import numpy as np
import sklearn
#import scipy
import torch
import torch.nn.functional
#sys.path.append(os.path.join('C:','Users','nosta','ML4Climate','Scripts','DLACs'))
#sys.path.append("C:\\Users\\nosta\\ML4Climate\\Scripts\\DLACs")
sys.path.append("../")
import dlacs
import dlacs.BayesConvLSTM
import dlacs.preprocess
import dlacs.function
# for visualization
import dlacs.visual
import matplotlib
# Generate images without having a window appear
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from matplotlib.pyplot import cm
import iris # also helps with regriding
import cartopy
import cartopy.crs as ccrs
# ignore all the DeprecationWarnings by pytorch
if not sys.warnoptions:
warnings.simplefilter("ignore")
# constants
constant = {'g' : 9.80616, # gravititional acceleration [m / s2]
'R' : 6371009, # radius of the earth [m]
'cp': 1004.64, # heat capacity of air [J/(Kg*K)]
'Lv': 2500000, # Latent heat of vaporization [J/Kg]
'R_dry' : 286.9, # gas constant of dry air [J/(kg*K)]
'R_vap' : 461.5, # gas constant for water vapour [J/(kg*K)]
'rho' : 1026, # sea water density [kg/m3]
}
# calculate the time for the code execution
start_time = tttt.time()
#################################################################################
######### datapath ########
#################################################################################
# ** Reanalysis **
# **ERA-Interim** 1979 - 2016 (ECMWF)
# **ORAS4** 1958 - 2014 (ECMWF)
# please specify data path
datapath = '/projects/0/blueactn/dataBayes'
output_path = '/home/lwc16308/BayesArctic/DLACs/models/'
#################################################################################
######### main ########
#################################################################################
# set up logging files
logging.basicConfig(filename = os.path.join(output_path,'logFile_Lorenz84_train.log'),
filemode = 'w+', level = logging.DEBUG,
format = '%(asctime)s - %(name)s - %(levelname)s - %(message)s')
logging.getLogger('matplotlib.font_manager').disabled = True
if __name__=="__main__":
print ('*********************** get the key to the datasets *************************')
#################################################################################
########### configure Lorenz 84 model ###########
#################################################################################
logging.info("Configure Lorenz 84 model")
# Lorenz paramters and initial conditions
x_init = 1.0 # strength of the symmetric globally encircling westerly current
y_init = 1.0 # strength of the cosine phases of a chain of superposedwaves (large scale eddies)
z_init = 1.0 # strength of the sine phases of a chain of superposedwaves (large scale eddies)
F = 8.0 # thermal forcing term
G = 1.0 # thermal forcing term
a = 0.25 # stiffness factor for westerly wind x
b = 4.0 # advection strength of the waves by the westerly current
# assuming the damping time for the waves is 5 days (Lorens 1984)
dt = 0.0333 # 1/30 unit of time unit (5 days)
num_steps = 1500
# cut-off point of initialization period
cut_off = 300
logging.info("#####################################")
logging.info("Summary of Lorenz 84 model")
logging.info("x = 1.0 y = 1.0 z = 1.0")
logging.info("F = 8.0 G = 1.0 a = 0.25 b = 4.0")
logging.info("unit time step 0.0333 (~5days)")
logging.info("series length 1500 steps")
logging.info("cut-off length 300 steps")
logging.info("#####################################")
#################################################################################
########### Lorens 84 model ###########
#################################################################################
def lorenz84(x, y, z, a = 0.25, b = 4.0, F = 8.0, G = 1.0):
"""
Solver of Lorens-84 model.
param x, y, z: location in a 3D space
param a, b, F, G: constants and forcing
"""
dx = - y**2 - z**2 - a * x + a * F
dy = x * y - b * x * z - y + G
dz = b * x * y + x * z - z
return dx, dy, dz
#################################################################################
########### Launch Lorenz 84 model ###########
#################################################################################
logging.info("Launch Lorenz 84 model")
# Need one more for the initial values
x = | np.empty(num_steps) | numpy.empty |
"""Test the features of the lightkurve.prf.tpfmodels module."""
import os
import pytest
from astropy.io import fits
import numpy as np
from numpy.testing import assert_allclose
from scipy.stats import mode
from lightkurve.prf import FixedValuePrior, GaussianPrior, UniformPrior
from lightkurve.prf import StarPrior, BackgroundPrior, FocusPrior, MotionPrior
from lightkurve.prf import TPFModel, PRFPhotometry
from lightkurve.prf import SimpleKeplerPRF, KeplerPRF
from .. import TESTDATA
def test_fixedvalueprior():
fvp = FixedValuePrior(1.5)
assert fvp.mean == 1.5
assert fvp(1.5) == 0
def test_starprior():
"""Tests the StarPrior class."""
col, row, flux = 1, 2, 3
sp = StarPrior(
col=GaussianPrior(mean=col, var=0.1),
row=GaussianPrior(mean=row, var=0.1),
flux=GaussianPrior(mean=flux, var=0.1),
)
assert sp.col.mean == col
assert sp.row.mean == row
assert sp.flux.mean == flux
assert sp.evaluate(col, row, flux) == 0
# The object should be callable
assert sp(col, row, flux + 0.1) == sp.evaluate(col, row, flux + 0.1)
# A point further away from the mean should have a larger negative log likelihood
assert sp.evaluate(col, row, flux) < sp.evaluate(col, row, flux + 0.1)
# Object should have a nice __repr__
assert "StarPrior" in str(sp)
def test_backgroundprior():
"""Tests the BackgroundPrior class."""
flux = 2.0
bp = BackgroundPrior(flux=flux)
assert bp.flux.mean == flux
assert bp(flux) == 0.0
assert not np.isfinite(bp(flux + 0.1))
def test_tpf_model_simple():
prf = SimpleKeplerPRF(channel=16, shape=[10, 10], column=15, row=15)
model = TPFModel(prfmodel=prf)
assert model.prfmodel.channel == 16
def test_tpf_model():
col, row, flux, bgflux = 1, 2, 3, 4
shape = (7, 8)
model = TPFModel(
star_priors=[
StarPrior(
col=GaussianPrior(mean=col, var=2 ** 2),
row=GaussianPrior(mean=row, var=2 ** 2),
flux=UniformPrior(lb=flux - 0.5, ub=flux + 0.5),
targetid="TESTSTAR",
)
],
background_prior=BackgroundPrior(flux=GaussianPrior(mean=bgflux, var=bgflux)),
focus_prior=FocusPrior(
scale_col=GaussianPrior(mean=1, var=0.0001),
scale_row=GaussianPrior(mean=1, var=0.0001),
rotation_angle=UniformPrior(lb=-3.1415, ub=3.1415),
),
motion_prior=MotionPrior(
shift_col=GaussianPrior(mean=0.0, var=0.01),
shift_row=GaussianPrior(mean=0.0, var=0.01),
),
prfmodel=KeplerPRF(channel=40, shape=shape, column=30, row=20),
fit_background=True,
fit_focus=False,
fit_motion=False,
)
# Sanity checks
assert model.star_priors[0].col.mean == col
assert model.star_priors[0].targetid == "TESTSTAR"
# Test initial guesses
params = model.get_initial_guesses()
assert params.stars[0].col == col
assert params.stars[0].row == row
assert params.stars[0].flux == flux
assert params.background.flux == bgflux
assert len(params.to_array()) == 4 # The model has 4 free parameters
assert_allclose([col, row, flux, bgflux], params.to_array(), rtol=1e-5)
# Predict should return an image
assert model.predict().shape == shape
# Test __repr__
assert "TESTSTAR" in str(model)
# Tagging the test below as `remote_data` because AppVeyor hangs on this test;
# at present we don't understand why.
@pytest.mark.remote_data
def test_tpf_model_fitting():
# Is the PRF photometry result consistent with simple aperture photometry?
tpf_fn = os.path.join(TESTDATA, "ktwo201907706-c01-first-cadence.fits.gz")
tpf = fits.open(tpf_fn)
col, row = 173, 526
fluxsum = np.sum(tpf[1].data)
bkg = mode(tpf[1].data, None)[0]
prfmodel = KeplerPRF(
channel=tpf[0].header["CHANNEL"], column=col, row=row, shape=tpf[1].data.shape
)
star_priors = [
StarPrior(
col=UniformPrior(lb=prfmodel.col_coord[0], ub=prfmodel.col_coord[-1]),
row=UniformPrior(lb=prfmodel.row_coord[0], ub=prfmodel.row_coord[-1]),
flux=UniformPrior(lb=0.5 * fluxsum, ub=1.5 * fluxsum),
)
]
background_prior = BackgroundPrior(flux=UniformPrior(lb=0.5 * bkg, ub=1.5 * bkg))
model = TPFModel(
star_priors=star_priors, background_prior=background_prior, prfmodel=prfmodel
)
# Does fitting run without errors?
result = model.fit(tpf[1].data)
# Can we change model parameters?
assert result.motion.fitted == False
model.fit_motion = True
result = model.fit(tpf[1].data)
assert result.motion.fitted == True
# Does fitting via the PRFPhotometry class run without errors?
phot = PRFPhotometry(model)
phot.run([tpf[1].data])
def test_empty_model():
"""Can we fit the background flux in a model without stars?"""
shape = (4, 3)
bgflux = 1.23
background_prior = BackgroundPrior(flux=UniformPrior(lb=0, ub=10))
model = TPFModel(background_prior=background_prior, fit_background=True)
background = bgflux * np.ones(shape=shape)
results = model.fit(background)
assert np.isclose(results.background.flux, bgflux, rtol=1e-2)
def test_model_with_one_star():
"""Can we fit the background flux in a model with one star?"""
channel = 42
shape = (10, 12)
starflux, col, row = 1000.0, 60.0, 70.0
bgflux = 10.0
scale_col, scale_row, rotation_angle = 1.2, 1.3, 0.2
prf = KeplerPRF(channel=channel, shape=shape, column=col, row=row)
star_prior = StarPrior(
col=GaussianPrior(col + 6, 0.01),
row=GaussianPrior(row + 6, 0.01),
flux=UniformPrior(lb=0.5 * starflux, ub=1.5 * starflux),
)
background_prior = BackgroundPrior(flux=UniformPrior(lb=0, ub=100))
focus_prior = FocusPrior(
scale_col=UniformPrior(lb=0.5, ub=1.5),
scale_row=UniformPrior(lb=0.5, ub=1.5),
rotation_angle=UniformPrior(lb=0.0, ub=0.5),
)
model = TPFModel(
star_priors=[star_prior],
background_prior=background_prior,
focus_prior=focus_prior,
prfmodel=prf,
fit_background=True,
fit_focus=True,
)
# Generate and fit fake data
fake_data = bgflux + prf(
col + 6,
row + 6,
starflux,
scale_col=scale_col,
scale_row=scale_row,
rotation_angle=rotation_angle,
)
results = model.fit(fake_data, tol=1e-12, options={"maxiter": 100})
# Do the results match the input?
assert np.isclose(results.stars[0].col, col + 6)
assert np.isclose(results.stars[0].row, row + 6)
assert | np.isclose(results.stars[0].flux, starflux) | numpy.isclose |
#!/usr/bin/env python
"""Tests of the geometry package."""
from math import sqrt
from numpy import (
all,
allclose,
arange,
array,
insert,
isclose,
mean,
ones,
sum,
take,
)
from numpy.linalg import inv, norm
from numpy.random import choice, dirichlet
from numpy.testing import assert_allclose
from cogent3.maths.geometry import (
aitchison_distance,
alr,
alr_inv,
center_of_mass,
center_of_mass_one_array,
center_of_mass_two_array,
clr,
clr_inv,
distance,
multiplicative_replacement,
sphere_points,
)
from cogent3.util.unit_test import TestCase, main
__author__ = "<NAME>"
__copyright__ = "Copyright 2007-2020, The Cogent Project"
__credits__ = ["<NAME>", "<NAME>", "<NAME>"]
__license__ = "BSD-3"
__version__ = "2020.6.30a"
__maintainer__ = "<NAME>"
__email__ = "<EMAIL>"
__status__ = "Production"
class CenterOfMassTests(TestCase):
"""Tests for the center of mass functions"""
def setUp(self):
"""setUp for all CenterOfMass tests"""
self.simple = | array([[1, 1, 1], [3, 1, 1], [2, 3, 2]]) | numpy.array |
# -*- coding: utf-8 -*-
"""
Muse LSL Example Auxiliary Tools
These functions perform the lower-level operations involved in buffering,
epoching, and transforming EEG data into frequency bands
@author: Cassani
"""
import numpy as np
from scipy.signal import butter, lfilter, lfilter_zi
NOTCH_B, NOTCH_A = butter(4, np.array([55, 65]) / (256 / 2), btype='bandstop')
def sigmoid(x):
"""
Returns the sigmoid of a value
"""
return(1 / (1 + np.exp(x)))
def compute_band_powers(eegdata, fs):
"""Extract the features (band powers) from the EEG.
Args:
eegdata (numpy.ndarray): array of dimension [number of samples,
number of channels]
fs (float): sampling frequency of eegdata
Returns:
(numpy.ndarray): feature matrix of shape [number of feature points,
number of different features]
"""
# 1. Compute the PSD
winSampleLength, nbCh = eegdata.shape
# Apply Hamming window
w = np.hamming(winSampleLength)
dataWinCentered = eegdata - np.mean(eegdata, axis=0) # Remove offset
dataWinCenteredHam = (dataWinCentered.T * w).T
NFFT = nextpow2(winSampleLength)
Y = np.fft.fft(dataWinCenteredHam, n=NFFT, axis=0) / winSampleLength
PSD = 2 * np.abs(Y[0:int(NFFT / 2), :])
f = fs / 2 * np.linspace(0, 1, int(NFFT / 2))
# SPECTRAL FEATURES
# Average of band powers
# Delta <4
ind_delta, = | np.where(f < 4) | numpy.where |
import pickle
import numpy as np
from TrainingFunctions.LoadDataStream import load_data_stream
separate_train_test_file = False
image_data = False
drift_labels_known = True
min_drift_distance = 300
path_A = "Generated_Streams/Drift_Labels/"
dataset_A = "RandomNumpyRandomNormalUniform_50DR_100Dims_1MinDimBroken_300MinL_2000MaxL_2021-08-06_10.53.pickle"
path_B = "Generated_Streams/Drift_And_Classifier_Labels/"
dataset_B = "RandomRandomRBF_50DR_100Dims_50Centroids_1MinDriftCentroids_300MinL_2000MaxL_2021-08-06_10.57.pickle"
# Load data stream A
proxy_evaluation_A = False
data_stream_A = load_data_stream(dataset=dataset_A, path=path_A, separate_train_test_file=separate_train_test_file,
image_data=image_data, drift_labels_known=drift_labels_known,
proxy_evaluation=proxy_evaluation_A)
# Load data stream B
proxy_evaluation_B = True
data_stream_B = load_data_stream(dataset=dataset_B, path=path_B, separate_train_test_file=separate_train_test_file,
image_data=image_data, drift_labels_known=drift_labels_known,
proxy_evaluation=proxy_evaluation_B)
# Separate drift labels and data stream
if drift_labels_known:
data_stream_A, drift_labels_A = data_stream_A[:, :-1], data_stream_A[:, -1]
drift_points_A = list( | np.where(drift_labels_A) | numpy.where |
#import the necessary packages
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report
from sklearn.datasets import make_blobs
import matplotlib.pyplot as plt
import numpy as np
def sigmoid_activation(x):
return 1.0/(1 + np.exp(-x))
def predict(X, W):
preds = X.dot(W)
#Since we're still doing a binary classifier, use step function
preds[preds <=0.5] = 0
preds[preds >0.5] = 1
return preds
#Generator to get data from the X and Y elements
def next_batch(X, y, batchSize):
for i in range(0, X.shape[0], batchSize):
yield(X[i:i + batchSize], y[i:i+batchSize])
#Generate 2 cllass classification problem with 1000 data points where each data point is a 2D feature vector.
(X, y) = make_blobs(n_samples=1000, n_features=2, centers=2, cluster_std=1.5, random_state=1)
y = y.reshape((y.shape[0], 1))
#Bias trick by adding a column of 1's in front of the X array
X = np.c_[np.ones(X.shape[0]), X]
#Split data into train test
(trainX, testX, trainY, testY) = train_test_split( X, y, test_size = 0.5, random_state=42)
print("[INFO] training...")
#Initialize our weight matrix and list of losses for future examination
W = np.random.randn(X.shape[1], 1)
losses = []
epochs = 100
batch_size = 32
alpha = 0.001
#learn
for epoch in range(epochs):
epochLoss = []
for(batchX, batchY) in next_batch(trainX, trainY, batch_size):
#perform SGD for the batch
preds = sigmoid_activation(batchX.dot(W))
#the error
errors = preds - batchY
epochLoss.append(np.sum(errors**2))
#the gradient descent step
gradient = batchX.T.dot(errors)
W = W - (alpha * gradient)
#Calculate the loss over all the batches in an epoch.
loss = np.average(epochLoss)
losses.append(loss)
#print every 5 epochs
if epoch ==0 or (epoch+1)%5==0:
print("[INFO] epoch = {}, loss = {:.7f}".format(int(epoch+1), loss))
#evaluate our model
print("[INFO] evaluating...")
preds = predict(testX, W)
print(classification_report(testY, preds))
#plot the testing classification data
plt.style.use("ggplot")
plt.figure()
plt.title("Data")
plt.scatter(testX[:, 1], testX[:, 2], marker = "o",c = testY[:,0], s = 30)
#Plot the loss over time
plt.style.use("ggplot")
plt.figure()
plt.plot( | np.arange(0, epochs) | numpy.arange |
# -*- coding: utf-8 -*-
from micropsi_core.nodenet.node import Node, Gate, Slot
from micropsi_core.nodenet.theano_engine.theano_link import TheanoLink
from micropsi_core.nodenet.theano_engine.theano_stepoperators import *
from micropsi_core.nodenet.theano_engine.theano_definitions import *
import numpy as np
class TheanoNode(Node):
"""
theano node proxy class
"""
def __init__(self, nodenet, partition, parent_uid, uid, type, parameters={}, **_):
self._numerictype = type
self._id = node_from_id(uid)
self._uid = uid
self._parent_id = nodespace_from_id(parent_uid)
self._nodenet = nodenet
self._partition = partition
self._state = {}
self.__gatecache = {}
self.__slotcache = {}
self.parameters = None
strtype = get_string_node_type(type, nodenet.native_modules)
Node.__init__(self, strtype, nodenet.get_nodetype(strtype))
if strtype in nodenet.native_modules or strtype == "Comment":
self.slot_activation_snapshot = {}
self._state = {}
if parameters is not None:
self.parameters = parameters.copy()
else:
self.parameters = {}
@property
def uid(self):
return self._uid
@property
def pid(self):
return self._partition.pid
@property
def index(self):
return self._id
@index.setter
def index(self, index):
raise NotImplementedError("index can not be set in theano_engine")
@property
def position(self):
return self._nodenet.positions.get(self.uid, [10, 10, 0])
@position.setter
def position(self, position):
if position is None and self.uid in self._nodenet.positions:
del self._nodenet.positions[self.uid]
else:
position = list(position)
position = (position + [0] * 3)[:3]
self._nodenet.positions[self.uid] = position
self._partition.node_changed(self.uid)
@property
def name(self):
return self._nodenet.names.get(self.uid, self.uid)
@name.setter
def name(self, name):
if name is None or name == "" or name == self.uid:
if self.uid in self._nodenet.names:
del self._nodenet.names[self.uid]
else:
self._nodenet.names[self.uid] = name
@property
def parent_nodespace(self):
return nodespace_to_id(self._parent_id, self._partition.pid)
@property
def activation(self):
return float(self._partition.a.get_value(borrow=True)[self._partition.allocated_node_offsets[self._id] + GEN])
@property
def activations(self):
return {"default": self.activation}
@activation.setter
def activation(self, activation):
a_array = self._partition.a.get_value(borrow=True)
a_array[self._partition.allocated_node_offsets[self._id] + GEN] = activation
self._partition.a.set_value(a_array, borrow=True)
def get_gate(self, type):
if type not in self.__gatecache:
self.__gatecache[type] = TheanoGate(type, self, self._nodenet, self._partition)
return self.__gatecache[type]
def set_gatefunction_name(self, gate_type, gatefunction_name):
self._nodenet.set_node_gatefunction_name(self.uid, gate_type, gatefunction_name)
def get_gatefunction_name(self, gate_type):
g_function_selector = self._partition.g_function_selector.get_value(borrow=True)
return get_string_gatefunction_type(g_function_selector[self._partition.allocated_node_offsets[self._id] + get_numerical_gate_type(gate_type, self.nodetype)])
def get_gatefunction_names(self):
result = {}
g_function_selector = self._partition.g_function_selector.get_value(borrow=True)
for numericalgate in range(0, get_gates_per_type(self._numerictype, self._nodenet.native_modules)):
result[get_string_gate_type(numericalgate, self.nodetype)] = \
get_string_gatefunction_type(g_function_selector[self._partition.allocated_node_offsets[self._id] + numericalgate])
return result
def set_gate_parameter(self, gate_type, parameter, value):
self._nodenet.set_node_gate_parameter(self.uid, gate_type, parameter, value)
def get_gate_parameters(self):
return self.clone_non_default_gate_parameters()
def clone_non_default_gate_parameters(self, gate_type=None):
g_threshold_array = self._partition.g_threshold.get_value(borrow=True)
g_amplification_array = self._partition.g_amplification.get_value(borrow=True)
g_min_array = self._partition.g_min.get_value(borrow=True)
g_max_array = self._partition.g_max.get_value(borrow=True)
g_theta = self._partition.g_theta.get_value(borrow=True)
gatemap = {}
gate_types = self.nodetype.gate_defaults.keys()
if gate_type is not None:
if gate_type in gate_types:
gate_types = [gate_type]
else:
return None
for gate_type in gate_types:
numericalgate = get_numerical_gate_type(gate_type, self.nodetype)
gate_parameters = {}
threshold = g_threshold_array[self._partition.allocated_node_offsets[self._id] + numericalgate].item()
if 'threshold' not in self.nodetype.gate_defaults[gate_type] or threshold != self.nodetype.gate_defaults[gate_type]['threshold']:
gate_parameters['threshold'] = threshold
amplification = g_amplification_array[self._partition.allocated_node_offsets[self._id] + numericalgate].item()
if 'amplification' not in self.nodetype.gate_defaults[gate_type] or amplification != self.nodetype.gate_defaults[gate_type]['amplification']:
gate_parameters['amplification'] = amplification
minimum = g_min_array[self._partition.allocated_node_offsets[self._id] + numericalgate].item()
if 'minimum' not in self.nodetype.gate_defaults[gate_type] or minimum != self.nodetype.gate_defaults[gate_type]['minimum']:
gate_parameters['minimum'] = minimum
maximum = g_max_array[self._partition.allocated_node_offsets[self._id] + numericalgate].item()
if 'maximum' not in self.nodetype.gate_defaults[gate_type] or maximum != self.nodetype.gate_defaults[gate_type]['maximum']:
gate_parameters['maximum'] = maximum
theta = g_theta[self._partition.allocated_node_offsets[self._id] + numericalgate].item()
if 'theta' not in self.nodetype.gate_defaults[gate_type] or theta != self.nodetype.gate_defaults[gate_type]['theta']:
gate_parameters['theta'] = theta
if not len(gate_parameters) == 0:
gatemap[gate_type] = gate_parameters
return gatemap
def take_slot_activation_snapshot(self):
a_array = self._partition.a.get_value(borrow=True)
self.slot_activation_snapshot.clear()
for slottype in self.nodetype.slottypes:
self.slot_activation_snapshot[slottype] = \
a_array[self._partition.allocated_node_offsets[self._id] + get_numerical_slot_type(slottype, self.nodetype)]
def get_slot(self, type):
if type not in self.__slotcache:
self.__slotcache[type] = TheanoSlot(type, self, self._nodenet, self._partition)
return self.__slotcache[type]
def unlink_completely(self):
self._partition.unlink_node_completely(self._id)
if self.uid in self._nodenet.proxycache:
del self._nodenet.proxycache[self.uid]
def unlink(self, gate_name=None, target_node_uid=None, slot_name=None):
for gate_name_candidate in self.nodetype.gatetypes:
if gate_name is None or gate_name == gate_name_candidate:
for link_candidate in self.get_gate(gate_name_candidate).get_links():
if target_node_uid is None or target_node_uid == link_candidate.target_node.uid:
if slot_name is None or slot_name == link_candidate.target_slot.type:
self._nodenet.delete_link(self.uid, gate_name_candidate, link_candidate.target_node.uid, link_candidate.target_slot.type)
def get_associated_node_uids(self):
numeric_ids_in_same_partition = self._partition.get_associated_node_ids(self._id)
ids = [node_to_id(id, self._partition.pid) for id in numeric_ids_in_same_partition]
# find this node in links coming in from other partitions to this node's partition
for partition_from_spid, inlinks in self._partition.inlinks.items():
for numeric_slot in range(0, get_slots_per_type(self._numerictype, self._nodenet.native_modules)):
element = self._partition.allocated_node_offsets[self._id] + numeric_slot
from_elements = inlinks[0].get_value(borrow=True)
to_elements = inlinks[1].get_value(borrow=True)
weights = inlinks[2].get_value(borrow=True)
if element in to_elements:
from_partition = self._nodenet.partitions[partition_from_spid]
element_index = np.where(to_elements == element)[0][0]
slotrow = weights[element_index]
links_indices = np.nonzero(slotrow)[0]
for link_index in links_indices:
source_id = from_partition.allocated_elements_to_nodes[from_elements[link_index]]
ids.append(node_to_id(source_id, from_partition.pid))
# find this node in links going out to other partitions
for partition_to_spid, to_partition in self._nodenet.partitions.items():
if self._partition.spid in to_partition.inlinks:
for numeric_gate in range(0, get_gates_per_type(self._numerictype, self._nodenet.native_modules)):
element = self._partition.allocated_node_offsets[self._id] + numeric_gate
inlinks = to_partition.inlinks[self._partition.spid]
from_elements = inlinks[0].get_value(borrow=True)
to_elements = inlinks[1].get_value(borrow=True)
weights = inlinks[2].get_value(borrow=True)
if element in from_elements:
element_index = np.where(from_elements == element)[0][0]
gatecolumn = weights[:, element_index]
links_indices = np.nonzero(gatecolumn)[0]
for link_index in links_indices:
target_id = to_partition.allocated_elements_to_nodes[to_elements[link_index]]
ids.append(node_to_id(target_id, to_partition.pid))
return ids
def get_parameter(self, parameter):
if self.type in self._nodenet.native_modules:
return self.parameters.get(parameter, self.nodetype.parameter_defaults.get(parameter, None))
else:
return self.clone_parameters().get(parameter, None)
def set_parameter(self, parameter, value):
if value == '' or value is None:
if parameter in self.nodetype.parameter_defaults:
value = self.nodetype.parameter_defaults[parameter]
else:
value = None
if self.type == "Sensor" and parameter == "datasource":
if value is not None and value != "":
datasources = self._nodenet.get_datasources()
sensor_element = self._partition.allocated_node_offsets[self._id] + GEN
old_datasource_index = np.where(self._partition.sensor_indices == sensor_element)[0]
self._partition.sensor_indices[old_datasource_index] = 0
if value not in datasources:
self.logger.warning("Datasource %s not known, will not be assigned." % value)
return
datasource_index = datasources.index(value)
if self._partition.sensor_indices[datasource_index] != sensor_element and \
self._partition.sensor_indices[datasource_index] > 0:
other_sensor_element = self._partition.sensor_indices[datasource_index]
other_sensor_id = node_to_id(self._partition.allocated_elements_to_nodes[other_sensor_element], self._partition.pid)
self.logger.warning("Datasource %s had already been assigned to sensor %s, which will now be unassigned." % (value, other_sensor_id))
self._nodenet.sensormap[value] = self.uid
self._partition.sensor_indices[datasource_index] = sensor_element
elif self.type == "Actor" and parameter == "datatarget":
if value is not None and value != "":
datatargets = self._nodenet.get_datatargets()
actuator_element = self._partition.allocated_node_offsets[self._id] + GEN
old_datatarget_index = np.where(self._partition.actuator_indices == actuator_element)[0]
self._partition.actuator_indices[old_datatarget_index] = 0
if value not in datatargets:
self.logger.warning("Datatarget %s not known, will not be assigned." % value)
return
datatarget_index = datatargets.index(value)
if self._partition.actuator_indices[datatarget_index] != actuator_element and \
self._partition.actuator_indices[datatarget_index] > 0:
other_actuator_element = self._partition.actuator_indices[datatarget_index]
other_actuator_id = node_to_id(self._partition.allocated_elements_to_nodes[other_actuator_element], self._partition.pid)
self.logger.warning("Datatarget %s had already been assigned to actuator %s, which will now be unassigned." % (value, other_actuator_id))
self._nodenet.actuatormap[value] = self.uid
self._partition.actuator_indices[datatarget_index] = actuator_element
elif self.type == "Activator" and parameter == "type":
if value != "sampling":
self._nodenet.set_nodespace_gatetype_activator(self.parent_nodespace, value, self.uid)
else:
self._nodenet.set_nodespace_sampling_activator(self.parent_nodespace, self.uid)
elif self.type == "Pipe" and parameter == "expectation":
g_expect_array = self._partition.g_expect.get_value(borrow=True)
g_expect_array[self._partition.allocated_node_offsets[self._id] + get_numerical_gate_type("gen")] = float(value)
g_expect_array[self._partition.allocated_node_offsets[self._id] + get_numerical_gate_type("sur")] = float(value)
g_expect_array[self._partition.allocated_node_offsets[self._id] + get_numerical_gate_type("por")] = float(value)
self._partition.g_expect.set_value(g_expect_array, borrow=True)
elif self.type == "Pipe" and parameter == "wait":
g_wait_array = self._partition.g_wait.get_value(borrow=True)
g_wait_array[self._partition.allocated_node_offsets[self._id] + get_numerical_gate_type("sur")] = int(value)
g_wait_array[self._partition.allocated_node_offsets[self._id] + get_numerical_gate_type("por")] = int(value)
self._partition.g_wait.set_value(g_wait_array, borrow=True)
elif self.type == "Comment" and parameter == "comment":
self.parameters[parameter] = value
elif self.type in self._nodenet.native_modules:
self.parameters[parameter] = value
def clear_parameter(self, parameter):
if self.type in self._nodenet.native_modules and parameter in self.parameters:
del self.parameters[parameter]
def clone_parameters(self):
parameters = {}
if self.type == "Sensor":
sensor_element = self._partition.allocated_node_offsets[self._id] + GEN
datasource_index = np.where(self._partition.sensor_indices == sensor_element)[0]
if len(datasource_index) == 0:
parameters['datasource'] = None
else:
parameters['datasource'] = self._nodenet.get_datasources()[datasource_index[0]]
elif self.type == "Actor":
actuator_element = self._partition.allocated_node_offsets[self._id] + GEN
datatarget_index = np.where(self._partition.actuator_indices == actuator_element)[0]
if len(datatarget_index) == 0:
parameters['datatarget'] = None
else:
parameters['datatarget'] = self._nodenet.get_datatargets()[datatarget_index[0]]
elif self.type == "Activator":
activator_type = None
if self._id in self._partition.allocated_nodespaces_por_activators:
activator_type = "por"
elif self._id in self._partition.allocated_nodespaces_ret_activators:
activator_type = "ret"
elif self._id in self._partition.allocated_nodespaces_sub_activators:
activator_type = "sub"
elif self._id in self._partition.allocated_nodespaces_sur_activators:
activator_type = "sur"
elif self._id in self._partition.allocated_nodespaces_cat_activators:
activator_type = "cat"
elif self._id in self._partition.allocated_nodespaces_exp_activators:
activator_type = "exp"
elif self._id in self._partition.allocated_nodespaces_sampling_activators:
activator_type = "sampling"
parameters['type'] = activator_type
elif self.type == "Pipe":
g_expect_array = self._partition.g_expect.get_value(borrow=True)
value = g_expect_array[self._partition.allocated_node_offsets[self._id] + get_numerical_gate_type("sur")].item()
parameters['expectation'] = value
g_wait_array = self._partition.g_wait.get_value(borrow=True)
parameters['wait'] = g_wait_array[self._partition.allocated_node_offsets[self._id] + get_numerical_gate_type("sur")].item()
elif self.type == "Comment":
parameters['comment'] = self.parameters['comment']
elif self.type in self._nodenet.native_modules:
# handle the defined ones, the ones with defaults and value ranges
for parameter in self.nodetype.parameters:
value = None
if parameter in self.parameters:
value = self.parameters[parameter]
elif parameter in self.nodetype.parameter_defaults:
value = self.nodetype.parameter_defaults[parameter]
parameters[parameter] = value
# see if something else has been set and return, if so
for parameter in self.parameters:
if parameter not in parameters:
parameters[parameter] = self.parameters[parameter]
return parameters
def get_state(self, state):
return self._state.get(state)
def set_state(self, state, value):
if isinstance(value, np.floating):
value = float(value)
self._state[state] = value
def clone_state(self):
if self._numerictype > MAX_STD_NODETYPE:
return self._state.copy()
else:
return None
def clone_sheaves(self):
return {"default": dict(uid="default", name="default", activation=self.activation)} # todo: implement sheaves
def node_function(self):
try:
self.nodetype.nodefunction(netapi=self._nodenet.netapi, node=self, sheaf="default", **self.clone_parameters())
except Exception:
self._nodenet.is_active = False
if self.nodetype is not None and self.nodetype.nodefunction is None:
self.logger.warn("No nodefunction found for nodetype %s. Node function definition is: %s" % (self.nodetype.name, self.nodetype.nodefunction_definition))
else:
raise
class TheanoGate(Gate):
"""
theano gate proxy clas
"""
@property
def type(self):
return self.__type
@property
def node(self):
return self.__node
@property
def empty(self):
w_matrix = self.__partition.w.get_value(borrow=True)
gatecolumn = w_matrix[:, self.__partition.allocated_node_offsets[node_from_id(self.__node.uid)] + self.__numerictype]
return len(np.nonzero(gatecolumn)[0]) == 0
@property
def activation(self):
return float(self.__partition.a.get_value(borrow=True)[self.__partition.allocated_node_offsets[node_from_id(self.__node.uid)] + self.__numerictype])
@activation.setter
def activation(self, value):
a_array = self.__partition.a.get_value(borrow=True)
a_array[self.__partition.allocated_node_offsets[node_from_id(self.__node.uid)] + self.__numerictype] = value
self.__partition.a.set_value(a_array, borrow=True)
@property
def activations(self):
return {'default': self.activation} # todo: implement sheaves
def __init__(self, type, node, nodenet, partition):
self.__type = type
self.__node = node
self.__nodenet = nodenet
self.__partition = partition
self.__numerictype = get_numerical_gate_type(type, node.nodetype)
self.__linkcache = None
def get_links(self):
if self.__linkcache is None:
self.__linkcache = []
w_matrix = self.__partition.w.get_value(borrow=True)
gatecolumn = w_matrix[:, self.__partition.allocated_node_offsets[node_from_id(self.__node.uid)] + self.__numerictype]
links_indices = np.nonzero(gatecolumn)[0]
for index in links_indices:
target_id = self.__partition.allocated_elements_to_nodes[index]
target_type = self.__partition.allocated_nodes[target_id]
target_nodetype = self.__nodenet.get_nodetype(get_string_node_type(target_type, self.__nodenet.native_modules))
target_slot_numerical = index - self.__partition.allocated_node_offsets[target_id]
target_slot_type = get_string_slot_type(target_slot_numerical, target_nodetype)
link = TheanoLink(self.__nodenet, self.__node.uid, self.__type, node_to_id(target_id, self.__partition.pid), target_slot_type)
self.__linkcache.append(link)
element = self.__partition.allocated_node_offsets[node_from_id(self.__node.uid)] + self.__numerictype
# does any of the inlinks in any partition orginate from me?
for partition_to_spid, to_partition in self.__nodenet.partitions.items():
if self.__partition.spid in to_partition.inlinks:
inlinks = to_partition.inlinks[self.__partition.spid]
from_elements = inlinks[0].get_value(borrow=True)
to_elements = inlinks[1].get_value(borrow=True)
weights = inlinks[2].get_value(borrow=True)
if element in from_elements:
element_index = np.where(from_elements == element)[0][0]
gatecolumn = weights[:, element_index]
links_indices = np.nonzero(gatecolumn)[0]
for link_index in links_indices:
target_id = to_partition.allocated_elements_to_nodes[to_elements[link_index]]
target_type = to_partition.allocated_nodes[target_id]
target_slot_numerical = to_elements[link_index] - to_partition.allocated_node_offsets[target_id]
target_nodetype = self.__nodenet.get_nodetype(get_string_node_type(target_type, self.__nodenet.native_modules))
target_slot_type = get_string_slot_type(target_slot_numerical, target_nodetype)
link = TheanoLink(self.__nodenet, self.__node.uid, self.__type, node_to_id(target_id, to_partition.pid), target_slot_type)
self.__linkcache.append(link)
return self.__linkcache
def invalidate_caches(self):
self.__linkcache = None
def get_parameter(self, parameter_name):
gate_parameters = self.__node.nodetype.gate_defaults[self.type]
gate_parameters.update(self.__node.clone_non_default_gate_parameters(self.type))
return gate_parameters[parameter_name]
def clone_sheaves(self):
return {"default": dict(uid="default", name="default", activation=self.activation)} # todo: implement sheaves
def gate_function(self, input_activation, sheaf="default"):
# in the theano implementation, this will only be called for native module gates, and simply write
# the value back to the activation vector for the theano math to take over
self.activation = input_activation
def open_sheaf(self, input_activation, sheaf="default"):
pass # todo: implement sheaves
class TheanoSlot(Slot):
"""
theano slot proxy class
"""
@property
def type(self):
return self.__type
@property
def node(self):
return self.__node
@property
def empty(self):
w_matrix = self.__partition.w.get_value(borrow=True)
slotrow = w_matrix[self.__partition.allocated_node_offsets[node_from_id(self.__node.uid)] + self.__numerictype]
if self.__partition.sparse:
return len(np.nonzero(slotrow)[1]) == 0
else:
return len(np.nonzero(slotrow)[0]) == 0
@property
def activation(self):
return self.__node.slot_activation_snapshot[self.__type]
@property
def activations(self):
return {
"default": self.activation
}
def __init__(self, type, node, nodenet, partition):
self.__type = type
self.__node = node
self.__nodenet = nodenet
self.__partition = partition
self.__numerictype = get_numerical_slot_type(type, node.nodetype)
self.__linkcache = None
def get_activation(self, sheaf="default"):
return self.activation
def get_links(self):
if self.__linkcache is None:
self.__linkcache = []
w_matrix = self.__partition.w.get_value(borrow=True)
slotrow = w_matrix[self.__partition.allocated_node_offsets[node_from_id(self.__node.uid)] + self.__numerictype]
if self.__partition.sparse:
links_indices = np.nonzero(slotrow)[1]
else:
links_indices = | np.nonzero(slotrow) | numpy.nonzero |
"""
This module is an implementation of a variety of tools for rotations in 3D space.
"""
from __future__ import print_function, absolute_import # Compatibility with python 2 and 3
import sys, numpy, types, pickle, time, math
import logging
logger = logging.getLogger(__name__)
from .log import log_and_raise_error,log_warning,log_info,log_debug
import condor.utils.linalg
# CANONICAL ROTATION MATRICES
# Rotation matrix around x-axis - observing the right hand rule
R_x = lambda t: numpy.array([[1., 0., 0.],
[0., numpy.cos(t), -numpy.sin(t)],
[0., numpy.sin(t), numpy.cos(t)]])
# Rotation matrix around y-axis - observing the right hand rule
R_y = lambda t: numpy.array([[numpy.cos(t), 0., numpy.sin(t)],
[0., 1., 0.],
[-numpy.sin(t), 0., numpy.cos(t)]])
# Rotation matrix around z-axis - observing the right hand rule
R_z = lambda t: numpy.array([[numpy.cos(t), -numpy.sin(t), 0.],
[numpy.sin(t), numpy.cos(t), 0.],
[0., 0., 1.]])
# Rotation of a given vector by a given angle with respect to one of the three principal axes
rot_x = lambda v,t: R_x(t).dot(v)
rot_y = lambda v,t: R_y(t).dot(v)
rot_z = lambda v,t: R_z(t).dot(v)
# CANONICAL QUATERNIONS
# Quaternion from angle and rotation unit vector coordinates (right-hand rule)
quat = lambda theta,ux,uy,uz: numpy.array([numpy.cos(theta/2.),
numpy.sin(theta/2.)*ux,
numpy.sin(theta/2.)*uy,
numpy.sin(theta/2.)*uz])
# Quaternions for roations with respect to the x-, y- or z-axis
quat_x = lambda theta: quat(theta,1.,0.,0.)
quat_y = lambda theta: quat(theta,0.,1.,0.)
quat_z = lambda theta: quat(theta,0.,0.,1.)
class Rotation:
r"""
Class for a rotation in 3D space
**Arguments:**
:values (array): Array of values that define the rotation. For random rotations set values=``None`` and for example formalism=``'random'``. (default ``None``)
:formalism: Formalism that defines how the argument values is interpreted. If ``None`` no rotation. (default ``None``)
*Rotation formalism can be one of the following:*
======================== =========================================================================================================================== ===============================================================================
``formalism`` Variables ``values``
======================== =========================================================================================================================== ===============================================================================
``'quaternion'`` :math:`q = w + ix + jy + kz` :math:`[w,x,y,z]`
``'rotation_matrix'`` :math:`R = \begin{pmatrix} R_{11} & R_{12} & R_{13} \\ R_{21} & R_{22} & R_{23} \\ R_{31} & R_{32} & R_{33} \end{pmatrix}` :math:`[[R_{11},R_{12},R_{13}],[R_{21},R_{22},R_{23}],[R_{31},R_{32},R_{33}]]`
``'euler_angles_zxz'`` :math:`e_1^{(z)}`, :math:`e_2^{(x)}`, :math:`e_3^{(z)}` :math:`[e_1^{(y)},e_2^{(z)},e_3^{(y)}]`
``'euler_angles_xyx'`` :math:`e_1^{(x)}`, :math:`e_2^{(y)}`, :math:`e_3^{(x)}` :math:`[e_1^{(x)},e_2^{(y)},e_3^{(x)}]`
``'euler_angles_xyz'`` :math:`e_1^{(x)}`, :math:`e_2^{(y)}`, :math:`e_3^{(z)}` :math:`[e_1^{(x)},e_2^{(y)},e_3^{(z)}]`
``'euler_angles_yzx'`` :math:`e_1^{(y)}`, :math:`e_2^{(z)}`, :math:`e_3^{(x)}` :math:`[e_1^{(y)},e_2^{(z)},e_3^{(x)}]`
``'euler_angles_zxy'`` :math:`e_1^{(z)}`, :math:`e_2^{(x)}`, :math:`e_3^{(y)}` :math:`[e_1^{(z)},e_2^{(x)},e_3^{(y)}]`
``'euler_angles_zyx'`` :math:`e_1^{(z)}`, :math:`e_2^{(y)}`, :math:`e_3^{(x)}` :math:`[e_1^{(z)},e_2^{(y)},e_3^{(x)}]`
``'euler_angles_yxz'`` :math:`e_1^{(y)}`, :math:`e_2^{(x)}`, :math:`e_3^{(z)}` :math:`[e_1^{(y)},e_2^{(x)},e_3^{(z)}]`
``'euler_angles_xzy'`` :math:`e_1^{(x)}`, :math:`e_2^{(z)}`, :math:`e_3^{(y)}` :math:`[e_1^{(x)},e_2^{(z)},e_3^{(y)}]`
``'random'`` *fully random rotation* ``None``
``'random_x'`` *random rotation around* :math:`x` *axis* ``None``
``'random_y'`` *random rotation around* :math:`y` *axis* ``None``
``'random_z'`` *random rotation around* :math:`z` *axis* ``None``
======================== =========================================================================================================================== ===============================================================================
"""
def __init__(self, values=None, formalism=None):
self.rotation_matrix = None
if values is None and formalism is None:
# No rotation (rotation matrix = identity matrix)
self.rotation_matrix = | numpy.ones(shape=(3,3)) | numpy.ones |
"""
Created on 2020
@author: <NAME>
"""
###############################################################################
#
# November 2020, Paris
#
# This file contains the main functions concerning the angular tansformations,
# sky projections and spherical trigonomtry.
#
# Documentation is provided on Vitral, 2021.
# If you have any further questions please email <EMAIL>
#
###############################################################################
import numpy as np
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# ------------------------------------------------------------------------------
"Global variables"
# ------------------------------------------------------------------------------
# Right ascention of the north galactic pole, in radians
a_NGP = 192.85947789 * (np.pi / 180)
# Declination of the north galactic pole, in radians
d_NGP = 27.12825241 * (np.pi / 180)
# Longitude of the north celestial pole, in radians
l_NCP = 122.93192526 * (np.pi / 180)
# Vertical waves in the solar neighbourhood in Gaia DR2
# Bennett & Bovy, 2019, MNRAS
# --> Sun Z position (kpc), in galactocentric coordinates
z_sun = 0.0208
# Sun Y position (kpc), in galactocentric coordinates, by definition.
y_sun = 0
# A geometric distance measurement to the Galactic center black hole
# with 0.3% uncertainty
# Gracity Collaboration, 2019, A&A
# --> Sun distance from the Galactic center, in kpc.
d_sun = 8.178
# Sun X position (kpc), in galactocentric coordinates
x_sun = np.sqrt(d_sun * d_sun - z_sun * z_sun)
# On the Solar Velocity
# <NAME> and <NAME>, 2018, RNAAS
# --> Sun X velocity (km/s), in galactocentric coordinates
vx_sun = -12.9
# --> Sun Y velocity (km/s), in galactocentric coordinates
vy_sun = 245.6
# --> Sun Z velocity (km/s), in galactocentric coordinates
vz_sun = 7.78
# Multuplying factor to pass from kpc to km
kpc_to_km = 3.086 * 10 ** 16
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# ------------------------------------------------------------------------------
"Angles handling"
# ------------------------------------------------------------------------------
def sky_distance_deg(RA, Dec, RA0, Dec0):
"""
Computes the sky distance (in degrees) between two sets of
sky coordinates, given also in degrees.
Parameters
----------
RA : array_like, float
Right ascension (in degrees) of object 1.
Dec : array_like (same shape as RA), float
Declination (in degrees) of object 1.
RA0 : array_like (same shape as RA), float
Right ascension (in degrees) of object 2.
Dec0 : array_like (same shape as RA), float
Declination (in degrees) of object 2.
Returns
-------
R : array_like, float
Sky distance (in degrees) between object 1 and object 2.
"""
RA = RA * np.pi / 180
Dec = Dec * np.pi / 180
RA0 = RA0 * np.pi / 180
Dec0 = Dec0 * np.pi / 180
R = (180 / np.pi) * np.arccos(
np.sin(Dec) * np.sin(Dec0) + np.cos(Dec) * np.cos(Dec0) * np.cos((RA - RA0))
)
return np.asarray(R)
def get_circle_sph_trig(r, a0, d0, nbins=500):
"""
Generates a circle in spherical coordinates.
Parameters
----------
r : float
Distance from the center, in degrees.
a0 : float
Right ascention from origin, in degrees.
d0 : float
Declination from origin in, in degrees.
nbins : int, optional
Number of circle points. The default is 500.
Returns
-------
ra : array_like
Right ascention in degrees.
dec : array_like
Declination in degrees.
"""
# Converts angles to radians
r = r * np.pi / 180
a0 = a0 * np.pi / 180
d0 = d0 * np.pi / 180
phi = np.linspace(0, 2 * np.pi, nbins)
a = np.zeros(nbins)
d = np.zeros(nbins)
for i in range(0, nbins):
a[i], d[i] = polar_to_sky(r, phi[i], a0, d0)
return a, d
def polar_to_sky(r, phi, a0, d0):
"""
Transforms spherical polar coordinates (r,phi) into sky coordinates,
in degrees (RA,Dec).
Parameters
----------
r : array_like
Radial distance from center.
phi : array_like
Angle between increasing declination and the projected radius
(pointing towards the source).
a0 : float
Right ascention from origin in radians.
d0 : float
Declination from origin in radians.
Returns
-------
ra : array_like
Right ascention in degrees.
dec : array_like
Declination in degrees.
"""
d = np.arcsin(np.cos(r) * np.sin(d0) + np.cos(d0) * np.cos(phi) * np.sin(r))
if phi < np.pi:
if (np.cos(r) - np.sin(d) * np.sin(d0)) / (np.cos(d) * np.cos(d0)) > 0:
a = a0 + np.arccos(np.sqrt(1 - (np.sin(phi) * np.sin(r) / np.cos(d)) ** 2))
else:
a = a0 + np.arccos(-np.sqrt(1 - (np.sin(phi) * np.sin(r) / np.cos(d)) ** 2))
if phi >= np.pi:
if (np.cos(r) - np.sin(d) * np.sin(d0)) / (np.cos(d) * np.cos(d0)) > 0:
a = a0 - np.arccos(np.sqrt(1 - (np.sin(phi) * np.sin(r) / np.cos(d)) ** 2))
else:
a = a0 - np.arccos(-np.sqrt(1 - (np.sin(phi) * np.sin(r) / np.cos(d)) ** 2))
ra = a * 180 / np.pi
dec = d * 180 / np.pi
return ra, dec
def sky_to_polar(a, d, a0, d0):
"""
Transforms sky coordinates, in degrees (RA,Dec), into
spherical polar coordinates (r,phi).
Parameters
----------
a : array_like
Right ascention in degrees.
d : array_like
Declination in degrees.
a0 : float
Right ascention from origin.
d0 : float
Declination from origin.
Returns
-------
r : array_like
Radial distance from center.
p : array_like
Angle between increasing declination and the projected radius
(pointing towards the source), in radians.
"""
r = sky_distance_deg(a, d, a0, d0) * np.pi / 180
a = a * np.pi / 180
d = d * np.pi / 180
sp = np.cos(d) * np.sin(a - (a0 * np.pi / 180)) / np.sin(r)
p = np.zeros(len(sp))
spp = np.where(sp > 0)
spm = np.where(sp <= 0)
dp = np.where(d > (d0 * np.pi / 180))
dm = np.where(d <= (d0 * np.pi / 180))
p[np.intersect1d(spp, dp)] = np.arcsin(sp[np.intersect1d(spp, dp)])
p[np.intersect1d(spp, dm)] = np.pi - np.arcsin(sp[np.intersect1d(spp, dm)])
p[np.intersect1d(spm, dp)] = 2 * np.pi + np.arcsin(sp[np.intersect1d(spm, dp)])
p[np.intersect1d(spm, dm)] = np.pi - np.arcsin(sp[np.intersect1d(spm, dm)])
return r, p
def angular_sep_vector(v0, v):
"""
Returns separation angle in radians between two 3D arrays.
Parameters
----------
v0 : 3D array
Vector 1.
v : 3D array
Vector 2.
Returns
-------
R : array_like
Separation between vector 1 and vector 2 in radians.
"""
try:
v0.shape
except NameError:
print("You did not give a valid input.")
return
v = v / np.linalg.norm(v)
B = np.arcsin(v[2])
cosA = v[0] / np.cos(B)
sinA = v[1] / np.cos(B)
A = np.arctan2(sinA, cosA)
v0 = v0 / np.linalg.norm(v0)
B0 = np.arcsin(v0[2])
cosA0 = v0[0] / np.cos(B0)
sinA0 = v0[1] / np.cos(B0)
A0 = np.arctan2(sinA0, cosA0)
cosR = np.sin(B0) * np.sin(B) + np.cos(B0) * np.cos(B) * np.cos(A - A0)
R = np.arccos(cosR)
return R
def rodrigues_formula(k, v, theta, debug=False):
"""
Returns the rotation of v of an angle theta with respect to the vector k
Applies the Rodrigues formula from:
https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
Parameters
----------
k : array_like
Vector with respect to which v will be rotated.
v : array_like
Vector to be rotated.
theta : float
Angle to rotate v.
debug : boolean, optional
True if the reader wants to print debug diagnistics.
The default is False.
Returns
-------
v_rot : array_like
Rotated vector.
"""
try:
v.shape
except NameError:
print("You did not give a valid input for the Rodrigues formula.")
return
if len(np.shape(v)) == 1 and len(v) == 3:
v_rot = (
v * np.cos(theta)
+ np.cross(k, v) * np.sin(theta)
+ k * np.dot(k, v) * (1 - np.cos(theta))
)
elif len(np.shape(v)) == 2 and np.shape(v)[0] == 3:
v_rot = np.zeros((np.shape(v)[1], 3))
for i in range(0, len(v_rot)):
v0 = np.asarray([v[0][i], v[1][i], v[2][i]])
v_rot[i] = (
v0 * np.cos(theta)
+ np.cross(k, v0) * np.sin(theta)
+ k * np.dot(v0, k) * (1 - np.cos(theta))
)
if debug is True and i < 10:
print("v0 :", v0)
print("v_rot:", v_rot[i])
else:
print("You did not give a valid input for the Rodrigues formula.")
return
return v_rot
def sky_coord_rotate(v_i, v0_i, v0_f, theta=0, debug=False):
"""
Gets new angles (RA,Dec) in degrees of a rotated vector.
Parameters
----------
v_i : array_like
Vectors to be rotated.
v0_i : array_like
Vector pointing to the initial centroid position.
v0_f : array_like
Vector pointing to the final centroid position.
theta : float, optional
Angle to rotate (for no translation), in radians. The default is 0.
debug : boolean, optional
True if the reader wants to print debug diagnistics.
The default is False.
Returns
-------
array_like, array_like
Arrays containing the new rotated (RA,Dec) positions.
"""
if (v0_i == v0_f).all():
if debug is True:
print("Pure rotation")
k = v0_i / np.linalg.norm(v0_i)
else:
if debug is True:
print("Translation in spherical geometry")
k = np.cross(v0_i, v0_f) / np.linalg.norm(np.cross(v0_i, v0_f))
theta = angular_sep_vector(v0_i, v0_f)
if debug is True:
print("Vector k:", k)
print("Angle of separation [degrees]:", theta * 180 / np.pi)
v_f = rodrigues_formula(k, v_i, theta)
try:
v_f.shape
except NameError:
print("You did not give a valid input for the Rodrigues formula.")
return
if len(np.shape(v_f)) == 1 and len(v_f) == 3:
v_f = v_f / np.linalg.norm(v_f)
B = np.arcsin(v_f[2])
cosA = v_f[0] / np.cos(B)
sinA = v_f[1] / np.cos(B)
A = np.arctan2(sinA, cosA)
elif len(np.shape(v_f)) == 2:
A = np.zeros(len(v_f))
B = np.zeros(len(v_f))
for i in range(0, len(v_f)):
v_f[i] = v_f[i] / np.linalg.norm(v_f[i])
B[i] = np.arcsin(v_f[i][2])
cosA = v_f[i][0] / np.cos(B[i])
sinA = v_f[i][1] / np.cos(B[i])
A[i] = np.arctan2(sinA, cosA)
if debug is True and i < 10:
print("A, B [degrees]:", A[i] * (180 / np.pi), B[i] * (180 / np.pi))
else:
print("You did not give a valid input for the Rodrigues formula.")
return
return A * (180 / np.pi), B * (180 / np.pi)
def sky_vector(a, d, a0, d0, af, df):
"""
Transforms sky coordinates in vectors to be used by sky_coord_rotate.
Parameters
----------
a : float, array_like
Original set of RA in degrees.
d : float, array_like
Original set of Dec in degrees.
a0 : float
Original centroid RA in degrees.
d0 : float
Original centroid Dec in degrees.
af : float
Final centroid RA in degrees.
df : float
Final centroid Dec in degrees.
Returns
-------
v_i : array_like
Vectors to be rotated.
v0_i : array_like
Vector pointing to the initial centroid position.
v0_f : array_like
Vector pointing to the final centroid position.
"""
a = a * (np.pi / 180)
d = d * (np.pi / 180)
a0 = a0 * (np.pi / 180)
d0 = d0 * (np.pi / 180)
af = af * (np.pi / 180)
df = df * (np.pi / 180)
v_i = np.asarray([np.cos(a) * np.cos(d), np.sin(a) * np.cos(d), np.sin(d)])
v0_i = np.asarray([np.cos(a0) * np.cos(d0), np.sin(a0) * np.cos(d0), np.sin(d0)])
v0_f = np.asarray([np.cos(af) * np.cos(df), np.sin(af) * np.cos(df), np.sin(df)])
return v_i, v0_i, v0_f
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# ------------------------------------------------------------------------------
"Axis rotation"
# ------------------------------------------------------------------------------
def transrot_source(a, d, a0, d0, af, df):
"""
Translades and then rotates a source in spherical coordinates, so
the original directions remain the same.
Parameters
----------
a : float, array_like
Original set of RA in degrees.
d : float, array_like
Original set of Dec in degrees.
a0 : float
Original centroid RA in degrees.
d0 : float
Original centroid Dec in degrees.
af : float
Final centroid RA in degrees.
df : float
Final centroid Dec in degrees.
Returns
-------
a : array_like
Right ascention in degrees.
d : array_like
Declination in degrees.
"""
v_i, v0_i, v0_f = sky_vector(a, d, a0, d0, af, df)
a, d = sky_coord_rotate(v_i, v0_i, v0_f)
rmax = np.nanmax(sky_distance_deg(a, d, af, df)) * (np.pi / 180)
narr = np.asarray([0, 0.1, 0.25, 0.5]) * rmax
vt = np.asarray(
[
np.cos(a0 + narr) * np.cos([d0, d0, d0, d0]),
np.sin(a0 + narr) * np.cos([d0, d0, d0, d0]),
np.sin([d0, d0, d0, d0]),
]
)
at, dt = sky_coord_rotate(vt, v0_i, v0_f)
r0, p0 = sky_to_polar(a0 + narr, d0 * np.ones(len(narr)), a0, d0)
rf, pf = sky_to_polar(at, dt, af, df)
phi = np.nanmean(pf - p0)
v_i, v0_i, v0_f = sky_vector(a, d, af, df, af, df)
a, d = sky_coord_rotate(v_i, v0_i, v0_f, theta=phi)
return a, d
def rotate_axis(x, y, theta, mu_x=0, mu_y=0):
"""
Rotates and translates the two main cartesian axis.
Parameters
----------
x : float or array_like
Data in x-direction.
y : float or array_like
Data in y-direction.
theta : float
Rotation angle in radians.
mu_x : float, optional
Center of new x axis in the old frame. The default is 0.
mu_y : float, optional
Center of new y axis in the old frame. The default is 0.
Returns
-------
x_new : float or array_like
Data in new x-direction.
y_new : float or array_like
Data in new y-direction.
"""
x_new = (x - mu_x) * np.cos(theta) + (y - mu_y) * np.sin(theta)
y_new = -(x - mu_x) * np.sin(theta) + (y - mu_y) * np.cos(theta)
return x_new, y_new
def get_ellipse(a, b, theta, nbins):
"""
Provides an array describing a rotated ellipse.
Parameters
----------
a : float
Ellipse semi-major axis.
b : float
Ellipse semi-minor axis.
theta : float
Rotation angle in radians.
nbins : int
Number of points in the final array.
Returns
-------
ellipse_rot : array_like
Rotated ellipse array.
"""
t = np.linspace(0, 2 * np.pi, nbins)
ellipse = np.array([a * np.cos(t), b * np.sin(t)])
m_rot = np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]])
ellipse_rot = np.zeros((2, ellipse.shape[1]))
for i in range(ellipse.shape[1]):
ellipse_rot[:, i] = np.dot(m_rot, ellipse[:, i])
return ellipse_rot
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# ------------------------------------------------------------------------------
"Transform coordinates"
# ------------------------------------------------------------------------------
def cart_to_sph(x, y, z, vx, vy, vz):
"""
Transforms 6D cartesian coordinates to spherical coordinates.
Parameters
----------
x : array_like, float
x-axis.
y : array_like, float
y-axis.
z : array_like, float
z-axis.
vx : array_like, float
x-axis velocity.
vy : array_like, float
y-axis velocity.
vz : array_like, float
z-axis velocity.
Returns
-------
r : array_like, float
r-axis.
phi : array_like, float
phi-angle.
theta : array_like, float
theta-angle.
vr : array_like, float
r-axis velocity.
vphi : array_like, float
phi-angle velocity.
vtheta : array_like, float
theta-angle velocity.
"""
r = np.sqrt(x * x + y * y + z * z)
phi = np.arctan2(y, x)
theta = np.arccos(z / r)
vr = (vx * x + vy * y + vz * z) / r
vphi = (vy * x - vx * y) / np.sqrt(x * x + y * y)
vtheta = -(vz * (x * x + y * y) - z * (vx * x + vy * y)) / (
np.sqrt(x * x + y * y) * r
)
return r, phi, theta, vr, vphi, vtheta
def sph_to_cart(r, phi, theta, vr, vphi, vtheta):
"""
Transforms 6D spherical coordinates to cartesian coordinates.
Parameters
----------
r : array_like, float
r-axis.
phi : array_like, float
phi-angle.
theta : array_like, float
theta-angle.
vr : array_like, float
r-axis velocity.
vphi : array_like, float
phi-angle velocity.
vtheta : array_like, float
theta-angle velocity.
Returns
-------
x : array_like, float
x-axis.
y : array_like, float
y-axis.
z : array_like, float
z-axis.
vx : array_like, float
x-axis velocity.
vy : array_like, float
y-axis velocity.
vz : array_like, float
z-axis velocity.
"""
x = r * np.sin(theta) * np.cos(phi)
y = r * np.sin(theta) * np.sin(phi)
z = r * np.cos(theta)
vx = (
vr * np.sin(theta) * np.cos(phi)
+ vtheta * np.cos(theta) * np.cos(phi)
- vphi * np.sin(phi)
)
vy = (
vr * np.sin(theta) * np.sin(phi)
+ vtheta * np.cos(theta) * np.sin(phi)
+ vphi * np.cos(phi)
)
vz = vr * np.cos(theta) - vtheta * np.sin(theta)
return x, y, z, vx, vy, vz
def radec_to_lb(a, d, dadt=None, dddt=None):
"""
Transforms celestial coordinates into galactic coordinates.
Parameters
----------
a : array_like, float
Right ascention in degrees.
d : array_like, float
Declination in degrees.
dadt : array_like, float, optional
Right ascention velocity (PMRA), in mas/yr.
The default is None
dddt : array_like, float, optional
Declination velocity (PMDec), in mas/yr.
The default is None
Returns
-------
lon : array_like, float
Galactic longitude, in degrees.
b : array_like, float
Galactic latitude, in degrees.
dldt : array_like, float, optional
Galactic longitude velocity, in mas/yr
dbdt : array_like, float, optional
Galactic latitude velocity, in mas/yr. The default is None
"""
a = a * (np.pi / 180)
d = d * (np.pi / 180)
sind = np.sin(d)
cosd = np.cos(d)
sind_NGP = np.sin(d_NGP)
cosd_NGP = np.cos(d_NGP)
cosda = np.cos(a - a_NGP)
sinda = np.sin(a - a_NGP)
sinb = sind_NGP * sind + cosd_NGP * cosd * cosda
cosb_sindl = cosd * sinda
cosb_cosdl = cosd_NGP * sind - sind_NGP * cosd * cosda
b = np.arcsin(sinb)
cosb = np.cos(b)
sindl = cosb_sindl / cosb
cosdl = cosb_cosdl / cosb
if np.isscalar(sindl):
lon = l_NCP - | np.arctan2(sindl, cosdl) | numpy.arctan2 |
'''
Dataset for training
Written by Whalechen
'''
import math
import os
import random
import numpy as np
from torch.utils.data import Dataset
import nibabel
from scipy import ndimage
class BrainS18Dataset(Dataset):
def __init__(self, root_dir, img_list, sets):
with open(img_list, 'r') as f:
self.img_list = [line.strip() for line in f]
print("Processing {} datas".format(len(self.img_list)))
self.root_dir = root_dir
self.input_D = sets.input_D
self.input_H = sets.input_H
self.input_W = sets.input_W
print('input D:', self.input_D)
print('input H:', self.input_H)
print('input W:', self.input_W)
self.phase = sets.phase
def __nii2tensorarray__(self, data):
[z, y, x] = data.shape
new_data = np.reshape(data, [1, z, y, x])
new_data = new_data.astype("float32")
return new_data
def __len__(self):
return len(self.img_list)
def __getitem__(self, idx):
if self.phase == "train":
# read image and labels
ith_info = self.img_list[idx].split(" ")
img_name = os.path.join(self.root_dir, ith_info[0])
label_name = os.path.join(self.root_dir, ith_info[1])
assert os.path.isfile(img_name)
assert os.path.isfile(label_name)
img = nibabel.load(img_name) # We have transposed the data from WHD format to DHW
assert img is not None
mask = nibabel.load(label_name)
assert mask is not None
# data processing
img_array, mask_array = self.__training_data_process__(img, mask)
# 2 tensor array
img_array = self.__nii2tensorarray__(img_array)
mask_array = self.__nii2tensorarray__(mask_array)
assert img_array.shape == mask_array.shape, "img shape:{} is not equal to mask shape:{}".format(img_array.shape, mask_array.shape)
return img_array, mask_array
elif self.phase == "test":
# read image
ith_info = self.img_list[idx].split(" ")
img_name = os.path.join(self.root_dir, ith_info[0])
print(img_name)
assert os.path.isfile(img_name)
img = nibabel.load(img_name)
assert img is not None
# data processing
img_array = self.__testing_data_process__(img)
# 2 tensor array
img_array = self.__nii2tensorarray__(img_array)
return img_array
def __drop_invalid_range__(self, volume, label=None):
"""
Cut off the invalid area
"""
zero_value = volume[0, 0, 0]
non_zeros_idx = np.where(volume != zero_value)
[max_z, max_h, max_w] = np.max(np.array(non_zeros_idx), axis=1)
[min_z, min_h, min_w] = np.min(np.array(non_zeros_idx), axis=1)
if label is not None:
return volume[min_z:max_z, min_h:max_h, min_w:max_w], label[min_z:max_z, min_h:max_h, min_w:max_w]
else:
return volume[min_z:max_z, min_h:max_h, min_w:max_w]
def __random_center_crop__(self, data, label):
from random import random
"""
Random crop
"""
target_indexs = np.where(label>0)
[img_d, img_h, img_w] = data.shape
[max_D, max_H, max_W] = np.max(np.array(target_indexs), axis=1)
[min_D, min_H, min_W] = np.min(np.array(target_indexs), axis=1)
[target_depth, target_height, target_width] = np.array([max_D, max_H, max_W]) - np.array([min_D, min_H, min_W])
Z_min = int((min_D - target_depth*1.0/2) * random())
Y_min = int((min_H - target_height*1.0/2) * random())
X_min = int((min_W - target_width*1.0/2) * random())
Z_max = int(img_d - ((img_d - (max_D + target_depth*1.0/2)) * random()))
Y_max = int(img_h - ((img_h - (max_H + target_height*1.0/2)) * random()))
X_max = int(img_w - ((img_w - (max_W + target_width*1.0/2)) * random()))
Z_min = np.max([0, Z_min])
Y_min = np.max([0, Y_min])
X_min = np.max([0, X_min])
Z_max = np.min([img_d, Z_max])
Y_max = np.min([img_h, Y_max])
X_max = | np.min([img_w, X_max]) | numpy.min |
from __future__ import division, absolute_import, print_function
import warnings
import numpy as np
from numpy.testing import (
run_module_suite, TestCase, assert_, assert_equal, assert_almost_equal,
assert_no_warnings, assert_raises, assert_array_equal, suppress_warnings
)
# Test data
_ndat = np.array([[0.6244, np.nan, 0.2692, 0.0116, np.nan, 0.1170],
[0.5351, -0.9403, np.nan, 0.2100, 0.4759, 0.2833],
[np.nan, np.nan, np.nan, 0.1042, np.nan, -0.5954],
[0.1610, np.nan, np.nan, 0.1859, 0.3146, np.nan]])
# Rows of _ndat with nans removed
_rdat = [np.array([0.6244, 0.2692, 0.0116, 0.1170]),
np.array([0.5351, -0.9403, 0.2100, 0.4759, 0.2833]),
np.array([0.1042, -0.5954]),
np.array([0.1610, 0.1859, 0.3146])]
# Rows of _ndat with nans converted to ones
_ndat_ones = np.array([[0.6244, 1.0, 0.2692, 0.0116, 1.0, 0.1170],
[0.5351, -0.9403, 1.0, 0.2100, 0.4759, 0.2833],
[1.0, 1.0, 1.0, 0.1042, 1.0, -0.5954],
[0.1610, 1.0, 1.0, 0.1859, 0.3146, 1.0]])
# Rows of _ndat with nans converted to zeros
_ndat_zeros = np.array([[0.6244, 0.0, 0.2692, 0.0116, 0.0, 0.1170],
[0.5351, -0.9403, 0.0, 0.2100, 0.4759, 0.2833],
[0.0, 0.0, 0.0, 0.1042, 0.0, -0.5954],
[0.1610, 0.0, 0.0, 0.1859, 0.3146, 0.0]])
class TestNanFunctions_MinMax(TestCase):
nanfuncs = [np.nanmin, np.nanmax]
stdfuncs = [np.min, np.max]
def test_mutation(self):
# Check that passed array is not modified.
ndat = _ndat.copy()
for f in self.nanfuncs:
f(ndat)
assert_equal(ndat, _ndat)
def test_keepdims(self):
mat = np.eye(3)
for nf, rf in zip(self.nanfuncs, self.stdfuncs):
for axis in [None, 0, 1]:
tgt = rf(mat, axis=axis, keepdims=True)
res = nf(mat, axis=axis, keepdims=True)
assert_(res.ndim == tgt.ndim)
def test_out(self):
mat = np.eye(3)
for nf, rf in zip(self.nanfuncs, self.stdfuncs):
resout = np.zeros(3)
tgt = rf(mat, axis=1)
res = nf(mat, axis=1, out=resout)
assert_almost_equal(res, resout)
assert_almost_equal(res, tgt)
def test_dtype_from_input(self):
codes = 'efdgFDG'
for nf, rf in zip(self.nanfuncs, self.stdfuncs):
for c in codes:
mat = np.eye(3, dtype=c)
tgt = rf(mat, axis=1).dtype.type
res = nf(mat, axis=1).dtype.type
assert_(res is tgt)
# scalar case
tgt = rf(mat, axis=None).dtype.type
res = nf(mat, axis=None).dtype.type
assert_(res is tgt)
def test_result_values(self):
for nf, rf in zip(self.nanfuncs, self.stdfuncs):
tgt = [rf(d) for d in _rdat]
res = nf(_ndat, axis=1)
assert_almost_equal(res, tgt)
def test_allnans(self):
mat = np.array([np.nan]*9).reshape(3, 3)
for f in self.nanfuncs:
for axis in [None, 0, 1]:
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter('always')
assert_(np.isnan(f(mat, axis=axis)).all())
assert_(len(w) == 1, 'no warning raised')
assert_(issubclass(w[0].category, RuntimeWarning))
# Check scalars
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter('always')
assert_(np.isnan(f(np.nan)))
assert_(len(w) == 1, 'no warning raised')
assert_(issubclass(w[0].category, RuntimeWarning))
def test_masked(self):
mat = np.ma.fix_invalid(_ndat)
msk = mat._mask.copy()
for f in [np.nanmin]:
res = f(mat, axis=1)
tgt = f(_ndat, axis=1)
assert_equal(res, tgt)
assert_equal(mat._mask, msk)
assert_(not np.isinf(mat).any())
def test_scalar(self):
for f in self.nanfuncs:
assert_(f(0.) == 0.)
def test_matrices(self):
# Check that it works and that type and
# shape are preserved
mat = np.matrix(np.eye(3))
for f in self.nanfuncs:
res = f(mat, axis=0)
assert_(isinstance(res, np.matrix))
assert_(res.shape == (1, 3))
res = f(mat, axis=1)
assert_(isinstance(res, np.matrix))
assert_(res.shape == (3, 1))
res = f(mat)
assert_(np.isscalar(res))
# check that rows of nan are dealt with for subclasses (#4628)
mat[1] = np.nan
for f in self.nanfuncs:
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter('always')
res = f(mat, axis=0)
assert_(isinstance(res, np.matrix))
assert_(not np.any(np.isnan(res)))
assert_(len(w) == 0)
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter('always')
res = f(mat, axis=1)
assert_(isinstance(res, np.matrix))
assert_(np.isnan(res[1, 0]) and not np.isnan(res[0, 0])
and not np.isnan(res[2, 0]))
assert_(len(w) == 1, 'no warning raised')
assert_(issubclass(w[0].category, RuntimeWarning))
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter('always')
res = f(mat)
assert_(np.isscalar(res))
assert_(res != np.nan)
assert_(len(w) == 0)
class TestNanFunctions_ArgminArgmax(TestCase):
nanfuncs = [np.nanargmin, np.nanargmax]
def test_mutation(self):
# Check that passed array is not modified.
ndat = _ndat.copy()
for f in self.nanfuncs:
f(ndat)
assert_equal(ndat, _ndat)
def test_result_values(self):
for f, fcmp in zip(self.nanfuncs, [np.greater, np.less]):
for row in _ndat:
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "invalid value encountered in")
ind = f(row)
val = row[ind]
# comparing with NaN is tricky as the result
# is always false except for NaN != NaN
assert_(not np.isnan(val))
assert_(not fcmp(val, row).any())
assert_(not np.equal(val, row[:ind]).any())
def test_allnans(self):
mat = np.array([np.nan]*9).reshape(3, 3)
for f in self.nanfuncs:
for axis in [None, 0, 1]:
assert_raises(ValueError, f, mat, axis=axis)
assert_raises(ValueError, f, np.nan)
def test_empty(self):
mat = np.zeros((0, 3))
for f in self.nanfuncs:
for axis in [0, None]:
assert_raises(ValueError, f, mat, axis=axis)
for axis in [1]:
res = f(mat, axis=axis)
assert_equal(res, np.zeros(0))
def test_scalar(self):
for f in self.nanfuncs:
assert_(f(0.) == 0.)
def test_matrices(self):
# Check that it works and that type and
# shape are preserved
mat = np.matrix(np.eye(3))
for f in self.nanfuncs:
res = f(mat, axis=0)
assert_(isinstance(res, np.matrix))
assert_(res.shape == (1, 3))
res = f(mat, axis=1)
assert_(isinstance(res, np.matrix))
assert_(res.shape == (3, 1))
res = f(mat)
assert_(np.isscalar(res))
class TestNanFunctions_IntTypes(TestCase):
int_types = (np.int8, np.int16, np.int32, np.int64, np.uint8,
np.uint16, np.uint32, np.uint64)
mat = np.array([127, 39, 93, 87, 46])
def integer_arrays(self):
for dtype in self.int_types:
yield self.mat.astype(dtype)
def test_nanmin(self):
tgt = np.min(self.mat)
for mat in self.integer_arrays():
assert_equal(np.nanmin(mat), tgt)
def test_nanmax(self):
tgt = np.max(self.mat)
for mat in self.integer_arrays():
assert_equal(np.nanmax(mat), tgt)
def test_nanargmin(self):
tgt = np.argmin(self.mat)
for mat in self.integer_arrays():
assert_equal(np.nanargmin(mat), tgt)
def test_nanargmax(self):
tgt = np.argmax(self.mat)
for mat in self.integer_arrays():
assert_equal(np.nanargmax(mat), tgt)
def test_nansum(self):
tgt = np.sum(self.mat)
for mat in self.integer_arrays():
assert_equal(np.nansum(mat), tgt)
def test_nanprod(self):
tgt = np.prod(self.mat)
for mat in self.integer_arrays():
assert_equal(np.nanprod(mat), tgt)
def test_nancumsum(self):
tgt = np.cumsum(self.mat)
for mat in self.integer_arrays():
assert_equal(np.nancumsum(mat), tgt)
def test_nancumprod(self):
tgt = np.cumprod(self.mat)
for mat in self.integer_arrays():
assert_equal(np.nancumprod(mat), tgt)
def test_nanmean(self):
tgt = np.mean(self.mat)
for mat in self.integer_arrays():
assert_equal(np.nanmean(mat), tgt)
def test_nanvar(self):
tgt = np.var(self.mat)
for mat in self.integer_arrays():
assert_equal(np.nanvar(mat), tgt)
tgt = np.var(mat, ddof=1)
for mat in self.integer_arrays():
assert_equal(np.nanvar(mat, ddof=1), tgt)
def test_nanstd(self):
tgt = np.std(self.mat)
for mat in self.integer_arrays():
assert_equal(np.nanstd(mat), tgt)
tgt = np.std(self.mat, ddof=1)
for mat in self.integer_arrays():
assert_equal(np.nanstd(mat, ddof=1), tgt)
class SharedNanFunctionsTestsMixin(object):
def test_mutation(self):
# Check that passed array is not modified.
ndat = _ndat.copy()
for f in self.nanfuncs:
f(ndat)
assert_equal(ndat, _ndat)
def test_keepdims(self):
mat = np.eye(3)
for nf, rf in zip(self.nanfuncs, self.stdfuncs):
for axis in [None, 0, 1]:
tgt = rf(mat, axis=axis, keepdims=True)
res = nf(mat, axis=axis, keepdims=True)
assert_(res.ndim == tgt.ndim)
def test_out(self):
mat = np.eye(3)
for nf, rf in zip(self.nanfuncs, self.stdfuncs):
resout = np.zeros(3)
tgt = rf(mat, axis=1)
res = nf(mat, axis=1, out=resout)
assert_almost_equal(res, resout)
assert_almost_equal(res, tgt)
def test_dtype_from_dtype(self):
mat = np.eye(3)
codes = 'efdgFDG'
for nf, rf in zip(self.nanfuncs, self.stdfuncs):
for c in codes:
with suppress_warnings() as sup:
if nf in {np.nanstd, np.nanvar} and c in 'FDG':
# Giving the warning is a small bug, see gh-8000
sup.filter(np.ComplexWarning)
tgt = rf(mat, dtype=np.dtype(c), axis=1).dtype.type
res = nf(mat, dtype=np.dtype(c), axis=1).dtype.type
assert_(res is tgt)
# scalar case
tgt = rf(mat, dtype=np.dtype(c), axis=None).dtype.type
res = nf(mat, dtype=np.dtype(c), axis=None).dtype.type
assert_(res is tgt)
def test_dtype_from_char(self):
mat = np.eye(3)
codes = 'efdgFDG'
for nf, rf in zip(self.nanfuncs, self.stdfuncs):
for c in codes:
with suppress_warnings() as sup:
if nf in {np.nanstd, np.nanvar} and c in 'FDG':
# Giving the warning is a small bug, see gh-8000
sup.filter(np.ComplexWarning)
tgt = rf(mat, dtype=c, axis=1).dtype.type
res = nf(mat, dtype=c, axis=1).dtype.type
assert_(res is tgt)
# scalar case
tgt = rf(mat, dtype=c, axis=None).dtype.type
res = nf(mat, dtype=c, axis=None).dtype.type
assert_(res is tgt)
def test_dtype_from_input(self):
codes = 'efdgFDG'
for nf, rf in zip(self.nanfuncs, self.stdfuncs):
for c in codes:
mat = np.eye(3, dtype=c)
tgt = rf(mat, axis=1).dtype.type
res = nf(mat, axis=1).dtype.type
assert_(res is tgt, "res %s, tgt %s" % (res, tgt))
# scalar case
tgt = rf(mat, axis=None).dtype.type
res = nf(mat, axis=None).dtype.type
assert_(res is tgt)
def test_result_values(self):
for nf, rf in zip(self.nanfuncs, self.stdfuncs):
tgt = [rf(d) for d in _rdat]
res = nf(_ndat, axis=1)
assert_almost_equal(res, tgt)
def test_scalar(self):
for f in self.nanfuncs:
assert_(f(0.) == 0.)
def test_matrices(self):
# Check that it works and that type and
# shape are preserved
mat = np.matrix(np.eye(3))
for f in self.nanfuncs:
res = f(mat, axis=0)
assert_(isinstance(res, np.matrix))
assert_(res.shape == (1, 3))
res = f(mat, axis=1)
assert_(isinstance(res, np.matrix))
assert_(res.shape == (3, 1))
res = f(mat)
assert_(np.isscalar(res))
class TestNanFunctions_SumProd(TestCase, SharedNanFunctionsTestsMixin):
nanfuncs = [np.nansum, np.nanprod]
stdfuncs = [np.sum, np.prod]
def test_allnans(self):
# Check for FutureWarning
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter('always')
res = np.nansum([np.nan]*3, axis=None)
assert_(res == 0, 'result is not 0')
assert_(len(w) == 0, 'warning raised')
# Check scalar
res = np.nansum(np.nan)
assert_(res == 0, 'result is not 0')
assert_(len(w) == 0, 'warning raised')
# Check there is no warning for not all-nan
np.nansum([0]*3, axis=None)
assert_(len(w) == 0, 'unwanted warning raised')
def test_empty(self):
for f, tgt_value in zip([np.nansum, np.nanprod], [0, 1]):
mat = np.zeros((0, 3))
tgt = [tgt_value]*3
res = f(mat, axis=0)
assert_equal(res, tgt)
tgt = []
res = f(mat, axis=1)
assert_equal(res, tgt)
tgt = tgt_value
res = f(mat, axis=None)
assert_equal(res, tgt)
class TestNanFunctions_CumSumProd(TestCase, SharedNanFunctionsTestsMixin):
nanfuncs = [np.nancumsum, np.nancumprod]
stdfuncs = [np.cumsum, np.cumprod]
def test_allnans(self):
for f, tgt_value in zip(self.nanfuncs, [0, 1]):
# Unlike other nan-functions, sum/prod/cumsum/cumprod don't warn on all nan input
with assert_no_warnings():
res = f([np.nan]*3, axis=None)
tgt = tgt_value*np.ones((3))
assert_(np.array_equal(res, tgt), 'result is not %s * np.ones((3))' % (tgt_value))
# Check scalar
res = f(np.nan)
tgt = tgt_value*np.ones((1))
assert_(np.array_equal(res, tgt), 'result is not %s * np.ones((1))' % (tgt_value))
# Check there is no warning for not all-nan
f([0]*3, axis=None)
def test_empty(self):
for f, tgt_value in zip(self.nanfuncs, [0, 1]):
mat = np.zeros((0, 3))
tgt = tgt_value*np.ones((0, 3))
res = f(mat, axis=0)
assert_equal(res, tgt)
tgt = mat
res = f(mat, axis=1)
assert_equal(res, tgt)
tgt = np.zeros((0))
res = f(mat, axis=None)
assert_equal(res, tgt)
def test_keepdims(self):
for f, g in zip(self.nanfuncs, self.stdfuncs):
mat = np.eye(3)
for axis in [None, 0, 1]:
tgt = f(mat, axis=axis, out=None)
res = g(mat, axis=axis, out=None)
assert_(res.ndim == tgt.ndim)
for f in self.nanfuncs:
d = np.ones((3, 5, 7, 11))
# Randomly set some elements to NaN:
rs = np.random.RandomState(0)
d[rs.rand(*d.shape) < 0.5] = np.nan
res = f(d, axis=None)
assert_equal(res.shape, (1155,))
for axis in np.arange(4):
res = f(d, axis=axis)
assert_equal(res.shape, (3, 5, 7, 11))
def test_matrices(self):
# Check that it works and that type and
# shape are preserved
mat = np.matrix(np.eye(3))
for f in self.nanfuncs:
for axis in np.arange(2):
res = f(mat, axis=axis)
assert_(isinstance(res, np.matrix))
assert_(res.shape == (3, 3))
res = f(mat)
assert_(res.shape == (1, 3*3))
def test_result_values(self):
for axis in (-2, -1, 0, 1, None):
tgt = np.cumprod(_ndat_ones, axis=axis)
res = np.nancumprod(_ndat, axis=axis)
assert_almost_equal(res, tgt)
tgt = np.cumsum(_ndat_zeros,axis=axis)
res = np.nancumsum(_ndat, axis=axis)
assert_almost_equal(res, tgt)
def test_out(self):
mat = np.eye(3)
for nf, rf in zip(self.nanfuncs, self.stdfuncs):
resout = np.eye(3)
for axis in (-2, -1, 0, 1):
tgt = rf(mat, axis=axis)
res = nf(mat, axis=axis, out=resout)
assert_almost_equal(res, resout)
assert_almost_equal(res, tgt)
class TestNanFunctions_MeanVarStd(TestCase, SharedNanFunctionsTestsMixin):
nanfuncs = [np.nanmean, np.nanvar, np.nanstd]
stdfuncs = [np.mean, np.var, np.std]
def test_dtype_error(self):
for f in self.nanfuncs:
for dtype in [np.bool_, np.int_, np.object_]:
assert_raises(TypeError, f, _ndat, axis=1, dtype=dtype)
def test_out_dtype_error(self):
for f in self.nanfuncs:
for dtype in [np.bool_, np.int_, np.object_]:
out = np.empty(_ndat.shape[0], dtype=dtype)
assert_raises(TypeError, f, _ndat, axis=1, out=out)
def test_ddof(self):
nanfuncs = [np.nanvar, np.nanstd]
stdfuncs = [np.var, np.std]
for nf, rf in zip(nanfuncs, stdfuncs):
for ddof in [0, 1]:
tgt = [rf(d, ddof=ddof) for d in _rdat]
res = nf(_ndat, axis=1, ddof=ddof)
assert_almost_equal(res, tgt)
def test_ddof_too_big(self):
nanfuncs = [np.nanvar, np.nanstd]
stdfuncs = [np.var, np.std]
dsize = [len(d) for d in _rdat]
for nf, rf in zip(nanfuncs, stdfuncs):
for ddof in range(5):
with suppress_warnings() as sup:
sup.record(RuntimeWarning)
sup.filter(np.ComplexWarning)
tgt = [ddof >= d for d in dsize]
res = nf(_ndat, axis=1, ddof=ddof)
assert_equal( | np.isnan(res) | numpy.isnan |
from builtins import *
import random
import sys
import os
import math
from abc import ABCMeta, abstractmethod
from collections import defaultdict, Counter
from functools import partial
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from .base_tabular_learner import Agent, StationaryAgent
import importlib
import maci.utils as utils
from copy import deepcopy
class BaseQAgent(Agent):
def __init__(self, name, id_, action_num, env, alpha_decay_steps=10000., alpha=0.01, gamma=0.95, episilon=0.1, verbose=True, **kwargs):
super().__init__(name, id_, action_num, env, **kwargs)
self.episilon = episilon
self.alpha_decay_steps = alpha_decay_steps
self.gamma = gamma
self.alpha = alpha
self.epoch = 0
self.Q = None
self.pi = defaultdict(partial(np.random.dirichlet, [1.0] * self.action_num))
self.record = defaultdict(list)
self.verbose = verbose
self.pi_history = [deepcopy(self.pi)]
def done(self, env):
if self.verbose:
utils.pv('self.full_name(game)')
utils.pv('self.Q')
utils.pv('self.pi')
numplots = env.numplots if env.numplots >= 0 else len(self.record)
for s, record in sorted(
self.record.items(), key=lambda x: -len(x[1]))[:numplots]:
self.plot_record(s, record, env)
self.record.clear()
# learning rate decay
def step_decay(self):
# drop = 0.5
# epochs_drop = 10000
# decay_alpha = self.alpha * math.pow(drop, math.floor((1 + self.epoch) / epochs_drop))
# return 1 / (1 / self.alpha + self.epoch * 1e-4)
return self.alpha_decay_steps / (self.alpha_decay_steps + self.epoch)
# return decay_alpha
# def alpha(self, t):
# return self.alpha_decay_steps / (self.alpha_decay_steps + t)
def act(self, s, exploration, game):
if exploration and random.random() < self.episilon:
return random.randint(0, self.action_num - 1)
else:
if self.verbose:
for s in self.Q.keys():
print('{}--------------'.format(self.id_))
print('Q of agent {}: state {}: {}'.format(self.id_, s, str(self.Q[s])))
# print('QAof agent {}: state {}: {}'.format(self.id_, s, str(self.Q_A[s])))
# self.Q_A
print('pi of agent {}: state {}: {}'.format(self.id_, s, self.pi[s]))
# print('pi of opponent agent {}: state{}: {}'.format(self.id_, s, self.opponent_best_pi[s]))
print('{}--------------'.format(self.id_))
# print()
return StationaryAgent.sample(self.pi[s])
@abstractmethod
def update(self, s, a, o, r, s2, env, done=False):
pass
@abstractmethod
def update_policy(self, s, a, env):
pass
def plot_record(self, s, record, env):
os.makedirs('policy/', exist_ok=True)
fig = plt.figure(figsize=(18, 10))
n = self.action_num
for a in range(n):
plt.subplot(n, 1, a + 1)
plt.tight_layout()
plt.gca().set_ylim([-0.05, 1.05])
plt.gca().set_xlim([1.0, env.t + 1.0])
plt.title('player: {}: state: {}, action: {}'.format(self.full_name(env), s, a))
plt.xlabel('step')
plt.ylabel('pi[a]')
plt.grid()
x, y = list(zip(*((t, pi[a]) for t, pi in record)))
x, y = list(x) + [env.t + 1.0], list(y) + [y[-1]]
plt.plot(x, y, 'r-')
fig.savefig('policy/{}_{}.pdf'.format(self.full_name(env), s))
plt.close(fig)
def record_policy(self, s, env):
pass
# if env.numplots != 0:
# if s in self.record:
# self.record[s].append((env.t - 0.01, self.record[s][-1][1]))
# self.record[s].append((env.t, np.copy(self.pi[s])))
class QAgent(BaseQAgent):
def __init__(self, id_, action_num, env, **kwargs):
super().__init__('q', id_, action_num, env, **kwargs)
self.Q = defaultdict(partial(np.random.rand, self.action_num))
self.R = defaultdict(partial(np.zeros, self.action_num))
self.count_R = defaultdict(partial(np.zeros, self.action_num))
def done(self, env):
self.R.clear()
self.count_R.clear()
super().done(env)
def update(self, s, a, o, r, s2, env, done=False):
self.count_R[s][a] += 1.0
self.R[s][a] += (r - self.R[s][a]) / self.count_R[s][a]
Q = self.Q[s]
V = self.val(s2)
decay_alpha = self.step_decay()
if done:
Q[a] = Q[a] + decay_alpha * (r - Q[a])
else:
Q[a] = Q[a] + decay_alpha * (r + self.gamma * V - Q[a])
if self.verbose:
print(self.epoch)
self.update_policy(s, a, env)
self.record_policy(s, env)
self.epoch += 1
def val(self, s):
return np.max(self.Q[s])
def update_policy(self, s, a, env):
Q = self.Q[s]
self.pi[s] = (Q == np.max(Q)).astype(np.double)
class PGAAPPAgent(QAgent):
def __init__(self, id_, action_num, env, eta=0.01, **kwargs):
super().__init__(id_, action_num, env, **kwargs)
self.name = 'pha-app'
self.eta = eta
self.pi_history = [deepcopy(self.pi)]
def update_policy(self, s, a, game):
V = np.dot(self.pi[s], self.Q[s])
delta_hat_A = np.zeros(self.action_num)
delta_A = np.zeros(self.action_num)
for ai in range(self.action_num):
if self.pi[s][ai] == 1:
delta_hat_A[ai]= self.Q[s][ai] - V
else:
delta_hat_A[ai] = (self.Q[s][ai] - V) / (1 - self.pi[s][ai])
delta_A[ai] = delta_hat_A[ai] - self.gamma * abs(delta_hat_A[ai]) *self.pi[s][ai]
self.pi[s] += self.eta * delta_A
StationaryAgent.normalize(self.pi[s])
self.pi_history.append(deepcopy(self.pi))
class GIGAWoLFAgent(QAgent):
def __init__(self, id_, action_num, env, eta=0.01, **kwargs):
super().__init__(id_, action_num, env, **kwargs)
self.name = 'giga-wolf'
self.eta = eta
self.pi_history = [deepcopy(self.pi)]
def update_policy(self, s, a, game):
V = np.dot(self.pi[s], self.Q[s])
delta_hat_A = np.zeros(self.action_num)
delta_A = np.zeros(self.action_num)
for ai in range(self.action_num):
if self.pi[s][ai] == 1:
delta_hat_A[ai]= self.Q[s][ai] - V
else:
delta_hat_A[ai] = (self.Q[s][ai] - V) / (1 - self.pi[s][ai])
delta_A[ai] = delta_hat_A[ai] - self.gamma * abs(delta_hat_A[ai]) *self.pi[s][ai]
self.pi[s] += self.eta * delta_A
StationaryAgent.normalize(self.pi[s])
self.pi_history.append(deepcopy(self.pi))
class EMAQAgent(QAgent):
def __init__(self, id_, action_num, env, delta1=0.001, delta2=0.002, **kwargs):
super().__init__(id_, action_num, env, **kwargs)
self.name = 'emaq'
self.delta1 = delta1
self.delta2 = delta2
self.pi_history = [deepcopy(self.pi)]
def update_policy(self, s, a, game):
if a == np.argmax(self.Q[s]):
delta = self.delta1
vi = np.zeros(self.action_num)
vi[a] = 1.
else:
delta = self.delta2
vi = np.zeros(self.action_num)
vi[a] = 0.
self.pi[s] = (1 - delta) * self.pi[s] + delta * vi
StationaryAgent.normalize(self.pi[s])
self.pi_history.append(deepcopy(self.pi))
class OMQAgent(QAgent):
def __init__(self, id_, action_num, env, **kwargs):
super().__init__(id_, action_num, env, **kwargs)
self.name = 'omq'
self.count_SO = defaultdict(partial(np.zeros, self.action_num))
self.opponent_pi = defaultdict(partial(np.random.dirichlet, [1.0] * self.action_num))
self.pi_history = [deepcopy(self.pi)]
self.opponent_pi_history = [deepcopy(self.opponent_pi)]
self.Q = defaultdict(partial(np.random.rand, *(self.action_num, self.action_num)))
self.R = defaultdict(partial(np.zeros, (self.action_num, self.action_num)))
self.count_R = defaultdict(partial(np.zeros, (self.action_num, self.action_num)))
def update(self, s, a, o, r, s2, env, done=False):
self.count_SO[s][o] += 1.
self.opponent_pi[s] = self.count_SO[s] / np.sum(self.count_SO[s])
self.count_R[s][a][o] += 1.0
self.R[s][a][o] += (r - self.R[s][a][o]) / self.count_R[s][a][o]
Q = self.Q[s]
V = self.val(s2)
decay_alpha = self.step_decay()
if done:
Q[a][o] = Q[a][o] + decay_alpha * (r - Q[a])
else:
Q[a][o] = Q[a][o] + decay_alpha * (r + self.gamma * V - Q[a][o])
if self.verbose:
print(self.epoch)
self.update_policy(s, a, env)
self.record_policy(s, env)
self.epoch += 1
def val(self, s):
return np.max(np.dot(self.Q[s], self.opponent_pi[s]))
def update_policy(self, s, a, game):
# print('Qs {}'.format(self.Q[s]))
# print('OPI {}'.format(self.opponent_best_pi[s]))
# print('pis: ' + str(np.dot(self.Q[s], self.opponent_best_pi[s])))
self.pi[s] = utils.softmax(np.dot(self.Q[s], self.opponent_pi[s]))
# print('pis: ' + str(np.sum(np.dot(self.Q[s], self.opponent_best_pi[s]))))
self.pi_history.append(deepcopy(self.pi))
self.opponent_pi_history.append(deepcopy(self.opponent_pi))
if self.verbose:
print('opponent pi of {}: {}'.format(self.id_, self.opponent_pi[s]))
class RRQAgent(QAgent):
def __init__(self, id_, action_num, env, phi_type='count', a_policy='softmax', **kwargs):
super().__init__(id_, action_num, env, **kwargs)
self.name = 'RR2Q'
self.phi_type = phi_type
self.a_policy = a_policy
self.count_AOS = defaultdict(partial(np.zeros, (self.action_num, self.action_num)))
self.count_OS = defaultdict(partial(np.zeros, (self.action_num, )))
self.opponent_best_pi = defaultdict(partial(np.random.dirichlet, [1.0] * self.action_num))
self.pi_history = [deepcopy(self.pi)]
self.opponent_best_pi_history = [deepcopy(self.opponent_best_pi)]
self.Q = defaultdict(partial(np.random.rand, *(self.action_num, self.action_num)))
self.Q_A = defaultdict(partial(np.random.rand, self.action_num))
self.R = defaultdict(partial(np.zeros, (self.action_num, self.action_num)))
self.count_R = defaultdict(partial(np.zeros, (self.action_num, self.action_num)))
def update(self, s, a, o, r, s2, env, done=False, tau=0.5):
self.count_AOS[s][a][o] += 1.0
self.count_OS[s][o] += 1.
decay_alpha = self.step_decay()
if self.phi_type == 'count':
count_sum = np.reshape(np.repeat(np.sum(self.count_AOS[s], 1), self.action_num), (self.action_num, self.action_num))
self.opponent_best_pi[s] = self.count_AOS[s] / (count_sum + 0.1)
self.opponent_best_pi[s] = self.opponent_best_pi[s] / (np.sum(self.opponent_best_pi[s]) + 0.1)
elif self.phi_type == 'norm-exp':
self.Q_A_reshaped = np.reshape(np.repeat(self.Q_A[s], self.action_num), (self.action_num, self.action_num))
self.opponent_best_pi[s] = np.log(np.exp((self.Q[s] - self.Q_A_reshaped)))
self.opponent_best_pi[s] = self.opponent_best_pi[s] / np.reshape(
np.repeat(np.sum(self.opponent_best_pi[s], 1), self.action_num), (self.action_num, self.action_num))
self.count_R[s][a][o] += 1.0
self.R[s][a][o] += (r - self.R[s][a][o]) / self.count_R[s][a][o]
Q = self.Q[s]
V = self.val(s2)
if done:
Q[a][o] = Q[a][o] + decay_alpha * (r - Q[a][o])
self.Q_A[s][a] = self.Q_A[s][a] + decay_alpha * (r - self.Q_A[s][a])
else:
Q[a][o] = Q[a][o] + decay_alpha * (r + self.gamma * V - Q[a][o])
self.Q_A[s][a] = self.Q_A[s][a] + decay_alpha * (r + self.gamma * V - self.Q_A[s][a])
if self.verbose:
print(self.epoch)
self.update_policy(s, a, env)
self.record_policy(s, env)
self.epoch += 1
def val(self, s):
return np.max(np.sum(np.multiply(self.Q[s], self.opponent_best_pi[s]), 1))
def update_policy(self, s, a, game):
if self.a_policy == 'softmax':
self.pi[s] = utils.softmax(np.sum(np.multiply(self.Q[s], self.opponent_best_pi[s]), 1))
else:
Q = np.sum(np.multiply(self.Q[s], self.opponent_best_pi[s]), 1)
self.pi[s] = (Q == np.max(Q)).astype(np.double)
self.pi_history.append(deepcopy(self.pi))
self.opponent_best_pi_history.append(deepcopy(self.opponent_best_pi))
if self.verbose:
print('opponent pi of {}: {}'.format(self.id_, self.opponent_best_pi))
class GRRQAgent(QAgent):
def __init__(self, id_, action_num, env, k=0, phi_type='count', a_policy='softmax', **kwargs):
super().__init__(id_, action_num, env, **kwargs)
self.name = 'GRRQ'
self.k = k
self.phi_type = phi_type
self.a_policy = a_policy
self.count_AOS = defaultdict(partial(np.zeros, (self.action_num, self.action_num)))
self.opponent_best_pi = defaultdict(partial(np.random.dirichlet, [1.0] * self.action_num))
self.pi_history = [deepcopy(self.pi)]
self.opponent_best_pi_history = [deepcopy(self.opponent_best_pi)]
self.Q = defaultdict(partial(np.random.rand, *(self.action_num, self.action_num)))
self.Q_A = defaultdict(partial(np.random.rand, self.action_num))
self.R = defaultdict(partial(np.zeros, (self.action_num, self.action_num)))
self.count_R = defaultdict(partial(np.zeros, (self.action_num, self.action_num)))
def update(self, s, a, o, r, s2, env, done=False):
self.count_AOS[s][a][o] += 1.0
decay_alpha = self.step_decay()
if self.phi_type == 'count':
count_sum = np.reshape(np.repeat(np.sum(self.count_AOS[s], 1), self.action_num), (self.action_num, self.action_num))
self.opponent_best_pi[s] = self.count_AOS[s] / (count_sum + 0.1)
elif self.phi_type == 'norm-exp':
self.Q_A_reshaped = np.reshape(np.repeat(self.Q_A[s], self.action_num), (self.action_num, self.action_num))
self.opponent_best_pi[s] = np.log(np.exp(self.Q[s] - self.Q_A_reshaped))
self.opponent_best_pi[s] = self.opponent_best_pi[s] / np.reshape(
np.repeat(np.sum(self.opponent_best_pi[s], 1), self.action_num), (self.action_num, self.action_num))
self.count_R[s][a][o] += 1.0
self.R[s][a][o] += (r - self.R[s][a][o]) / self.count_R[s][a][o]
Q = self.Q[s]
V = self.val(s2)
if done:
Q[a][o] = Q[a][o] + decay_alpha * (r - Q[a][o])
self.Q_A[s][a] = self.Q_A[s][a] + decay_alpha * (r - self.Q_A[s][a])
else:
Q[a][o] = Q[a][o] + decay_alpha * (r + self.gamma * V - Q[a][o])
self.Q_A[s][a] = self.Q_A[s][a] + decay_alpha * (r + self.gamma * V - self.Q_A[s][a])
print(self.epoch)
self.update_policy(s, a, env)
self.record_policy(s, env)
self.epoch += 1
def val(self, s):
return np.max(np.sum(np.multiply(self.Q[s], self.opponent_best_pi[s]), 1))
def update_policy(self, s, a, game):
if self.a_policy == 'softmax':
self.pi[s] = utils.softmax(np.sum(np.multiply(self.Q[s], self.opponent_best_pi[s]), 1))
else:
Q = np.sum(np.multiply(self.Q[s], self.opponent_best_pi[s]), 1)
self.pi[s] = (Q == np.max(Q)).astype(np.double)
self.pi_history.append(deepcopy(self.pi))
self.opponent_best_pi_history.append(deepcopy(self.opponent_best_pi))
print('opponent pi of {}: {}'.format(self.id_, self.opponent_best_pi))
class MinimaxQAgent(BaseQAgent):
def __init__(self, id_, action_num, env, opp_action_num):
super().__init__('minimax', id_, action_num, env)
self.solvers = []
self.opp_action_num = opp_action_num
self.pi_history = [deepcopy(self.pi)]
self.Q = defaultdict(partial(np.random.rand, self.action_num, self.opp_action_num))
def done(self, env):
self.solvers.clear()
super().done(env)
def val(self, s):
Q = self.Q[s]
pi = self.pi[s]
return min(np.dot(pi, Q[:, o]) for o in range(self.opp_action_num))
def update(self, s, a, o, r, s2, env):
Q = self.Q[s]
V = self.val(s2)
decay_alpha = self.step_decay()
Q[a, o] = Q[a, o] + decay_alpha * (r + self.gamma * V - Q[a, o])
self.update_policy(s, a, env)
self.record_policy(s, env)
def update_policy(self, s, a, env):
self.initialize_solvers()
for solver, lib in self.solvers:
try:
self.pi[s] = self.lp_solve(self.Q[s], solver, lib)
StationaryAgent.normalize(self.pi[s])
self.pi_history.append(deepcopy(self.pi))
except Exception as e:
print('optimization using {} failed: {}'.format(solver, e))
continue
else: break
def initialize_solvers(self):
if not self.solvers:
for lib in ['gurobipy', 'scipy.optimize', 'pulp']:
try: self.solvers.append((lib, importlib.import_module(lib)))
except: pass
def lp_solve(self, Q, solver, lib):
ret = None
if solver == 'scipy.optimize':
c = np.append(np.zeros(self.action_num), -1.0)
A_ub = np.c_[-Q.T, np.ones(self.opp_action_num)]
b_ub = np.zeros(self.opp_action_num)
A_eq = np.array([np.append(np.ones(self.action_num), 0.0)])
b_eq = np.array([1.0])
bounds = [(0.0, 1.0) for _ in range(self.action_num)] + [(-np.inf, np.inf)]
res = lib.linprog(
c=c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, bounds=bounds)
ret = res.x[:-1]
elif solver == 'gurobipy':
m = lib.Model('LP')
m.setParam('OutputFlag', 0)
m.setParam('LogFile', '')
m.setParam('LogToConsole', 0)
v = m.addVar(name='v')
pi = {}
for a in range(self.action_num):
pi[a] = m.addVar(lb=0.0, ub=1.0, name='pi_{}'.format(a))
m.update()
m.setObjective(v, sense=lib.GRB.MAXIMIZE)
for o in range(self.opp_action_num):
m.addConstr(
lib.quicksum(pi[a] * Q[a, o] for a in range(self.action_num)) >= v,
name='c_o{}'.format(o))
m.addConstr(lib.quicksum(pi[a] for a in range(self.action_num)) == 1, name='c_pi')
m.optimize()
ret = np.array([pi[a].X for a in range(self.action_num)])
elif solver == 'pulp':
v = lib.LpVariable('v')
pi = lib.LpVariable.dicts('pi', list(range(self.action_num)), 0, 1)
prob = lib.LpProblem('LP', lib.LpMaximize)
prob += v
for o in range(self.opp_action_num):
prob += lib.lpSum(pi[a] * Q[a, o] for a in range(self.action_num)) >= v
prob += lib.lpSum(pi[a] for a in range(self.action_num)) == 1
prob.solve(lib.GLPK_CMD(msg=0))
ret = np.array([lib.value(pi[a]) for a in range(self.action_num)])
if not (ret >= 0.0).all():
raise Exception('{} - negative probability error: {}'.format(solver, ret))
return ret
class MetaControlAgent(Agent):
def __init__(self, id_, action_num, env, opp_action_num):
super().__init__('metacontrol', id_, action_num, env)
self.agents = [QAgent(id_, action_num, env), MinimaxQAgent(id_, action_num, env, opp_action_num)]
self.n = np.zeros(len(self.agents))
self.controller = None
def act(self, s, exploration, env):
print([self.val(i, s) for i in range(len(self.agents))])
self.controller = np.argmax([self.val(i, s) for i in range(len(self.agents))])
return self.agents[self.controller].act(s, exploration, env)
def done(self, env):
for agent in self.agents:
agent.done(env)
def val(self, i, s):
return self.agents[i].val(s)
def update(self, s, a, o, r, s2, env):
for agent in self.agents:
agent.update(s, a, o, r, s2, env)
self.n[self.controller] += 1
print('id: {}, n: {} ({}%)'.format(self.id_, self.n, 100.0 * self.n / | np.sum(self.n) | numpy.sum |
import numpy as np
from models import Policy, ValueFunction
def one_step_actor_critic(mdp, value_function_alpha, policy_alpha, iterations, episodes, max_actions, final_performance_episodes):
#print("One Step actor critic with mdp: " + mdp.name)
actions_vs_episodes_all = np.zeros((iterations, episodes))
for i in range(iterations):
policy = Policy(policy_alpha, mdp.state_features_length, mdp.actions_length)
value_function = ValueFunction(value_function_alpha, mdp.state_features_length)
#print("Iteration: " + str(i))
actions_vs_episodes = []
for episode in range(episodes):
state = mdp.get_start_state()
state_features = mdp.get_state_features(state)
#print(state_features)
state_value = value_function.evaluate_state(state_features)
actions = 0
while not mdp.episode_over(state):
actions += 1
if actions == max_actions:
break
# draw action from policy
action, action_probabilities = policy.get_action(state_features, True)
# execute action a, observe r and s'
next_state = mdp.get_next_state(state, action)
reward = mdp.get_reward(next_state)
# get state features from state
next_state_features = mdp.get_state_features(next_state)
# compute TD error
next_state_value = value_function.evaluate_state(next_state_features)
target = reward + mdp.discount * next_state_value
td_error = target - state_value
# update actor & critic
policy.update_parameters(td_error, state_features)
value_function.update_parameters(td_error, state_features)
# s = s'
state = next_state
state_features = next_state_features
state_value = next_state_value
actions_vs_episodes.append(actions)
actions_vs_episodes_all[i] = np.array(actions_vs_episodes)
return collect_statistics(actions_vs_episodes_all, final_performance_episodes)
# ppo works by running the environment for some steps and then computing stochastic gradient descent on the collected s,a,r,s' examples
# I use a value function for the baseline just like in actor-critic
def proximal_policy_optimization(mdp, value_function_alpha, policy_alpha, clip, iterations, episodes, max_actions, rollout_episodes, epochs, final_performance_episodes):
#print("Proximal Policy Optimization with mdp: " + mdp.name)
actions_vs_episodes_all = np.zeros((iterations, episodes))
for i in range(iterations):
#print("Iteration: " + str(i))
policy = Policy(policy_alpha, mdp.state_features_length, mdp.actions_length, clip)
value_function = ValueFunction(value_function_alpha, mdp.state_features_length)
actions_vs_episodes = []
episode = 0
while episode < episodes:
current_rollout_episodes = min(episodes - episode, rollout_episodes)
# run the environment
state_features, actions, action_probabilities, targets, advantages, episode_lengths = ppo_rollout(mdp, policy, value_function, current_rollout_episodes, max_actions)
episode += rollout_episodes
actions_vs_episodes += episode_lengths
# SGD on policy and value function
for j in range(epochs):
policy.ppo_gradient_step(state_features, action_probabilities, actions, advantages)
state_values = value_function.evaluate_state(state_features)
errors = targets - state_values
value_function.update_parameters(errors, state_features)
# going to take average over all ppo iterations
actions_vs_episodes_all[i] = np.array(actions_vs_episodes)
return collect_statistics(actions_vs_episodes_all, final_performance_episodes)
def ppo_rollout(mdp, policy, value_function, rollout_episodes, max_actions):
state_features = []
actions = []
action_probabilities = []
rewards = []
last_state_features = []
episode_lengths = []
# collect rollout_episodes trajectories
for ep in range(rollout_episodes):
state = mdp.get_start_state()
state_feature = mdp.get_state_features(state)
actions_taken = 0
while not mdp.episode_over(state):
if actions_taken == max_actions:
break
# draw action from policy
action, action_probability = policy.get_action(state_feature, False)
# execute action a, observe r and s'
next_state = mdp.get_next_state(state, action)
reward = mdp.get_reward(next_state)
# record for stachastic gradient descent later
state_features.append(state_feature[0])
actions.append(action)
action_probabilities.append(action_probability)
rewards.append(reward)
# s = s'
state = next_state
state_feature = mdp.get_state_features(state)
actions_taken += 1
last_state_features.append(state_feature) # v(s') for the last example in this episode batch (need for Advantage function)
episode_lengths.append(actions_taken)
state_features = np.array(state_features)
actions = np.array(actions)
action_probabilities = np.array(action_probabilities)
rewards = np.array(rewards)
# make sure state_values and next_state_values line up
ep_begin = 0
state_values = np.squeeze(value_function.evaluate_state(state_features))
last_state_values = np.reshape(np.squeeze(value_function.evaluate_state(last_state_features)), (-1))
next_state_values = np.zeros(state_values.shape)
# this makes sure the state_value array and next_next_value arrays are lined up so that the td errors can easily be computed
for i in range(rollout_episodes):
l = episode_lengths[i]
next_state_values[ep_begin: ep_begin+l-1] = state_values[ep_begin+1:ep_begin+l]
next_state_values[ep_begin+l-1] = last_state_values[i]
ep_begin += l
targets = rewards + mdp.discount * next_state_values # super easy td error calculation
advantages = targets - state_values
return (state_features, actions, action_probabilities, targets, advantages, episode_lengths)
# basic statistics for my plots
def collect_statistics(actions_vs_episodes_all, final_performance_episodes):
actions_taken_average = np.mean(actions_vs_episodes_all, 0)
actions_taken_std = np.std(actions_vs_episodes_all, 0)
final_performance_mean = np.mean(actions_taken_average[-final_performance_episodes:])
final_performance_std = | np.mean(actions_taken_std[-final_performance_episodes:]) | numpy.mean |
from __future__ import print_function
import os
import argparse
import torch
import torch.backends.cudnn as cudnn
import numpy as np
import time
import model
from data import DatasetLoader
import cv2
import torchvision.models as models
import numpy as np
from scipy.optimize import leastsq
import random
import torch.nn.functional as F
import math
from glob import glob
import matplotlib.pyplot as plt
from sklearn.metrics import mean_absolute_error # 平方绝对误差
os.environ["CUDA_VISIBLE_DEVICES"] = "0"
def check_keys(model, pretrained_state_dict):
ckpt_keys = set(pretrained_state_dict.keys())
model_keys = set(model.state_dict().keys())
used_pretrained_keys = model_keys & ckpt_keys
unused_pretrained_keys = ckpt_keys - model_keys
missing_keys = model_keys - ckpt_keys
print('Missing keys:{}'.format(len(missing_keys)))
print('Unused checkpoint keys:{}'.format(len(unused_pretrained_keys)))
print('Used keys:{}'.format(len(used_pretrained_keys)))
assert len(used_pretrained_keys) > 0, 'load NONE from pretrained checkpoint'
return True
def remove_prefix(state_dict, prefix):
''' Old style model is stored with all names of parameters sharing common prefix 'module.' '''
print('remove prefix \'{}\''.format(prefix))
f = lambda x: x.split(prefix, 1)[-1] if x.startswith(prefix) else x
return {f(key): value for key, value in state_dict.items()}
def load_model(model, pretrained_path, load_to_cpu):
print('Loading pretrained model from {}'.format(pretrained_path))
if load_to_cpu:
pretrained_dict = torch.load(pretrained_path, map_location=lambda storage, loc: storage)
else:
device = torch.cuda.current_device()
pretrained_dict = torch.load(pretrained_path, map_location=lambda storage, loc: storage.cuda(device))
if "state_dict" in pretrained_dict.keys():
pretrained_dict = remove_prefix(pretrained_dict['state_dict'], 'module.')
else:
pretrained_dict = remove_prefix(pretrained_dict, 'module.')
check_keys(model, pretrained_dict)
model.load_state_dict(pretrained_dict, strict=False)
return model
def test_move(net,save_path,img_list,save_image=False,size=256):
if not os.path.exists(save_path):
os.makedirs(save_path)
points1 = np.float32([[75,55], [340,55], [33,435], [400,433]])
points2 = np.float32([[0,0], [360,0], [0,420], [360,420]])
M = cv2.getPerspectiveTransform(points1, points2)
###eval
count=0
distance_homo_sum=0
distance_orb_sum=0
distance_sift_sum=0
pass_homo_total=0
pass_orb_total=0
pass_sift_total=0
for image_path in img_list:
count=count+1
img1 = cv2.imread(image_path)[:,:,0]#BGR
img1=cv2.resize(img1,(size+32,size+32))
rho=12
# rand_num=random.randint(0, 12)
# #random move
# if rand_num<=2:#0 1 2
# randmovex=0
# randmovey=0
# elif rand_num<=4:#3 4 5
# randmovex=random.randint(-rho, rho)
# randmovey=0
# elif rand_num<=6:#6 7 8
# randmovex=0
# randmovey=random.randint(-rho, rho)
# else:#9 10 11
# randmovex=random.randint(-rho, rho)
# randmovey=random.randint(-rho, rho)
randmovex=random.randint(-rho, rho)
randmovey=random.randint(-rho, rho)
#H_groundtruth
H_groundtruth = np.array([[1,0,randmovex],[0,1,randmovey],[0,0,1]]).astype(np.float64)
H_inverse =np.array([[1,0,-randmovex],[0,1,-randmovey],[0,0,1]]).astype(np.float64)
imout1=img1[16:16 + size, 16:16 + size]
imgOut = cv2.warpPerspective(img1, H_inverse, (img1.shape[1],img1.shape[0]),flags=cv2.INTER_CUBIC + cv2.WARP_INVERSE_MAP)
imout2=imgOut[16:16 + size, 16:16 + size]
target=np.array([randmovex,randmovey])
im_zero=np.zeros((size,size))
training_image = np.dstack((imout1, imout2,im_zero))
img = training_image.transpose(2, 0, 1)#(3,300,300)
img= torch.from_numpy(img).unsqueeze(0)
img=img.float()
img = img.cuda()
#fast homography estimate network
start_time1 = time.time()
out = net(img)/100 #from img2 2 img1
movexf=float(out[0][0])
moveyf=float(out[0][1])
movex=round(movexf)
movey=round(moveyf)
H_predict=np.array([[1,0,movex],[0,1,movey],[0,0,1]]).astype(np.float64)
pass_1=time.time()-start_time1
pass_homo_total+=pass_1
#orb
start_time2 = time.time()
H_orb=img_orb(imout1,imout2)
pass_2=time.time()-start_time2
pass_orb_total+=pass_2
#distance_homo
distance_homo=mean_absolute_error(H_predict,H_groundtruth)
distance_homo_sum=distance_homo_sum+distance_homo
#distance_orb
distance_orb=mean_absolute_error(H_orb,H_groundtruth)
distance_orb_sum=distance_orb_sum+distance_orb
print("distances(homo,orb): ",distance_homo,distance_orb)
# save image
if save_image:
name = os.path.join(save_path,image_path.split("/")[-1])
name=name[:-4]
imgOut2_homo = cv2.warpPerspective(imout2, H_predict, (imout1.shape[1],imout1.shape[0]),flags=cv2.INTER_CUBIC + cv2.WARP_INVERSE_MAP)
err_img_homo=cv2.absdiff(imout1,imgOut2_homo)
imgOut2_orb = cv2.warpPerspective(imout2, H_orb, (imout1.shape[1],imout1.shape[0]),flags=cv2.INTER_CUBIC + cv2.WARP_INVERSE_MAP)
err_img_orb=cv2.absdiff(imout1,imgOut2_orb)
err_imgs=np.hstack([err_img_homo,err_img_orb])
cv2.imwrite(name+"-errs.jpg",err_imgs)
err_homo=float(distance_homo_sum)/float(count)
err_orb=float(distance_orb_sum)/float(count)
fps_homo=count/pass_homo_total
fps_orb=count/pass_orb_total
print("homo/orb(err|fps): ",err_homo,fps_homo,err_orb,fps_orb)
return err_homo
def img_orb(img1,img2):
# find the keypoints and descriptors with ORB
orb = cv2.ORB_create()
kp1, des1 = orb.detectAndCompute(img1,None)
kp2, des2 = orb.detectAndCompute(img2,None)
# create BFMatcher object
bf = cv2.BFMatcher(cv2.NORM_HAMMING, crossCheck=True)
# Match descriptors.
matches = bf.match(des1,des2)
# Sort them in the order of their distance.
matches = sorted(matches, key = lambda x:x.distance)
# Draw first 20 matches.
# img3 = cv2.drawMatches(img1,kp1,img2,kp2,matches[:20],None, flags=2)
goodMatch = matches[:20]
if len(goodMatch) > 4:
ptsA= np.float32([kp1[m.queryIdx].pt for m in goodMatch]).reshape(-1, 1, 2)
ptsB = np.float32([kp2[m.trainIdx].pt for m in goodMatch]).reshape(-1, 1, 2)
ransacReprojThreshold = 4
H, status =cv2.findHomography(ptsA,ptsB,cv2.RANSAC,ransacReprojThreshold)
else:
H=np.array([[1,0,0],[0,1,0],[0,0,1]]).astype(np.float64)
return H
def img_anto_4temp(img1,img2):
#1
img2_patch1=img2[16:16 + 97, 16:16 + 97]#64,64
img1_1=img1[0:0 + 127, 0:0 + 127]
res = cv2.matchTemplate(img1_1,img2_patch1,cv2.TM_CCOEFF)
#寻找最值
min_val, max_val, min_loc, max_loc = cv2.minMaxLoc(res)
loc_x1=max_loc[0]-16
loc_y1=max_loc[1]-16
c10=np.array([[64],[64],[1]])
c1=np.array([[64+loc_x1],[64+loc_y1],[1]])
#2
img2_patch1=img2[16+127:16+97+127, 16:16 + 97]#191,64
img1_1=img1[0+ 127:0 + 127+ 127, 0:0 + 127]
res = cv2.matchTemplate(img1_1,img2_patch1,cv2.TM_CCOEFF)
#寻找最值
min_val, max_val, min_loc, max_loc = cv2.minMaxLoc(res)
loc_x1=max_loc[0]-16
loc_y1=max_loc[1]-16
c20=np.array([[191],[64],[1]])
c2= | np.array([[191+loc_x1],[64+loc_y1],[1]]) | numpy.array |
# Copyright (c) 2019 PaddlePaddle Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from __future__ import print_function
import paddle
import paddle.fluid as fluid
import paddle.fluid.core as core
from paddle.fluid import Program, program_guard
import paddle.compat as cpt
import unittest
import numpy as np
from op_test import OpTest
class TestFillAnyLikeOp(OpTest):
def setUp(self):
self.op_type = "fill_any_like"
self.dtype = np.int32
self.value = 0.0
self.init()
self.inputs = {'X': np.random.random((219, 232)).astype(self.dtype)}
self.attrs = {'value': self.value}
self.outputs = {'Out': self.value * np.ones_like(self.inputs["X"])}
def init(self):
pass
def test_check_output(self):
self.check_output()
class TestFillAnyLikeOpFloat32(TestFillAnyLikeOp):
def init(self):
self.dtype = np.float32
self.value = 0.0
class TestFillAnyLikeOpValue1(TestFillAnyLikeOp):
def init(self):
self.value = 1.0
class TestFillAnyLikeOpValue2(TestFillAnyLikeOp):
def init(self):
self.value = 1e-10
class TestFillAnyLikeOpValue3(TestFillAnyLikeOp):
def init(self):
self.value = 1e-100
class TestFillAnyLikeOpType(TestFillAnyLikeOp):
def setUp(self):
self.op_type = "fill_any_like"
self.dtype = np.int32
self.value = 0.0
self.init()
self.inputs = {'X': np.random.random((219, 232)).astype(self.dtype)}
self.attrs = {
'value': self.value,
'dtype': int(core.VarDesc.VarType.FP32)
}
self.outputs = {
'Out':
self.value * np.ones_like(self.inputs["X"]).astype(np.float32)
}
class TestFillAnyLikeOpOverflow(TestFillAnyLikeOp):
def init(self):
self.value = 1e100
def test_check_output(self):
exception = None
try:
self.check_output(check_dygraph=False)
except core.EnforceNotMet as ex:
exception = ex
self.assertIsNotNone(exception)
class TestFillAnyLikeOpFloat16(TestFillAnyLikeOp):
def init(self):
self.dtype = np.float16
class TestFillAnyLikeOp_attr_out(unittest.TestCase):
""" Test fill_any_like op(whose API is full_like) for attr out. """
def test_attr_tensor_API(self):
startup_program = fluid.Program()
train_program = fluid.Program()
with fluid.program_guard(train_program, startup_program):
fill_value = 2.0
input = fluid.data(name='input', dtype='float32', shape=[2, 3])
output = paddle.full_like(input, fill_value)
place = fluid.CPUPlace()
if fluid.core.is_compiled_with_cuda():
place = fluid.CUDAPlace(0)
exe = fluid.Executor(place)
exe.run(startup_program)
img = np.array([[1, 2, 3], [4, 5, 6]]).astype(np.float32)
res = exe.run(train_program,
feed={'input': img},
fetch_list=[output])
out_np = np.array(res[0])
self.assertTrue(
not (out_np - np.full_like(img, fill_value)).any(),
msg="full_like output is wrong, out = " + str(out_np))
class TestFillAnyLikeOpError(unittest.TestCase):
def test_errors(self):
with program_guard(Program(), Program()):
#for ci coverage
input_data = fluid.data(name='input', dtype='float32', shape=[2, 3])
output = paddle.full_like(input_data, 2.0)
def test_input_dtype():
paddle.full_like
self.assertRaises(
ValueError,
paddle.full_like,
input=input_data,
fill_value=2,
dtype='uint4')
self.assertRaises(
TypeError,
paddle.full_like,
input=input_data,
fill_value=2,
dtype='int16')
class ApiOnesLikeTest(unittest.TestCase):
def test_out(self):
with fluid.program_guard(fluid.Program()):
data = fluid.data(shape=[10], dtype="float64", name="data")
ones = paddle.ones_like(data, device="cpu")
place = fluid.CPUPlace()
exe = fluid.Executor(place)
result, = exe.run(feed={"data": np.random.rand(10)},
fetch_list=[ones])
expected_result = | np.ones(10, dtype="float64") | numpy.ones |
import numpy as np
import sys, os
import cv2
import transformations
import features
import traceback
from PIL import Image
# Saving and loading cv2 points
def pickle_cv2(arr):
index = []
for point in arr:
temp = (point.pt, point.size, point.angle, point.response, point.octave, point.class_id)
index.append(temp)
return np.array(index)
def unpickle_cv2(arr):
index = []
for point in arr:
temp = cv2.KeyPoint(x=point[0][0], y=point[0][1], _size=point[1], _angle=point[2], _response=point[3],
_octave=point[4], _class_id=point[5])
index.append(temp)
return np.array(index)
# Functions for testing elementwise correctness
def compare_array(arr1, arr2):
return np.allclose(arr1, arr2, rtol=1e-3, atol=1e-5)
def compare_cv2_points(pnt1, pnt2):
if not np.isclose(pnt1.pt[0], pnt2.pt[0], rtol=1e-3, atol=1e-5): return False
if not np.isclose(pnt1.pt[1], pnt2.pt[1], rtol=1e-3, atol=1e-5): return False
if not np.isclose(pnt1.angle, pnt2.angle, rtol=1e-3, atol=1e-5): return False
if not np.isclose(pnt1.response, pnt2.response, rtol=1e-3, atol=1e-5): return False
return True
# Testing function
def try_this(todo, run, truth, compare, *args, **kargs):
'''
Run a function, test the output with compare, and print and error if it doesn't work
@arg todo (int or str): The Todo number
@arg run (func): The function to run
@arg truth (any): The correct output of the function
@arg compare (func->bool): Compares the output of the `run` function to truth and provides a boolean if correct
@arg *args (any): Any arguments that should be passed to `run`
@arg **kargs (any): Any kargs that should be passed to compare
@return (int): The amount of things that failed
'''
print('Starting test for TODO {}'.format(todo))
failed = 0
try:
output = run(*args)
except Exception as e:
traceback.print_exc()
print("TODO {} threw an exception, see exception above".format(todo))
return
if type(output) is list or type(output) is tuple:
for i in range(len(output)):
if not compare(output[i], truth[i], **kargs):
print("TODO {} doesn't pass test: {}".format(todo, i))
failed += 1
else:
if not compare(output, truth, **kargs):
print("TODO {} doesn't pass test".format(todo))
failed += 1
return failed
HKD = features.HarrisKeypointDetector()
SFD = features.SimpleFeatureDescriptor()
MFD = features.MOPSFeatureDescriptor()
SSDFM = features.SSDFeatureMatcher()
image = np.array(Image.open('resources/triangle1.jpg'))
grayImage = cv2.cvtColor(image.astype(np.float32) / 255.0, cv2.COLOR_BGR2GRAY)
def compute_and_save():
(a, b) = HKD.computeHarrisValues(grayImage) # Todo1
c = HKD.computeLocalMaxima(a) # Todo2
d = HKD.detectKeypoints(image) # Todo3
e = SFD.describeFeatures(image, d) # Todo 4
f = MFD.describeFeatures(image, d) # Todo 5,6
# No test for Todo 7 or 8
d_proc = pickle_cv2(d)
| np.savez('resources/arrays', a=a, b=b, c=c, d_proc=d_proc, e=e, f=f) | numpy.savez |
import numpy as np
import pytest
from fdm import forward_fdm, backward_fdm, central_fdm, FDM
from .util import approx
def test_construction():
with pytest.raises(ValueError):
FDM([-1, 0, 1], 3)
@pytest.mark.parametrize("f", [forward_fdm, backward_fdm, central_fdm])
def test_correctness(f):
approx(f(10, 1)(np.sin, 1), | np.cos(1) | numpy.cos |
import os
import csv
import time
from pathlib import Path
import fire
import matplotlib.pyplot as plt
import numpy as np
from alive_progress import alive_bar
from dask.distributed import Client, LocalCluster
from ribs.archives import CVTArchive, GridArchive
from ribs.emitters import (GaussianEmitter, ImprovementEmitter, IsoLineEmitter,
GradientEmitter, GradientImprovementEmitter)
from ribs.optimizers import Optimizer
from ribs.visualize import grid_archive_heatmap
def calc_sphere(sol):
dim = sol.shape[1]
# Shift the Sphere function so that the optimal value is at x_i = 2.048.
target_shift = 5.12 * 0.4
# Normalize the objective to the range [0, 100] where 100 is optimal.
best_obj = 0.0
worst_obj = (-5.12 - target_shift)**2 * dim
raw_obj = np.sum(np.square(sol - target_shift), axis=1)
objs = (raw_obj - worst_obj) / (best_obj - worst_obj) * 100
derivatives = -2 * (sol - target_shift)
return objs, derivatives
def calc_rastrigin(sol):
A = 10.0
dim = sol.shape[1]
# Shift the Rastrigin function so that the optimal value is at x_i = 2.048.
target_shift = 5.12 * 0.4
best_obj = np.zeros(len(sol))
displacement = -5.12 * np.ones(sol.shape) - target_shift
sum_terms = np.square(displacement) - A * np.cos(2 * np.pi * displacement)
worst_obj = 10 * dim + np.sum(sum_terms, axis=1)
displacement = sol - target_shift
sum_terms = | np.square(displacement) | numpy.square |
import numpy as np
import pandas as pd
import lightgbm as lgb
import re
from pitci.lightgbm import LGBMBoosterLeafNodeScaledConformalPredictor
import pitci
import pytest
class TestInit:
"""Tests for the LGBMBoosterLeafNodeScaledConformalPredictor._init__ method."""
def test_inheritance(self):
"""Test that LGBMBoosterLeafNodeScaledConformalPredictor inherits from
LeafNodeScaledConformalPredictor.
"""
assert (
LGBMBoosterLeafNodeScaledConformalPredictor.__mro__[1]
is pitci.base.LeafNodeScaledConformalPredictor
), (
"LGBMBoosterLeafNodeScaledConformalPredictor does not inherit from "
"LeafNodeScaledConformalPredictor"
)
def test_model_type_exception(self):
"""Test an exception is raised if model is not a lgb.Booster object."""
with pytest.raises(
TypeError,
match=re.escape(
f"model is not in expected types {[lgb.basic.Booster]}, got {list}"
),
):
LGBMBoosterLeafNodeScaledConformalPredictor([1, 2, 3])
def test_attributes_set(self, lgb_booster_1_split_1_tree):
"""Test that SUPPORTED_OBJECTIVES, version and model attributes are set."""
confo_model = LGBMBoosterLeafNodeScaledConformalPredictor(
lgb_booster_1_split_1_tree
)
assert (
confo_model.__version__ == pitci.__version__
), "__version__ attribute not set to package version value"
assert (
confo_model.model is lgb_booster_1_split_1_tree
), "model attribute not set with the value passed in init"
assert (
confo_model.SUPPORTED_OBJECTIVES
== pitci.lightgbm.SUPPORTED_OBJECTIVES_ABSOLUTE_ERROR
), "SUPPORTED_OBJECTIVES attribute incorrect"
def test_check_objective_supported_called(self, mocker, lgb_booster_1_split_1_tree):
"""Test that check_objective_supported is called in init."""
mocked = mocker.patch.object(pitci.lightgbm, "check_objective_supported")
LGBMBoosterLeafNodeScaledConformalPredictor(lgb_booster_1_split_1_tree)
assert (
mocked.call_count == 1
), "check_objective_supported not called (once) in init"
call_args = mocked.call_args_list[0]
call_pos_args = call_args[0]
call_kwargs = call_args[1]
assert call_pos_args == (
lgb_booster_1_split_1_tree,
pitci.lightgbm.SUPPORTED_OBJECTIVES_ABSOLUTE_ERROR,
), "positional args in check_objective_supported call not correct"
assert (
call_kwargs == {}
), "keyword args in check_objective_supported call not correct"
def test_super_init_call(self, mocker, lgb_booster_1_split_1_tree):
"""Test that LeafNodeScaledConformalPredictor.__init__ is called."""
mocked = mocker.patch.object(
pitci.base.LeafNodeScaledConformalPredictor, "__init__"
)
LGBMBoosterLeafNodeScaledConformalPredictor(lgb_booster_1_split_1_tree)
assert (
mocked.call_count == 1
), "LeafNodeScaledConformalPredictor.__init__ not called (once) in init"
call_args = mocked.call_args_list[0]
call_pos_args = call_args[0]
call_kwargs = call_args[1]
assert (
call_pos_args == ()
), "positional args in LeafNodeScaledConformalPredictor.__init__ call not correct"
assert call_kwargs == {
"model": lgb_booster_1_split_1_tree
}, "keyword args in LeafNodeScaledConformalPredictor.__init__ call not correct"
class TestCalibrate:
"""Tests for the LGBMBoosterLeafNodeScaledConformalPredictor.calibrate method."""
def test_data_exception(self, lgb_booster_1_split_1_tree):
"""Test that an exception is raised if data is not a np.array or pd.Series."""
confo_model = LGBMBoosterLeafNodeScaledConformalPredictor(
lgb_booster_1_split_1_tree
)
with pytest.raises(
TypeError,
match=re.escape(
f"data is not in expected types {[np.ndarray, pd.DataFrame]}, got {int}"
),
):
confo_model.calibrate(data=1, response=np.ndarray([1, 2]), alpha=0.8)
def test_train_data_type_exception(self, lgb_booster_1_split_1_tree):
"""Test that an exception is raised if train_data is not a np.array or pd.Series."""
confo_model = LGBMBoosterLeafNodeScaledConformalPredictor(
lgb_booster_1_split_1_tree
)
with pytest.raises(
TypeError,
match=re.escape(
f"train_data is not in expected types {[np.ndarray, pd.DataFrame, type(None)]}, got {bool}"
),
):
confo_model.calibrate(
data=np.ndarray([1, 2]), response=np.ndarray([1, 2]), train_data=True
)
def test_super_calibrate_call(
self, mocker, np_2x1_with_label, lgb_booster_1_split_1_tree
):
"""Test that LeafNodeScaledConformalPredictor.calibrate is called correctly."""
confo_model = LGBMBoosterLeafNodeScaledConformalPredictor(
lgb_booster_1_split_1_tree
)
mocked = mocker.patch.object(
pitci.base.LeafNodeScaledConformalPredictor, "calibrate"
)
train_data_array = np.array([6, 9])
confo_model.calibrate(
data=np_2x1_with_label[0],
alpha=0.99,
response=np_2x1_with_label[1],
train_data=train_data_array,
)
assert (
mocked.call_count == 1
), "incorrect number of calls to LeafNodeScaledConformalPredictor.calibrate"
call_args = mocked.call_args_list[0]
call_pos_args = call_args[0]
call_kwargs = call_args[1]
assert (
call_pos_args == ()
), "positional args incorrect in call to LeafNodeScaledConformalPredictor.calibrate"
assert call_kwargs["alpha"] == 0.99
np.testing.assert_array_equal(call_kwargs["data"], np_2x1_with_label[0])
np.testing.assert_array_equal(call_kwargs["response"], np_2x1_with_label[1])
np.testing.assert_array_equal(call_kwargs["train_data"], train_data_array)
class TestPredictWithInterval:
"""Tests for the LGBMBoosterLeafNodeScaledConformalPredictor.predict_with_interval method."""
def test_data_type_exception(self, lgb_booster_1_split_1_tree):
"""Test an exception is raised if data is not a xgb.DMatrix object."""
confo_model = LGBMBoosterLeafNodeScaledConformalPredictor(
lgb_booster_1_split_1_tree
)
confo_model.calibrate(
data=np.array([[1], [2], [3]]),
response=np.array([1, 2, 3]),
)
with pytest.raises(
TypeError,
match=re.escape(
f"data is not in expected types {[np.ndarray, pd.DataFrame]}, got {int}"
),
):
confo_model.predict_with_interval(1)
def test_super_predict_with_interval_call(self, mocker, lgb_booster_1_split_1_tree):
"""Test that LeafNodeScaledConformalPredictor.predict_with_interval is called and the
outputs of this are returned from the method.
"""
confo_model = LGBMBoosterLeafNodeScaledConformalPredictor(
lgb_booster_1_split_1_tree
)
confo_model.calibrate(np.array([[1], [2], [3]]), response=np.array([1, 2, 3]))
predict_return_value = np.array([200, 101, 1234])
mocked = mocker.patch.object(
pitci.base.LeafNodeScaledConformalPredictor,
"predict_with_interval",
return_value=predict_return_value,
)
data_array = | np.array([[11], [21], [31]]) | numpy.array |
import numpy as np
# 2013-10-31 Added MultiRate class, simplified fitting methods, removed full_output parameter
# 2014-12-18 Add loading of Frequency, Integration time and Iterations, calculate lower
# bound on errors from Poisson distribution
# 2015-01-28 Simplified fitting again. Needs more work
# 2015-03-02 Added functions for number density calculation
_verbosity = 2
def set_verbosity(level):
"""
0: serious/unrecoverable error
1: recoverable error
2: warning
3: information
"""
global _verbosity
_verbosity = level
def warn(message, level):
if level <= _verbosity:
print(message)
def fitter(p0, errfunc, args):
from lmfit import minimize
result = minimize(errfunc, p0, args=args, nan_policy="omit")
if not result.success:
msg = " Optimal parameters not found: " + result.message
raise RuntimeError(msg)
for i, name in enumerate(result.var_names):
if result.params[name].value == result.init_vals[i]:
warn("Warning: fitter: parameter \"%s\" was not changed, it is probably redundant"%name, 2)
from scipy.stats import chi2
chi = chi2.cdf(result.chisqr, result.nfree)
if chi > 0.5: pval = -(1-chi)*2
else: pval = chi*2
pval = 1-chi
return result.params, pval, result
def dict2Params(dic):
from lmfit import Parameters
if isinstance(dic, Parameters): return dic.copy()
p = Parameters()
for key, val in dic.items():
p.add(key, value=val)
return p
P = dict2Params
class Rate:
def __init__(self, fname, full_data=False, skip_iter=[]):
import re
import datetime as dt
fr = open(fname)
state = -1
npoints = 0
nions = 0
pointno = 0
iterno = 0
ioniter = []
ionname = []
frequency = 0
integration = 0
poisson_error = True
# -1 header
# 0 init
# 1 read time
# 2 read data
for lineno, line in enumerate(fr):
# read header
if state == -1:
if lineno == 2:
T1 = line[:22].split()
T2 = line[22:].split()
self.starttime = dt.datetime.strptime(" ".join(T1), "%Y-%m-%d %H:%M:%S.%f")
self.stoptime = dt.datetime.strptime(" ".join(T2), "%Y-%m-%d %H:%M:%S.%f")
if lineno == 3:
state = 0
toks = line.split()
if len(toks) == 0:
continue
if state == 0:
if re.search("Period \(s\)=", line):
frequency = 1/float(re.search("Period \(s\)=([0-9.]+)", line).group(1))
if re.search("Frequency=", line):
frequency = float(re.search("Frequency=([0-9.]+)", line).group(1))
if re.search("Integration time \(s\)", line):
integration = float(re.search("Integration time \(s\)=([0-9.]+)", line).group(1))
if re.search("Number of Points=", line):
npoints = int(re.search("Number of Points=(\d+)", line).group(1))
if re.search("Number of Iterations=", line):
self.niter = int(re.search("Number of Iterations=(\d+)", line).group(1))
if toks[0] == "[Ion":
nions += 1
if re.search("^Iterations=", line) :
ioniter.append(int(re.search("Iterations=(\d+)", line).group(1)))
if re.search("^Name=", line) :
ionname.append(re.search("Name=(.+)$", line).group(1).strip('\"'))
if toks[0] == "Time":
if len(toks)-2 != nions:
print("Corrupt file", fname, "Wrong number of ions in the header. Trying to recover")
# Assume that the Time header is correct:
nions = len(toks)-2
ioniter = ioniter[:nions]
if len(ioniter) < nions:
warn("Corrupt file " + str(fname) + ": Iterations for all species not recorded, guessing...", 1)
while len(ioniter) < nions:
ioniter.append(ioniter[-1])
if len(ionname) < nions:
warn("Corrupt file " + str(fname) + ": Names for all species not recorded, making something up...", 2)
ionname += toks[len(ionname)+2:]
state = 1
time = []
data = np.zeros((nions, npoints, self.niter))
continue
if state == 1:
try:
newtime = float(toks[0])
except ValueError:
if pointno != npoints:
warn("Corrupt file " + fname + " trying to guess number of points", 2)
npoints = pointno
data.resize((nions, npoints, self.niter))
time = np.array(time)
state = 2
else:
time.append(newtime)
pointno += 1
if state == 2:
if toks[0] == "Iteration":
iterno = int(toks[1])-1
if iterno+1 > self.niter:
warn("Corrupt file " + fname + " trying to guess number of iterations", 2)
#msg = "Corrupt file: " + fname
#raise IOError(msg)
self.niter = iterno+1
data.resize((nions, npoints, self.niter))
pointno = 0
continue
try:
data[:, pointno, iterno] = [float(x) for x in toks][1:-1]
except ValueError:
warn("Error in file " + fname + " number of ions probably wrong")
pointno += 1
ioniter = np.array(ioniter)
# in case of multiple measurements per iteration
if iterno+1 != self.niter:
if self.niter % (iterno+1) != 0:
msg = "Corrupt file: " + fname
print(("Corrupt file " + fname + " trying to guess number of iterations:" + str(iterno+1)))
if iterno+1 < self.niter:
data = data[:,:,:iterno+1]
else:
newdata = np.zeros((nions, npoints, iterno+1))
newdata[:,:,:self.niter] = data
print(data, newdata)
data = newdata
#data.resize((nions, npoints, iterno+1))
self.niter = iterno+1
data = data[:,:,:iterno+1]
#print skip_iter, np.shape(skip_iter)
if len(skip_iter)!=0:
skip_iter = np.array(skip_iter)
indices = np.ones(self.niter, dtype=bool)
indices[skip_iter] = False
data = data[:,:,indices]
# XXX frequency is sometimes wrong in the files
# use some heuristics to estimate the frequency
# repetition time is usually set in multiples of 0.1s
measurement_time = np.ceil(time[-1]/0.1)*0.1
if frequency*measurement_time > 1.1 or frequency*measurement_time < 0.4:
warn("Recorded frequency in " + fname + " is probably wrong. Using estimate %f" % (1/measurement_time), 1)
frequency = 1/measurement_time
# this is later used to estimate Poisson error
self.total_iterations = ioniter[:,None]*integration*frequency*self.niter
self.nions = nions
self.ionname = ionname
self.time = time
self.data = data
self.fname = fname
self.average()
if not full_data:
self.data = None
self.mask = None
def average(self):
data_mean = np.mean(self.data, axis=2)
data_std = np.std(self.data, axis=2)/np.sqrt(self.niter)
#print(np.shape(self.data), np.shape(data_mean), np.shape(self.total_iterations))
data_counts = data_mean*self.total_iterations
# divide by sqrt(total_iterations) twice - once to get Poisson
# variance of measured data and once to the error of estimated mean
# this should be verified, but it is in agreement with errors obtained
# by treating data as normal variables for large numbers
data_poiss_err = np.sqrt(np.maximum(data_counts, 3))/self.total_iterations
# we assume that if 0 counts are observed, 3 counts is within confidence interval
# we use std error if it is larger than poisson error to capture other sources
# of error e.g. fluctuations
data_std = np.maximum(data_std, data_poiss_err)
self.data_mean = data_mean
self.data_std = data_std
def merge(self, rate2):
self.data_mean = np.concatenate((self.data_mean, rate2.data_mean), axis=1)
self.data_std = np.concatenate((self.data_std, rate2.data_std), axis=1)
self.time = np.concatenate((self.time, rate2.time), axis=0)
#print " ** merging ** "
#print self.data_mean, self.data_std, self.time
def poisson_test1(self):
shape = np.shape(self.data_mean)
#check only H- XXX
shape = (1, shape[1])
pval = np.zeros(shape)
for specno in range(shape[0]):
for pointno in range(shape[1]):
if self.mask != None:
dataline = self.data[specno, pointno, self.mask[specno, pointno, :]]
else:
dataline = self.data[specno, pointno, :]
mean = np.mean(dataline)
Q = np.sum((dataline-mean)**2)/mean
niter = len(dataline[~np.isnan(dataline)])
dof = niter-1
from scipy.stats import chi2
chi = chi2.cdf(Q, dof)
if chi > 0.5: pval[specno, pointno] = (1-chi)*2
else: pval[specno, pointno] = chi*2
print((chi, Q, pval[specno, pointno]))
return np.min(pval)
def cut3sigma(self, nsigma=3):
shape = np.shape(self.data)
self.mask = np.zeros(shape, dtype=bool)
for specno in range(shape[0]):
for pointno in range(shape[1]):
stddev = self.data_std[specno, pointno]*np.sqrt(self.niter)
low = self.data_mean[specno, pointno] - nsigma*stddev
high = self.data_mean[specno, pointno] + nsigma*stddev
dataline = self.data[specno, pointno, :]
mask = (dataline > low) & (dataline < high)
#self.data[specno, pointno, ~mask] = float("nan")
self.mask[specno, pointno, :] = mask
self.data_mean[specno, pointno] = np.mean(dataline[mask])
self.data_std[specno, pointno] = np.std(dataline[mask])/np.sqrt(self.niter)
#data_mean = np.mean(self.data[self.mask], axis=2)
#data_std = np.std(self.data, axis=2)/np.sqrt(self.niter)
#print self.data_mean, self.data_std
#self.data[self.data<120] = 130
def fit_ode_mpmath(self, p0=[60.0, .1], columns=[0]):
from mpmath import odefun
def fitfunc(p, x):
eqn = lambda x, y: -p[1]*y
y0 = p[0]
f = odefun(eqn, 0, y0)
g = np.vectorize(lambda x: float(f(x)))
return g(x)
return self._fit(fitfunc, p0, columns)
def fit_ode_scipy(self, p0=[60.0, .1], columns=[0]):
from scipy.integrate import odeint
def fitfunc(p, x):
eqn = lambda y, x: -p[1]*y
y0 = p[0]
t = np.r_[0., x]
y = odeint(eqn, y0, t)
return y[1:,0]
return self._fit(fitfunc, p0, columns)
def fit_inc(self, p0=[1.0, .01, 0.99], columns=[1]):
#fitfuncinc = lambda p, x: p[0]*(1-np.exp(-x/p[1]))+p[2]
fitfunc = lambda p, x: -abs(p[0])*np.exp(-x/abs(p[1]))+abs(p[2])
return self._fit(fitfunc, p0, columns)
def fit_equilib(self, p0=[70.0, .1, 1], columns=[0]):
fitfunc = lambda p, x: abs(p[0])*np.exp(-x/abs(p[1]))+abs(p[2])
return self._fit(fitfunc, p0, columns)
class MultiRate:
def __init__(self, fnames, directory=""):
if isinstance(fnames, str): fnames = [fnames]
self.rates = [Rate(directory+fname, full_data=True) for fname in fnames]
# if True, a normalization factor for each rate with respect to rates[0] is a free fitting param
self.normalized = True
self.norms = [1]*len(self.rates)
self.fitfunc = None
self.fitparam = None
self.fitresult = None
self.fitcolumns = None
self.fitmask = slice(None)
self.fnames = fnames
self.sigma_min = 0.01 # lower bound on the measurement accuracy
def plot_to_file(self, fname, comment=None, figsize=(6,8.5), logx=False, *args, **kwargs):
import matplotlib.pyplot as plt
from lmfit import fit_report
f = plt.figure(figsize=figsize)
ax = f.add_axes([.15, .5, .8, .45])
self.plot(ax=ax, show=False, *args, **kwargs)
ax.set_yscale("log")
if logx: ax.set_xscale("log")
ax.legend(loc="lower right", fontsize=5)
ax.set_title(comment, size=8)
if self.fitresult is not None:
f.text(0.1, 0.44, "p-value = %.2g\n"%self.fitpval
+ fit_report(self.fitresult, min_correl=0.5), size=6, va="top", family='monospace')
if ax.get_ylim()[0] < 1e-4: ax.set_ylim(bottom=1e-4)
ax.set_xlabel(r"$t (\rm s)$")
ax.set_ylabel(r"$N_{\rm i}$")
if self.fitresult is not None:
ax2 = f.add_axes([.55, .345, .40, .10])
if logx: ax2.set_xscale("log")
self.plot_residuals(ax=ax2, show=False, weighted=True)
ax2.tick_params(labelsize=7)
ax2.set_title("weighted residuals", size=7)
ax2.set_xlabel(r"$t (\rm s)$", size=7)
ax2.set_ylabel(r"$R/\sigma$", size=7)
f.savefig(fname, dpi=200)
plt.close(f)
def plot(self, ax=None, show=False, plot_fitfunc=True, symbols=["o", "s", "v", "^", "D", "h"], colors=["r", "g", "b", "m", "k", "orange"],\
opensymbols=False, fitfmt="-", fitcolor=None, hide_uncertain=False, plot_columns=None):
import matplotlib.pyplot as plt
if ax is None:
ax = plt.gca()
lines = {}
if plot_columns is None: plot_columns = range(self.rates[0].nions)
for i in plot_columns:
if opensymbols:
kwargs = {"markeredgewidth":1, "markerfacecolor":"w", "markeredgecolor": colors[i], "color":colors[i]}
else:
kwargs = {"markeredgewidth":0, "color":colors[i]}
l = None
for j, rate in enumerate(self.rates):
norm = 1/self.norms[j]
I = rate.data_std[i] < rate.data_mean[i] if hide_uncertain else slice(None)
if l==None:
l = ax.errorbar(rate.time[I], rate.data_mean[i][I]*norm, yerr=rate.data_std[i][I]*norm, label=rate.ionname[i],
fmt = symbols[i], **kwargs)
color = l.get_children()[0].get_color()
else:
l = ax.errorbar(rate.time[I], rate.data_mean[i][I]*norm, yerr=rate.data_std[i][I]*norm,
fmt = symbols[i], color=color, markeredgewidth=0)
lines[i] = l
# plot sum
for j, rate in enumerate(self.rates):
# calculate the sum over the plotted data only
S = np.sum(rate.data_mean[plot_columns], axis=0)
label = "sum" if j==0 else None
ax.plot(rate.time, S/self.norms[j], ".", c="0.5", label=label)
if self.fitfunc != None and self.fitparam != None:
mintime = np.min([np.min(r.time[self.fitmask]) for r in self.rates])
maxtime = np.max([np.max(r.time[self.fitmask]) for r in self.rates])
x = np.logspace(np.log10(mintime), np.log10(maxtime), 500)-self.fit_t0
x = x[x>=0.]
fit = self.fitfunc(self.fitparam, x)
for i, column in enumerate(self.fitcolumns):
if column not in plot_columns: continue
if fitcolor == None: c = lines[column].get_children()[0].get_color()
else: c = fitcolor
ax.plot(x+self.fit_t0, fit[i], fitfmt, c=c)
if len(self.fitcolumns) > 1:
ax.plot(x+self.fit_t0, np.sum(fit, axis=0), c="k")
if show == True:
ax.set_yscale("log")
ax.legend()
plt.show()
return ax
def plot_residuals(self, ax=None, show=False, weighted=False, symbols=["o", "s", "v", "^", "D", "h"], colors=["r", "g", "b", "m", "k", "orange"],\
opensymbols=False, plot_columns=None):
import matplotlib.pyplot as plt
if ax is None:
ax = plt.gca()
if plot_columns is None: plot_columns = range(self.rates[0].nions)
cdict = {col: i for i, col in enumerate(plot_columns)}
lines = {}
for j, rate in enumerate(self.rates):
t = rate.time[self.fitmask]
#print("\n"*3 + "*"*80)
#print(rate.fname)
fit = self.fitfunc(self.fitparam, t-self.fit_t0)
for i, column in enumerate(self.fitcolumns):
"""
print("\n"*2 + "*"*3 + " " + rate.ionname[column])
print(rate.time)
print(t - self.fit_t0)
print(rate.data_mean[column])
print(rate.data_std[column])
print(fit[i])
print((rate.data_mean[column][self.fitmask] - fit[i])/rate.data_std[column][self.fitmask])
"""
if column in plot_columns:
j = cdict[column]
if weighted:
ax.plot(t, (rate.data_mean[column][self.fitmask] - fit[i])/rate.data_std[column][self.fitmask],
symbols[j], color=colors[j], lw=0.5, ms=2)
else:
ax.errorbar(t, rate.data_mean[column][self.fitmask] - fit[i], yerr=rate.data_std[column][self.fitmask],
fmt=symbols[j], color=colors[j], lw=0.5, ms=2)
#ax.set_yscale("symlog", linthresh=10)
if show == True:
ax.set_yscale("log")
ax.legend()
plt.show()
return ax
def save_data(self, filename):
to_save = []
for j, rate in enumerate(self.rates):
norm = 1/self.norms[j]
to_save.append(np.hstack((rate.time[:,np.newaxis], rate.data_mean.T, rate.data_std.T)))
to_save = np.vstack(to_save)
np.savetxt(filename, to_save)
def save_fit(self, filename, time = None):
if time is None:
mintime = np.min([np.min(r.time[self.fitmask]) for r in self.rates])
maxtime = np.max([np.max(r.time[self.fitmask]) for r in self.rates])
time = np.logspace(np.log10(mintime), np.log10(maxtime), 500)
time = time[time-self.fit_t0 >= 0.]
fit = self.fitfunc(self.fitparam, time-self.fit_t0)
to_save = np.vstack((time, np.vstack(fit))).T
np.savetxt(filename, to_save)
def save_data_fit_excel(self, filename, time=None, normalize=False, metadata={}):
import pandas as pd
dfs = []
for j, rate in enumerate(self.rates):
df = pd.DataFrame(rate.time, columns=["tt"])
if self.normalized:
df["norm"] = 1/self.norms[j]
if normalize:
norm = 1/self.norms[j]
else:
norm = 1
for k, name in enumerate(rate.ionname):
df[name] = rate.data_mean[k]*norm
df[name+"_err"] = rate.data_std[k]*norm
df["rate"] = rate.fname
dfs.append(df)
df = pd.concat(dfs, ignore_index=True)
writer = pd.ExcelWriter(filename)
df.to_excel(writer, "data")
if self.fitfunc != None and self.fitparam != None:
if time is None:
mintime = np.min([np.min(r.time[self.fitmask]) for r in self.rates])
maxtime = np.max([np.max(r.time[self.fitmask]) for r in self.rates])
time = np.logspace(np.log10(mintime), np.log10(maxtime), 500)
time = time[time-self.fit_t0 >= 0.]
fit = self.fitfunc(self.fitparam, time-self.fit_t0)
df_fit = pd.DataFrame(time, columns = ["tt"])
for i, column in enumerate(self.fitcolumns):
name = self.rates[0].ionname[column]
df_fit[name] = fit[i]
df_fit.to_excel(writer, "fit")
for key in metadata.keys():
metadata[key].to_excel(writer, key)
writer.save()
def _errfunc(self, p, bounds={}):
def errfunc_single( p, x, y, xerr, norm=1):
res = (self.fitfunc(p, x)*norm-y[self.fitcolumns,:])/\
(xerr[self.fitcolumns,:] + self.sigma_min)
return res.ravel()
# sum errors over all files (normalize if requested)
err = []
mask = self.fitmask
for i, rate in enumerate(self.rates):
norm = p["n%d"%i].value if (i>0 and self.normalized) else 1
err.append(errfunc_single(p, rate.time[mask] - self.fit_t0, rate.data_mean[:,mask], rate.data_std[:,mask], norm))
# add penalty for bounded fitting
penalty = [weight*(np.fmax(lo-p[key], 0) + np.fmax(0, p[key]-hi))\
for key, (lo, hi, weight) in bounds.items()]
err.append(penalty)
#print("err = ", np.sum(np.hstack(err)**2))
return np.hstack(err)
def _errfunc_species(self, p, species, bounds={}):
def errfunc_single( p, x, y, xerr, norm=1):
res = (self.fitfunc(p, x)[species]*norm-y[self.fitcolumns,:][species])/\
(xerr[self.fitcolumns,:][species] + self.sigma_min)
return res.ravel()
# sum errors over all files (normalize if requested)
err = []
mask = self.fitmask
for i, rate in enumerate(self.rates):
norm = p["n%d"%i].value if (i>0 and self.normalized) else 1
err.append(errfunc_single(p, rate.time[mask] - self.fit_t0, rate.data_mean[:,mask], rate.data_std[:,mask], norm))
# add penalty for bounded fitting
penalty = [weight*(np.fmax(lo-p[key], 0) + np.fmax(0, p[key]-hi))\
for key, (lo, hi, weight) in bounds.items()]
err.append(penalty)
#print("err = ", np.sum(np.hstack(err)**2))
return np.hstack(err)
def fit_model(self, model, p0, columns, mask=slice(None), t0=0., quadratic_bounds=True, boundweight=1e3):
self.fitfunc = model.func # store the fitfunc for later
self.model = model
self.fitcolumns = columns
self.fit_t0 = t0
self.fitmask = mask
p0 = model.init_params(p0)
# use custom implementation of bounded parameters, which can
# estimate errors even if the parameter is "forced" outside the interval
# idea: detect if fitted parameter is close to boundary, then make it fixed...
bounds = {}
if quadratic_bounds:
for key, p in p0.items():
if np.any( | np.isfinite([p.min, p.max]) | numpy.isfinite |
from typing import Any, Set, Tuple, Union, Optional
from pathlib import Path
from collections import defaultdict
from html.parser import HTMLParser
import pytest
from anndata import AnnData
import numpy as np
import xarray as xr
from imageio import imread, imsave
import tifffile
from squidpy.im import ImageContainer
from squidpy.im._utils import CropCoords, CropPadding, _NULL_COORDS
from squidpy._constants._pkg_constants import Key
class SimpleHTMLValidator(HTMLParser): # modified from CellRank
def __init__(self, n_expected_rows: int, expected_tags: Set[str], **kwargs: Any):
super().__init__(**kwargs)
self._cnt = defaultdict(int)
self._n_rows = 0
self._n_expected_rows = n_expected_rows
self._expected_tags = expected_tags
def handle_starttag(self, tag: str, attrs: Any) -> None:
self._cnt[tag] += 1
self._n_rows += tag == "strong"
def handle_endtag(self, tag: str) -> None:
self._cnt[tag] -= 1
def validate(self) -> None:
assert self._n_rows == self._n_expected_rows
assert set(self._cnt.keys()) == self._expected_tags
if len(self._cnt):
assert set(self._cnt.values()) == {0}
class TestContainerIO:
def test_empty_initialization(self):
img = ImageContainer()
assert not len(img)
assert isinstance(img.data, xr.Dataset)
assert img.shape == (0, 0)
assert str(img)
assert repr(img)
def _test_initialize_from_dataset(self):
dataset = xr.Dataset({"foo": xr.DataArray(np.zeros((100, 100, 3)))}, attrs={"foo": "bar"})
img = ImageContainer._from_dataset(data=dataset)
assert img.data is not dataset
assert "foo" in img
assert img.shape == (100, 100)
np.testing.assert_array_equal(img.data.values(), dataset.values)
assert img.data.attrs == dataset.attrs
def test_save_load_zarr(self, tmpdir):
img = ImageContainer(np.random.normal(size=(100, 100, 1)))
img.data.attrs["scale"] = 42
img.save(Path(tmpdir) / "foo")
img2 = ImageContainer.load(Path(tmpdir) / "foo")
np.testing.assert_array_equal(img["image"].values, img2["image"].values)
np.testing.assert_array_equal(img.data.dims, img2.data.dims)
np.testing.assert_array_equal(sorted(img.data.attrs.keys()), sorted(img2.data.attrs.keys()))
for k, v in img.data.attrs.items():
assert type(v) == type(img2.data.attrs[k]) # noqa: E721
assert v == img2.data.attrs[k]
def test_load_zarr_2_objects_can_overwrite_store(self, tmpdir):
img = ImageContainer(np.random.normal(size=(100, 100, 1)))
img.data.attrs["scale"] = 42
img.save(Path(tmpdir) / "foo")
img2 = ImageContainer.load(Path(tmpdir) / "foo")
img2.data.attrs["sentinel"] = "foobar"
img2["image"].values += 42
img2.save(Path(tmpdir) / "foo")
img3 = ImageContainer.load(Path(tmpdir) / "foo")
assert "sentinel" in img3.data.attrs
assert img3.data.attrs["sentinel"] == "foobar"
np.testing.assert_array_equal(img3["image"].values, img2["image"].values)
np.testing.assert_allclose(img3["image"].values - 42, img["image"].values)
@pytest.mark.parametrize(
("shape1", "shape2"),
[
((100, 200, 3), (100, 200, 1)),
((100, 200, 3), (100, 200)),
],
)
def test_add_img(self, shape1: Tuple[int, ...], shape2: Tuple[int, ...]):
img_orig = np.random.randint(low=0, high=255, size=shape1, dtype=np.uint8)
cont = ImageContainer(img_orig, layer="img_orig")
img_new = np.random.randint(low=0, high=255, size=shape2, dtype=np.uint8)
cont.add_img(img_new, layer="img_new", channel_dim="mask")
assert "img_orig" in cont
assert "img_new" in cont
np.testing.assert_array_equal(np.squeeze(cont.data["img_new"]), np.squeeze(img_new))
@pytest.mark.parametrize("shape", [(100, 200, 3), (100, 200, 1)])
def test_load_jpeg(self, shape: Tuple[int, ...], tmpdir):
img_orig = np.random.randint(low=0, high=255, size=shape, dtype=np.uint8)
fname = tmpdir / "tmp.jpeg"
imsave(str(fname), img_orig)
gt = imread(str(fname)) # because of compression, we load again
cont = ImageContainer(str(fname))
np.testing.assert_array_equal(cont["image"].values.squeeze(), gt.squeeze())
@pytest.mark.parametrize("shape", [(100, 200, 3), (100, 200, 1), (10, 100, 200, 1)])
def test_load_tiff(self, shape: Tuple[int, ...], tmpdir):
img_orig = np.random.randint(low=0, high=255, size=shape, dtype=np.uint8)
fname = tmpdir / "tmp.tiff"
tifffile.imsave(fname, img_orig)
cont = ImageContainer(str(fname))
if len(shape) > 3: # multi-channel tiff
np.testing.assert_array_equal(cont["image"], img_orig[..., 0].transpose(1, 2, 0))
else:
np.testing.assert_array_equal(cont["image"], img_orig)
def test_load_netcdf(self, tmpdir):
arr = np.random.normal(size=(100, 10, 4))
ds = xr.Dataset({"quux": xr.DataArray(arr, dims=["foo", "bar", "baz"])})
fname = tmpdir / "tmp.nc"
ds.to_netcdf(str(fname))
cont = ImageContainer(str(fname))
assert len(cont) == 1
assert "quux" in cont
np.testing.assert_array_equal(cont["quux"], ds["quux"])
@pytest.mark.parametrize(
"array", [np.zeros((10, 10, 3), dtype=np.uint8), np.random.rand(10, 10, 1).astype(np.float32)]
)
def test_array_dtypes(self, array: Union[np.ndarray, xr.DataArray]):
img = ImageContainer(array)
np.testing.assert_array_equal(img["image"].data, array)
assert img["image"].data.dtype == array.dtype
img = ImageContainer(xr.DataArray(array))
np.testing.assert_array_equal(img["image"].data, array)
assert img["image"].data.dtype == array.dtype
def test_add_img_invalid_yx(self, small_cont_1c: ImageContainer):
arr = xr.DataArray( | np.empty((small_cont_1c.shape[0] - 1, small_cont_1c.shape[1])) | numpy.empty |
import numpy as np
a=np.arange(10)
print(a)
#save numpy array
np.save("saved",a)
#new file is craeted with name saved.npy
new_a=np.load("saved.npy") #load the saved file
print(new_a)
#saving multiple arrays as zip or archive file
a1=np.arange(25)
a2=np.arange(30)
| np.savez("saved_archive.npz",x=a1,y=a2) | numpy.savez |
import argparse
import json
import os
import time
from bisect import bisect
from functools import partial, reduce
from itertools import product
from operator import itemgetter
import kornia
import matplotlib
import matplotlib.pyplot as plt
from sklearn.metrics import average_precision_score, roc_auc_score, precision_recall_curve, roc_curve
import pickle
import numpy as np
import sklearn
import sklearn.datasets
import torch
import torch.nn as nn
import torch.nn.functional as F
import torchvision
from torch.nn.utils import spectral_norm, clip_grad_norm_
from torchvision.utils import save_image
from models.mcmc import short_run_mcmc, \
DiffSampler, DiffSamplerMultiDim, get_one_hot, get_onehots, convert_struct_onehot, \
get_onehot_struct_mask, get_label_axes, get_diff_label_axes, get_struct_mask, per_example_mask
from utils import get_logger, makedirs, save_ckpt
from utils.data import MNISTWithAttributes
from utils.downsample import Downsample
from utils.dsprites import get_dsprites_dset
from utils.process import utzappos_tensor_dset, utzappos_zero_shot_tensor_dset, split_utzappos, \
celeba_tensor_dset, split_celeba, cub_tensor_dset, split_cub, get_data_gen, log_dset_label_info, \
CELEBA_ZERO_SHOT_COMBOS, CELEBA_ZERO_SHOT_ATTRIBUTES, find_combos_in_tst_set, lbl_in_combos, index_by_combo_name
from utils.visualize_flow import plt_flow_density, plt_samples
# noinspection PyUnresolvedReferences
torch.backends.cudnn.benchmark = True
# noinspection PyUnresolvedReferences
torch.backends.cudnn.enabled = True
matplotlib.use("Agg")
IMG_DSETS = ["mnist", "fashionmnist", "celeba", "mwa", "dsprites", "utzappos", "cub"]
UTZAPPOS_TEST_LEN = CELEBA_TEST_LEN = CUB_TEST_LEN = 5000
def xor(x, y):
return (x or y) and not (x and y)
def implies(x, y):
return (not x) or y
def clamp_x(x, min_val=0, max_val=1):
return torch.clamp(x, min=min_val, max=max_val)
def deq_x(x):
return (255 * x + torch.rand_like(x)) / 256.
def cond_attributes_from_labels(labels_b, cond_cls):
cond_cls_ind, cond_cls_val = cond_cls
return labels_b[:, cond_cls_ind] == cond_cls_val
def f1_score_missing(y_true, y_pred, individual=False, micro=False):
"""
Compute the f1 score, accounting for missing labels in `y_true`.
"""
assert not (individual and micro)
assert y_true.shape == y_pred.shape
assert len(y_true.shape) == 2
if micro:
# average over attributes using "micro" method (treat each attribute as a separate sample)
y_true = y_true.view(-1)
y_pred = y_pred.view(-1)
missing_mask = y_true != -1
tp = (y_true == y_pred) * (y_true == 1)
err = (y_true != y_pred)
# any missing values don't contribute to the sums
tp = (tp * missing_mask).sum(0)
err = (err * missing_mask).sum(0)
f1 = (tp / (tp + .5 * err))
if not individual:
# if no individual scores desired, average over attributes ("macro" average)
f1 = f1.mean()
return f1
def get_calibration(y, p_mean, num_bins=20, axis=-1, multi_label=True, individual=False, micro=False,
debug=False):
"""Compute the calibration.
Modified from: https://github.com/xwinxu/bayesian-sde/blob/main/brax/utils/utils.py
References:
https://arxiv.org/abs/1706.04599
https://arxiv.org/abs/1807.00263
Args:
y: class labels (binarized)
p_mean: numpy array, size (batch_size, num_classes)
containing the mean output predicted probabilities
num_bins: number of bins
axis: Axis of the labels
multi_label: Multiple labels
individual: Return ECE for individual labels
micro: Return micro average of ECE scores across attributes
debug: Return debug information
Returns:
cal: a dictionary
{
reliability_diag: realibility diagram
ece: Expected Calibration Error
nb_items: nb_items_bin/np.sum(nb_items_bin)
}
"""
assert implies(individual or micro, multi_label)
assert not (individual and micro)
if micro:
y = y.view(-1)
p_mean = p_mean.view(-1, p_mean.shape[2])
# compute predicted class and its associated confidence (probability)
conf, class_pred = p_mean.max(axis)
assert y.shape[0] == p_mean.shape[0]
assert len(p_mean.shape) == len(y.shape) + 1
assert p_mean.shape[1] > 1
if multi_label and not micro:
assert len(y.shape) == 2
assert y.shape[1] > 1
assert p_mean.shape[2] > 1
else:
assert len(y.shape) == 1
tau_tab = torch.linspace(0, 1, num_bins + 1, device=p_mean.device)
conf = conf[None]
for _ in range(len(y.shape)):
tau_tab = tau_tab.unsqueeze(-1)
sec = (conf < tau_tab[1:]) & (conf >= tau_tab[:-1])
nb_items_bin = sec.sum(1)
mean_conf = (conf * sec).sum(1) / nb_items_bin
acc_tab = ((class_pred == y)[None] * sec).sum(1) / nb_items_bin
_weights = nb_items_bin.float() / nb_items_bin.sum(0)
ece = ((mean_conf - acc_tab).abs() * _weights).nansum(0)
if not individual:
# pytorch doesn't have a built in nanmean
ece[ece.isnan()] = 0
ece = ece.mean(0)
cal = {
'reliability_diag': (mean_conf, acc_tab),
'ece': ece,
'_weights': _weights,
}
if debug:
cal.update({
'conf': conf,
'sec': sec,
'tau_tab': tau_tab,
'acc_tab': acc_tab,
'p_mean': p_mean
})
return cal
def ap_score(y_true, y_pred, individual=False, micro=False):
assert not (individual and micro)
assert y_true.shape == y_pred.shape
assert len(y_true.shape) == 2
if (y_true == -1).any():
raise NotImplementedError(f"Missing AP score not implemented.")
if micro:
y_true = y_true.view(-1)
y_pred = y_pred.view(-1)
return average_precision_score(y_true=y_true.cpu().numpy(),
y_score=y_pred.cpu().numpy())
else:
y_true = y_true.cpu().numpy()
y_pred = y_pred.cpu().numpy()
individual_ap = [average_precision_score(y_true=y_true[:, label_dim_],
y_score=y_pred[:, label_dim_])
for label_dim_ in range(y_true.shape[1])]
individual_ap = torch.tensor(individual_ap)
if not individual:
return individual_ap.mean()
return individual_ap
def auroc_score(y_true, y_pred, individual=False, micro=False):
assert not (individual and micro)
assert y_true.shape == y_pred.shape
assert len(y_true.shape) == 2
if (y_true == -1).any():
raise NotImplementedError(f"Missing AP score not implemented.")
if micro:
y_true = y_true.view(-1)
y_pred = y_pred.view(-1)
return roc_auc_score(y_true=y_true.cpu().numpy(), y_score=y_pred.cpu().numpy())
else:
y_true = y_true.cpu().numpy()
y_pred = y_pred.cpu().numpy()
individual_ap = [roc_auc_score(y_true=y_true[:, label_dim_], y_score=y_pred[:, label_dim_])
for label_dim_ in range(y_true.shape[1])]
individual_ap = torch.tensor(individual_ap)
if not individual:
return individual_ap.mean()
return individual_ap
class ReplayBuffer:
def __init__(self, max_size, example_sample):
"""
Parameters
----------
max_size: int
Max number of transitions to store in the buffer. When the buffer
overflows the old memories are dropped.
example_sample:
Example samples (shape and device)
"""
self._storage = example_sample
self.buffer_len = 0
self.max_size = max_size
self._next_idx = 0
def __len__(self):
return self.buffer_len
def _add_full_buffer(self, x, which_added=None):
batch_size = x.shape[0]
if which_added is None:
if batch_size + self._next_idx < self.max_size:
self._storage[self._next_idx:self._next_idx + batch_size] = x
which_added = torch.arange(self._next_idx, self._next_idx + batch_size)
else:
split_idx = self.max_size - self._next_idx
self._storage[self._next_idx:] = x[:split_idx]
self._storage[:batch_size - split_idx] = x[split_idx:]
which_added = torch.cat([torch.arange(batch_size - split_idx),
torch.arange(self._next_idx, len(self._storage))], dim=0)
else:
self._storage[which_added] = x
assert len(which_added) == batch_size
return batch_size, which_added
def add(self, x, which_added=None):
num_added, which_added = self._add_full_buffer(x, which_added)
batch_size = x.shape[0]
self._next_idx = (self._next_idx + batch_size) % self.max_size
self.buffer_len = min(self.max_size, self.buffer_len + batch_size)
return num_added, which_added
def sample(self, batch_size, inds=None):
if inds is None:
inds = torch.randint(0, len(self._storage), (batch_size,))
return self._storage[inds], inds
class ReservoirBuffer(ReplayBuffer):
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs)
self._n = 0
def _add_full_buffer(self, x, which_added_add_inds_mask=None):
batch_size = x.shape[0]
if which_added_add_inds_mask is None:
if self._next_idx >= len(self):
num_added, which_added = super()._add_full_buffer(x, which_added_add_inds_mask)
add_inds_mask = torch.ones(which_added.shape, device=which_added.device, dtype=torch.bool)
which_added_add_inds_mask = (which_added, add_inds_mask)
else:
randint_bounds = self._n + 1 + torch.arange(batch_size)
inds = (torch.rand((batch_size,)) * randint_bounds).floor().long()
add_inds_mask = inds < len(self)
which_added = inds[add_inds_mask]
self._storage[which_added] = x[add_inds_mask]
num_added = add_inds_mask.sum()
which_added_add_inds_mask = (which_added, add_inds_mask)
self._n += batch_size
else:
which_added, add_inds_mask = which_added_add_inds_mask
self._storage[which_added] = x[add_inds_mask]
num_added = len(which_added)
return num_added, which_added_add_inds_mask
class GaussianBlur:
def __init__(self, min_val=0.1, max_val=2.0, kernel_size=9):
self.min_val = min_val
self.max_val = max_val
self.kernel_size = kernel_size
def __call__(self, sample):
# blur the image with a 50% chance
prob = np.random.random_sample()
if prob < 0.5:
sigma = (self.max_val - self.min_val) * np.random.random_sample() + self.min_val
sample = kornia.filters.GaussianBlur2d((self.kernel_size, self.kernel_size), (sigma, sigma))(sample)
return sample
def get_color_distortion(s=1.0):
color_jitter = kornia.augmentation.ColorJitter(0.8 * s, 0.8 * s, 0.8 * s, 0.4 * s)
rnd_color_jitter = torchvision.transforms.RandomApply([color_jitter], p=0.8)
rnd_gray = kornia.augmentation.RandomGrayscale(p=0.2)
color_distort = torchvision.transforms.Compose([rnd_color_jitter, rnd_gray])
return color_distort
class AISModel(nn.Module):
def __init__(self, model, init_dist):
super().__init__()
self.model = model
self.init_dist = init_dist
def forward(self, x, beta):
logpx = self.model(x).squeeze()
logpi = self.init_dist.log_prob(x).sum(-1)
return logpx * beta + logpi * (1. - beta)
def repeat_x(x):
repeat_shape = (x.shape[0],) + tuple(1 for _ in range(len(x.shape) - 1))
return x[0][None].repeat(*repeat_shape)
def get_data(args, dataset, batch_size, device, return_dset=False, zero_shot=False, return_trn_len=False,
return_tst_dset=False):
if return_dset and dataset not in ("utzappos", "celeba", "cub"):
raise NotImplementedError(f"Returning dataset is not implemented for {dataset}.")
if zero_shot and dataset != "utzappos":
raise NotImplementedError(f"Zero-shot learning is not implemented for {dataset}.")
if return_trn_len and dataset not in ["celeba", "utzappos"]:
raise NotImplementedError(f"Returning dataset length not configured for {dataset}.")
if not implies(return_tst_dset, dataset == "celeba" and args.dset_split_type == "zero_shot"):
raise NotImplementedError(f"Retuning tst dataset not configured for {dataset} and {args.dset_split_type}.")
assert implies(zero_shot, return_dset), f"Must be returning dataset labels when doing zero-shot."
assert implies(return_dset, args.full_test), f"Must be using test set when returning dataset labels."
if dataset == "mnist":
if args.small_cnn:
assert args.img_size == 32
transforms = [
torchvision.transforms.Resize(args.img_size),
torchvision.transforms.ToTensor(),
lambda x: (255 * x + torch.rand_like(x)) / 256.,
]
if args.logit:
logger("================= DOING LOGIT TRANSFORM BOIII =================")
transforms += [
lambda x: x * (1 - 2 * 1e-6) + 1e-6,
lambda x: x.log() - (1. - x).log()
]
else:
transforms = [
torchvision.transforms.ToTensor(),
lambda x: x.view(-1),
lambda x: (255 * x + torch.rand_like(x)) / 256.,
]
if not args.cnn and args.logit:
logger("================= DOING LOGIT TRANSFORM BOIII =================")
transforms += [
lambda x: x * (1 - 2 * 1e-6) + 1e-6,
lambda x: x.log() - (1. - x).log()
]
dset_train = torchvision.datasets.MNIST(root="./data", train=True, download=True,
transform=torchvision.transforms.Compose(transforms))
dset_test = torchvision.datasets.MNIST(root="./data", train=False, download=True,
transform=torchvision.transforms.Compose(transforms))
trn_batch = get_data_gen(dataset=dset_train, batch_size=batch_size, split="trn", device=device)
tst_batch = get_data_gen(dataset=dset_test, batch_size=batch_size, split="tst", device=device)
return trn_batch, tst_batch
elif dataset == "dsprites":
print("================= DOING LOGIT TRANSFORM BOIII =================")
if args.cnn:
transforms = []
else:
transforms = [lambda x: x.view(-1)]
transforms += [
lambda x: (7. * x + torch.rand_like(x)) / 8.,
lambda x: x * (1 - 2 * 1e-6) + 1e-6,
lambda x: x.log() - (1. - x).log()
]
dset = get_dsprites_dset(args.root, torchvision.transforms.Compose(transforms), test=args.dsprites_test)
if args.dsprites_test:
dset_train, dset_test = dset
trn_batch = get_data_gen(dataset=dset_train, batch_size=batch_size, split="trn", device=device)
tst_batch = get_data_gen(dataset=dset_test, batch_size=batch_size, split="tst", device=device)
return trn_batch, tst_batch
else:
batch = get_data_gen(dataset=dset, batch_size=batch_size, split="trn", device=device)
return batch, None
elif dataset == "fashionmnist":
dset_train = torchvision.datasets.FashionMNIST(root="./data", train=True, download=True,
transform=torchvision.transforms.Compose([
torchvision.transforms.ToTensor(),
lambda x: x.view(-1),
lambda x: (255 * x + torch.rand_like(x)) / 256.,
lambda x: x * (1 - 2 * 1e-6) + 1e-6,
lambda x: x.log() - (1. - x).log()
]))
batch = get_data_gen(dataset=dset_train, batch_size=batch_size, split="trn", device=device)
return batch
elif dataset == "celeba":
transforms = [
lambda x: (255 * x + torch.rand_like(x)) / 256.,
lambda x: x + args.img_sigma * torch.randn_like(x)
]
if args.clamp_data:
transforms.append(clamp_x)
root = os.path.join(args.root, "celeba")
dset, dset_label_info, cache_fn = celeba_tensor_dset(root=root,
img_size=args.img_size,
transform=torchvision.transforms.Compose(transforms),
attr_fn=os.path.join(root, "list_attr_celeba.txt"),
pkl_fn=os.path.join(root, "cache.pickle"),
cache_fn=os.path.join(root, "dset.pickle"),
drop_infreq=args.celeba_drop_infreq)
log_dset_label_info(logger, dset_label_info)
if args.full_test:
# overwrite dset instead of naming it trn_dset, since we return a copy not a pointer?
dset, tst_dset = split_celeba(dset, root=root, cache_fn=cache_fn,
split_len=CELEBA_TEST_LEN,
split_type=args.dset_split_type,
balanced_split_ratio=args.dset_balanced_split_ratio,
dset_label_info=dset_label_info)
trn_batch = get_data_gen(dataset=dset, batch_size=batch_size, split="trn", device=device)
tst_batch = get_data_gen(dataset=tst_dset, batch_size=batch_size, split="tst", device=device)
return_tpl = (trn_batch, tst_batch, dset_label_info, len(tst_dset))
if return_tst_dset:
return_tpl += (tst_dset,)
if return_dset:
# get all labels in the train set
return_tpl += (dset[:][1].float().mean(0)[:, None].to(args.device),)
if args.dset_split_type == "zero_shot":
logger("=========== ZERO SHOT ATTRIBUTE COMBINATION SAMPLING ===========")
tst_combos = find_combos_in_tst_set(dset[:][1], tst_dset[:][1], dset_label_info,
CELEBA_ZERO_SHOT_COMBOS)
trn_combos = [combo for combo in CELEBA_ZERO_SHOT_COMBOS if combo not in tst_combos]
assert len(trn_combos) + len(tst_combos) == len(CELEBA_ZERO_SHOT_COMBOS)
logger(f"{len(tst_combos)} COMBOS HELD OUT IN TEST SET")
for tst_combo in tst_combos:
logger(tst_combo)
# find mutually exclusive labels in the test set
tst_labels_combos = lbl_in_combos(tst_dset[:][1], dset_label_info, tst_combos)
tst_labels_combos_filter = tst_labels_combos.sum(1) == 1
tst_labels_combos_nums = tst_labels_combos.sum(0) > 0
logger(f"Found {tst_labels_combos_filter.sum()} of {len(tst_dset)} "
f"in test set with mutually exclusive labels.")
logger(f"Found {tst_labels_combos_nums.sum()} of {len(tst_combos)} "
f"mutually exclusive combos in the test set.")
return_tpl += (tst_combos,)
trn_labels_combos = lbl_in_combos(tst_dset[:][1], dset_label_info, trn_combos)
trn_labels_combos_filter = trn_labels_combos.sum(1) == 1
trn_labels_combos_nums = trn_labels_combos.sum(0) > 0
logger(f"Found trn {trn_labels_combos_filter.sum()} of {len(tst_dset)} "
f"in test set with mutually exclusive labels.")
logger(f"Found trn {trn_labels_combos_nums.sum()} of {len(trn_combos)} "
f"mutually exclusive combos in the test set.")
else:
trn_batch = get_data_gen(dataset=dset, batch_size=batch_size, split="trn", device=device)
return_tpl = (trn_batch, dset_label_info)
if return_trn_len:
return_tpl += (len(dset),)
return return_tpl
elif "utzappos" in dataset:
transforms = [
lambda x: (255 * x + torch.rand_like(x)) / 256.,
lambda x: x + args.img_sigma * torch.randn_like(x)
]
if args.clamp_data:
transforms.append(clamp_x)
if zero_shot:
root = os.path.join(args.root, "utzappos", "zero-shot")
_dset_kwargs = {
"root": os.path.join(root, "images"),
"attr_fn": root,
"pkl_fn": os.path.join(root, "cache.pickle"),
"cache_fn": os.path.join(root, "dset.pickle"),
"transform": torchvision.transforms.Compose(transforms)
}
else:
root = os.path.join(args.root, "utzappos", "ut-zap50k-images-square")
_dset_kwargs = {
"root": root,
"attr_fn": os.path.join(root, "meta-data.csv"),
"pkl_fn": os.path.join(root, "cache.pickle"),
"cache_fn": os.path.join(root, "dset.pickle"),
"transform": torchvision.transforms.Compose(transforms)
}
if zero_shot:
_dset_kwargs.update({
"img_size": args.img_size
})
elif dataset == "utzappos":
_dset_kwargs.update({
"observed": True,
"binarized": True,
"drop_infreq": args.utzappos_drop_infreq,
"img_size": args.img_size
})
else:
assert dataset == "utzappos_old", f"Unrecognized dataset {dataset}"
assert False
if zero_shot:
trn_dset, dset_label_info, cache_fn = utzappos_zero_shot_tensor_dset(split="trn", **_dset_kwargs)
val_dset, *_ = utzappos_zero_shot_tensor_dset(split="val", **_dset_kwargs)
tst_dset, *_ = utzappos_zero_shot_tensor_dset(split="tst", **_dset_kwargs)
dset_lengths = {'trn': len(trn_dset), 'val': len(val_dset), 'tst': len(tst_dset)}
log_dset_label_info(logger, dset_label_info)
trn_batch = get_data_gen(dataset=trn_dset, batch_size=batch_size, split="trn", device=device, zs_mode=True)
val_batch = get_data_gen(dataset=val_dset, batch_size=batch_size, split="tst", device=device, zs_mode=True)
tst_batch = get_data_gen(dataset=tst_dset, batch_size=batch_size, split="tst", device=device, zs_mode=True)
return_tpl = (trn_batch, val_batch, tst_batch, dset_label_info, dset_lengths)
if return_dset:
# get all labels in the train set
trn_labels = trn_dset[:][1] # trn_dset is a CustomTensorDataset, we need special indexing
return_tpl += (trn_labels.float().mean(0)[:, None].to(args.device),)
if return_trn_len:
return_tpl += (len(trn_dset),)
else:
dset, dset_label_info, cache_fn = utzappos_tensor_dset(**_dset_kwargs)
log_dset_label_info(logger, dset_label_info)
# find_duplicates_in_dsets(dset, dset, itself=True)
if args.full_test:
trn_dset, tst_dset = split_utzappos(dset, root=root, cache_fn=cache_fn,
split_len=UTZAPPOS_TEST_LEN,
split_type=args.dset_split_type,
balanced_split_ratio=args.dset_balanced_split_ratio)
trn_batch = get_data_gen(dataset=trn_dset, batch_size=batch_size, split="trn", device=device)
tst_batch = get_data_gen(dataset=tst_dset, batch_size=batch_size, split="tst", device=device)
return_tpl = (trn_batch, tst_batch, dset_label_info, len(tst_dset))
if return_dset:
# get all labels in the train set
trn_labels = trn_dset[:][1] # trn_dset is a CustomTensorDataset, we need special indexing
return_tpl += (trn_labels.float().mean(0)[:, None].to(args.device),)
# find_duplicates_in_dsets(trn_dset, tst_dset)
if return_trn_len:
return_tpl += (len(trn_dset),)
else:
trn_batch = get_data_gen(dataset=dset, batch_size=batch_size, split="trn", device=device)
return_tpl = (trn_batch, dset_label_info)
if return_trn_len:
return_tpl += (len(dset),)
return return_tpl
elif dataset == "cub":
transforms = [
lambda x: (255 * x + torch.rand_like(x)) / 256.,
lambda x: x + args.img_sigma * torch.randn_like(x)
]
if args.clamp_data:
transforms.append(clamp_x)
root = os.path.join(args.root, "CUB")
dset, dset_label_info, cache_fn = cub_tensor_dset(root=root,
img_size=args.img_size,
transform=torchvision.transforms.Compose(transforms),
drop_infreq=args.cub_drop_infreq,
attr_fn=os.path.join(root, "CUB_200_2011", "attributes",
"image_attribute_labels.txt"),
attr_name_fn=os.path.join(root, "attributes.txt"),
img_id_fn=os.path.join(root, "CUB_200_2011",
"images.txt"),
bb_fn=os.path.join(root, "CUB_200_2011",
"bounding_boxes.txt"),
pkl_fn=os.path.join(root, "cache.pickle"),
cache_fn=os.path.join(root, "dset.pickle"))
log_dset_label_info(logger, dset_label_info)
if args.full_test:
trn_dset, tst_dset = split_cub(dset, root=root, cache_fn=cache_fn,
split_len=CUB_TEST_LEN,
split_type=args.dset_split_type,
balanced_split_ratio=args.dset_balanced_split_ratio)
trn_batch = get_data_gen(dataset=trn_dset, batch_size=batch_size, split="trn", device=device)
tst_batch = get_data_gen(dataset=tst_dset, batch_size=batch_size, split="tst", device=device)
return_tpl = (trn_batch, tst_batch, dset_label_info)
if return_dset:
# get all labels in the train set
trn_labels = trn_dset[:][1] # trn_dset is a CustomTensorDataset, we need special indexing
return_tpl += (trn_labels.float().mean(0)[:, None].to(args.device),)
else:
trn_batch = get_data_gen(dataset=dset, batch_size=batch_size, split="trn", device=device)
return_tpl = (trn_batch, dset_label_info)
return return_tpl
elif dataset == "mwa":
transforms = [
torchvision.transforms.Normalize((.5, .5, .5), (.5, .5, .5)),
lambda x: x + args.img_sigma * torch.randn_like(x)
]
dset = MNISTWithAttributes(root="data", img_size=args.img_size,
transform=torchvision.transforms.Compose(transforms))
batch = get_data_gen(dataset=dset, batch_size=batch_size, split="trn", device=device)
return batch
elif dataset == "moons":
data, labels = sklearn.datasets.make_moons(n_samples=batch_size, noise=0.1)
data = data.astype("float32")
data = data * 2 + np.array([-1, -0.2])
elif dataset == "swissroll":
data, labels = sklearn.datasets.make_swiss_roll(n_samples=batch_size, noise=1.0)
data = data.astype("float32")[:, [0, 2]]
data /= 5
elif dataset in ["rings", "rings_struct"]:
rng = np.random.RandomState()
obs = batch_size
batch_size *= 20
n_samples4 = n_samples3 = n_samples2 = batch_size // 4
n_samples1 = batch_size - n_samples4 - n_samples3 - n_samples2
# so as not to have the first point = last point, we set endpoint=False
linspace4 = np.linspace(0, 2 * np.pi, n_samples4, endpoint=False)
linspace3 = np.linspace(0, 2 * np.pi, n_samples3, endpoint=False)
linspace2 = np.linspace(0, 2 * np.pi, n_samples2, endpoint=False)
linspace1 = np.linspace(0, 2 * np.pi, n_samples1, endpoint=False)
circ4_x = np.cos(linspace4)
circ4_y = np.sin(linspace4)
circ3_x = np.cos(linspace4) * 0.75
circ3_y = np.sin(linspace3) * 0.75
circ2_x = np.cos(linspace2) * 0.5
circ2_y = np.sin(linspace2) * 0.5
circ1_x = np.cos(linspace1) * 0.25
circ1_y = np.sin(linspace1) * 0.25
X = np.vstack([
np.hstack([circ4_x, circ3_x, circ2_x, circ1_x]),
np.hstack([circ4_y, circ3_y, circ2_y, circ1_y])
]).T * 3.0
Y = np.array([0] * n_samples1 + [1] * n_samples2 + [2] * n_samples3 + [3] * n_samples4)
# Add noise
X += rng.normal(scale=0.08, size=X.shape)
inds = np.random.choice(list(range(batch_size)), obs)
data = X[inds].astype("float32")
labels = Y[inds]
if dataset == "rings_struct":
labels_1 = (labels < 2).astype(int)
labels_2 = (labels % 2)
labels = np.hstack((labels_1[:, None], labels_2[:, None]))
elif dataset == "circles":
data, labels = sklearn.datasets.make_circles(n_samples=batch_size, factor=.5, noise=0.08)
data = data.astype("float32")
data *= 3
elif dataset == "checkerboard":
# uniform on (-2, 2)
x1 = np.random.rand(batch_size) * 4 - 2
# uniform on (0, 1) U (-2, -1)
row = np.random.randint(0, 2, batch_size)
x2_ = np.random.rand(batch_size) - row * 2
# add {-2, -1, 0, 1} -> {0, 1} -> {(-2, -1), (-1, 0), (0, 1), (1, 2)}
x2 = x2_ + (np.floor(x1) % 2)
data = np.concatenate([x1[:, None], x2[:, None]], 1) * 2
col = (np.floor(x1) + 2).astype(int)
labels = col * 2 + row
elif "8gaussians" in dataset:
centers = [
(0, -1), (1, 0), (0, 1), (-1, 0),
(1. / np.sqrt(2), -1. / np.sqrt(2)),
(1. / np.sqrt(2), 1. / np.sqrt(2)),
(-1. / np.sqrt(2), 1. / np.sqrt(2)),
(-1. / np.sqrt(2), -1. / np.sqrt(2))
]
centers = 4. * np.array(centers)
labels = np.random.randint(8, size=batch_size)
points = np.random.randn(batch_size, 2) * 0.5
data = centers[labels] + points
data /= 1.414
if "struct" in dataset:
labels_1 = (labels < 4).astype(int)
labels_2 = labels % 4
labels = np.hstack((labels_1[:, None], labels_2[:, None]))
elif "multi" in dataset:
labels_1 = (labels < 4).astype(int)
labels_2 = labels % 2
labels_3 = (labels // 2) % 2
labels = np.hstack((labels_1[:, None], labels_2[:, None], labels_3[:, None]))
elif "hierarch" in dataset:
labels_1 = (labels < 4).astype(int)
labels_2 = np.isin(labels, [0, 1, 4, 7]).astype(int)
labels_3 = np.isin(labels, [0, 2, 4, 5]).astype(int)
labels = np.hstack((labels_1[:, None], labels_2[:, None], labels_3[:, None]))
else:
raise ValueError(f"Unrecognized dataset {dataset}")
else:
assert False, f"Unknown dataset {dataset}"
if "missing" in dataset:
mask_ind = np.array(list(product(*(range(2) for _ in range(labels.shape[1]))))).astype(bool)
assert mask_ind[-1].all() # corresponds to removing all labels
num_label_masks = 2 ** labels.shape[1]
if "unsup" not in dataset:
num_label_masks -= 1 # don't choose the option to remove all labels
labels_to_mask = np.random.choice(num_label_masks, labels.shape[0])
labels_mask = mask_ind[labels_to_mask]
labels[labels_mask] = -1
return torch.tensor(data).to(device).float(), torch.tensor(labels).to(device)
def get_data_batch(args, dataset, batch_size, device, return_dset=False, zero_shot=False, return_trn_len=False,
return_tst_dset=False):
if dataset in IMG_DSETS:
return get_data(args, dataset, batch_size, device, return_dset, zero_shot, return_trn_len, return_tst_dset)
else:
return lambda: get_data(args, dataset, batch_size, device, zero_shot)
class SpectralLinear(nn.Module):
def __init__(self, nin, nout, init_scale=1):
super().__init__()
self.linear = spectral_norm(nn.Linear(nin, nout))
self.log_scale = nn.Parameter(torch.zeros(1,) + np.log(init_scale), requires_grad=True)
@property
def scale(self):
return self.log_scale.exp()
def forward(self, x):
return self.scale * self.linear(x)
def smooth_mlp_ebm_big(nin, nout=1):
return nn.Sequential(
nn.Linear(nin, 1000),
nn.ELU(),
nn.Linear(1000, 1000),
nn.ELU(),
nn.Linear(1000, 500),
nn.ELU(),
nn.Linear(500, nout),
)
def smooth_mlp_ebm_bigger(act, nin, nout=1, spectral=False):
"""
Large MLP EBM.
"""
if act == "elu":
assert not spectral
return nn.Sequential(
nn.Linear(nin, 1000),
nn.ELU(),
nn.Linear(1000, 500),
nn.ELU(),
nn.Linear(500, 500),
nn.ELU(),
nn.Linear(500, 250),
nn.ELU(),
nn.Linear(250, 250),
nn.ELU(),
nn.Linear(250, 250),
nn.ELU(),
nn.Linear(250, nout)
)
elif act == "lrelu":
assert not spectral
return nn.Sequential(
nn.Linear(nin, 1000),
nn.LeakyReLU(.2, inplace=True),
nn.Linear(1000, 500),
nn.LeakyReLU(.2, inplace=True),
nn.Linear(500, 500),
nn.LeakyReLU(.2, inplace=True),
nn.Linear(500, 250),
nn.LeakyReLU(.2, inplace=True),
nn.Linear(250, 250),
nn.LeakyReLU(.2, inplace=True),
nn.Linear(250, 250),
nn.LeakyReLU(.2, inplace=True),
nn.Linear(250, nout)
)
elif act == "swish":
if spectral:
return nn.Sequential(
spectral_norm(nn.Linear(nin, 1000)),
nn.SiLU(inplace=True),
spectral_norm(nn.Linear(1000, 500)),
nn.SiLU(inplace=True),
spectral_norm(nn.Linear(500, 500)),
nn.SiLU(inplace=True),
spectral_norm(nn.Linear(500, 250)),
nn.SiLU(inplace=True),
spectral_norm(nn.Linear(250, 250)),
nn.SiLU(inplace=True),
spectral_norm(nn.Linear(250, 250)),
nn.SiLU(inplace=True),
spectral_norm(nn.Linear(250, nout))
)
else:
return nn.Sequential(
nn.Linear(nin, 1000),
nn.SiLU(inplace=True),
nn.Linear(1000, 500),
nn.SiLU(inplace=True),
nn.Linear(500, 500),
nn.SiLU(inplace=True),
nn.Linear(500, 250),
nn.SiLU(inplace=True),
nn.Linear(250, 250),
nn.SiLU(inplace=True),
nn.Linear(250, 250),
nn.SiLU(inplace=True),
nn.Linear(250, nout)
)
else:
assert f"act {act} not known"
def smooth_mlp_ebm(spectral, nin, nout=1, init_scale=1):
if spectral:
net = nn.Sequential(
SpectralLinear(nin, 256, init_scale),
nn.ELU(),
SpectralLinear(256, 256, init_scale),
nn.ELU(),
SpectralLinear(256, 256, init_scale),
nn.ELU(),
SpectralLinear(256, nout, init_scale),
)
else:
net = nn.Sequential(
nn.Linear(nin, 256),
nn.ELU(),
nn.Linear(256, 256),
nn.ELU(),
nn.Linear(256, 256),
nn.ELU(),
nn.Linear(256, nout),
)
return net
def small_mlp_ebm(nin, nout=1, nhidden=256, spectral=False):
if spectral:
net = nn.Sequential(
spectral_norm(nn.Linear(nin, nhidden)),
nn.SiLU(inplace=True),
spectral_norm(nn.Linear(nhidden, nhidden)),
nn.SiLU(inplace=True),
spectral_norm(nn.Linear(nhidden, nout)),
)
else:
net = nn.Sequential(
nn.Linear(nin, nhidden),
nn.SiLU(inplace=True),
nn.Linear(nhidden, nhidden),
nn.SiLU(inplace=True),
nn.Linear(nhidden, nout),
)
return net
class WSConv2d(nn.Conv2d):
def __init__(self, in_channels, out_channels, kernel_size, stride=1,
padding=0, dilation=1, groups=1, bias=True):
super(WSConv2d, self).__init__(in_channels, out_channels, kernel_size, stride, padding, dilation, groups, bias)
def forward(self, x):
weight = self.weight
weight_mean = weight.mean(dim=1, keepdim=True).mean(dim=2,
keepdim=True).mean(dim=3, keepdim=True)
weight = weight - weight_mean
std = weight.view(weight.size(0), -1).std(dim=1).view(-1, 1, 1, 1) + 1e-5
weight = weight / std.expand_as(weight)
return F.conv2d(x, weight, self.bias, self.stride,
self.padding, self.dilation, self.groups)
class CondResBlock(nn.Module):
def __init__(self,
args,
downsample=True,
rescale=True,
filters=64,
latent_dim=64,
im_size=64,
classes=512,
norm=True,
spec_norm=False):
super(CondResBlock, self).__init__()
self.filters = filters
self.latent_dim = latent_dim
self.im_size = im_size
self.downsample = downsample
if filters <= 128:
self.bn1 = nn.InstanceNorm2d(filters, affine=True)
else:
self.bn1 = nn.GroupNorm(32, filters)
if not norm:
self.bn1 = None
self.args = args
if spec_norm:
self.conv1 = spectral_norm(nn.Conv2d(filters, filters, kernel_size=3, stride=1, padding=1))
else:
self.conv1 = WSConv2d(filters, filters, kernel_size=3, stride=1, padding=1)
if filters <= 128:
self.bn2 = nn.InstanceNorm2d(filters, affine=True)
else:
self.bn2 = nn.GroupNorm(32, filters, affine=True)
if not norm:
self.bn2 = None
if spec_norm:
self.conv2 = spectral_norm(nn.Conv2d(filters, filters, kernel_size=3, stride=1, padding=1))
else:
self.conv2 = WSConv2d(filters, filters, kernel_size=3, stride=1, padding=1)
self.dropout = nn.Dropout(0.2)
# Upscale to an mask of image
self.latent_map = nn.Linear(classes, 2*filters)
self.latent_map_2 = nn.Linear(classes, 2*filters)
self.relu = torch.nn.ReLU(inplace=True)
self.act = nn.SiLU(inplace=True)
# Upscale to mask of image
if downsample:
if rescale:
self.conv_downsample = nn.Conv2d(filters, 2 * filters, kernel_size=3, stride=1, padding=1)
if args.alias:
self.avg_pool = Downsample(channels=2*filters)
else:
self.avg_pool = nn.AvgPool2d(3, stride=2, padding=1)
else:
self.conv_downsample = nn.Conv2d(filters, filters, kernel_size=3, stride=1, padding=1)
if args.alias:
self.avg_pool = Downsample(channels=filters)
else:
self.avg_pool = nn.AvgPool2d(3, stride=2, padding=1)
def forward(self, x, y):
if y is not None:
latent_map = self.latent_map(y).view(-1, 2*self.filters, 1, 1)
gain = latent_map[:, :self.filters]
bias = latent_map[:, self.filters:]
else:
gain = bias = None # appeasing the linter
x = self.conv1(x)
if self.bn1 is not None:
x = self.bn1(x)
if y is not None:
x = gain * x + bias
x = self.act(x)
if y is not None:
latent_map = self.latent_map_2(y).view(-1, 2*self.filters, 1, 1)
gain = latent_map[:, :self.filters]
bias = latent_map[:, self.filters:]
x = self.conv2(x)
if self.bn2 is not None:
x = self.bn2(x)
if y is not None:
x = gain * x + bias
x = self.act(x)
x_out = x
if self.downsample:
x_out = self.conv_downsample(x_out)
x_out = self.act(self.avg_pool(x_out))
return x_out
class Self_Attn(nn.Module):
""" Self attention Layer"""
def __init__(self, in_dim, activation):
super(Self_Attn, self).__init__()
self.chanel_in = in_dim
self.activation = activation
self.query_conv = nn.Conv2d(in_channels=in_dim, out_channels=in_dim//8, kernel_size=1)
self.key_conv = nn.Conv2d(in_channels=in_dim, out_channels=in_dim//8, kernel_size=1)
self.value_conv = nn.Conv2d(in_channels=in_dim, out_channels=in_dim, kernel_size=1)
self.gamma = nn.Parameter(torch.zeros(1))
self.softmax = nn.Softmax(dim=-1)
def forward(self, x):
"""
inputs :
x : input feature maps( B X C X W X H)
returns :
out : self attention value + input feature
attention: B X N X N (N is Width*Height)
"""
m_batchsize, C, width, height = x.size()
proj_query = self.query_conv(x).view(m_batchsize, -1, width * height).permute(0, 2, 1) # B X CX(N)
proj_key = self.key_conv(x).view(m_batchsize, -1, width * height) # B X C x (W * H)
energy = torch.bmm(proj_query, proj_key) # transpose check
attention = self.softmax(energy) # BX (N) X (N)
proj_value = self.value_conv(x).view(m_batchsize, -1, width * height) # B X C X N
out = torch.bmm(proj_value, attention.permute(0, 2, 1))
out = out.view(m_batchsize, C, width, height)
out = self.gamma * out + x
return out, attention
class MNISTModel(nn.Module):
def __init__(self, args):
super(MNISTModel, self).__init__()
self.act = nn.SiLU(inplace=True)
self.args = args
self.n_f = args.n_f
self.init_main_model()
self.init_label_map()
self.cond = False
def init_main_model(self):
args = self.args
filter_dim = self.n_f
im_size = 28
self.conv1 = nn.Conv2d(1, filter_dim, kernel_size=3, stride=1, padding=1)
self.res1 = CondResBlock(args, filters=filter_dim, latent_dim=1, im_size=im_size)
self.res2 = CondResBlock(args, filters=2*filter_dim, latent_dim=1, im_size=im_size)
self.res3 = CondResBlock(args, filters=4*filter_dim, latent_dim=1, im_size=im_size)
self.energy_map = nn.Linear(filter_dim*8, 1)
def init_label_map(self):
self.map_fc1 = nn.Linear(10, 256)
self.map_fc2 = nn.Linear(256, 256)
def main_model(self, x, latent):
x = x.view(-1, 1, 28, 28)
x = self.act(self.conv1(x))
x = self.res1(x, latent)
x = self.res2(x, latent)
x = self.res3(x, latent)
x = self.act(x)
x = x.mean(dim=2).mean(dim=2)
energy = self.energy_map(x)
return energy
def label_map(self, latent):
x = self.act(self.map_fc1(latent))
x = self.map_fc2(x)
return x
def forward(self, x, latent=None):
x = x.view(x.size(0), -1)
if self.cond:
latent = self.label_map(latent)
energy = self.main_model(x, latent)
return energy
class CNNCond(nn.Module):
def __init__(self, n_c=3, n_f=32, cnn_out_dim=512, label_dim=0, uncond=False):
super(CNNCond, self).__init__()
self.label_dim = label_dim
self.cnn_out_dim = cnn_out_dim
self.uncond = uncond
self.cnn = nn.Sequential(
nn.Conv2d(n_c, n_f, 3, 1, 1),
nn.LeakyReLU(.2),
nn.Conv2d(n_f, n_f * 2, 4, 2, 1),
nn.LeakyReLU(.2),
nn.Conv2d(n_f * 2, n_f * 4, 4, 2, 1),
nn.LeakyReLU(.2),
nn.Conv2d(n_f * 4, n_f * 8, 4, 2, 1),
nn.LeakyReLU(.2),
nn.Conv2d(n_f * 8, n_f, 1, 1, 0),
nn.Flatten()
)
self.mlp = smooth_mlp_ebm(spectral=False, nin=label_dim + cnn_out_dim, nout=1)
def forward(self, x, label=None):
x = self.cnn(x)
if label is None:
assert self.uncond
return self.mlp(x)
else:
label = label.flatten(start_dim=1)
return self.mlp(torch.cat([x, label], dim=1))
class CelebAModel(nn.Module):
def __init__(self, args, debug=False):
super(CelebAModel, self).__init__()
self.act = nn.SiLU(inplace=True)
self.max_pool = nn.MaxPool2d(kernel_size=3, stride=2, padding=1)
self.cond = False
self.args = args
self.init_main_model()
if args.multiscale:
self.init_mid_model()
self.init_small_model()
self.relu = torch.nn.ReLU(inplace=True)
self.downsample = Downsample(channels=3)
self.heir_weight = nn.Parameter(torch.Tensor([1.0, 1.0, 1.0]))
self.debug = debug
def init_main_model(self):
args = self.args
filter_dim = args.n_f
latent_dim = args.n_f
im_size = args.img_size
self.conv1 = nn.Conv2d(3, filter_dim // 2, kernel_size=3, stride=1, padding=1)
self.res_1a = CondResBlock(args,
filters=filter_dim // 2,
latent_dim=latent_dim,
im_size=im_size,
downsample=True,
classes=2,
norm=args.norm,
spec_norm=args.spec_norm)
self.res_1b = CondResBlock(args,
filters=filter_dim,
latent_dim=latent_dim,
im_size=im_size,
rescale=False,
classes=2,
norm=args.norm,
spec_norm=args.spec_norm)
self.res_2a = CondResBlock(args,
filters=filter_dim,
latent_dim=latent_dim,
im_size=im_size,
downsample=True,
rescale=False,
classes=2,
norm=args.norm,
spec_norm=args.spec_norm)
self.res_2b = CondResBlock(args,
filters=filter_dim,
latent_dim=latent_dim,
im_size=im_size,
rescale=True,
classes=2,
norm=args.norm,
spec_norm=args.spec_norm)
self.res_3a = CondResBlock(args,
filters=2 * filter_dim,
latent_dim=latent_dim,
im_size=im_size,
downsample=False,
classes=2,
norm=args.norm,
spec_norm=args.spec_norm)
self.res_3b = CondResBlock(args,
filters=2 * filter_dim,
latent_dim=latent_dim,
im_size=im_size,
rescale=True,
classes=2,
norm=args.norm,
spec_norm=args.spec_norm)
self.res_4a = CondResBlock(args,
filters=4 * filter_dim,
latent_dim=latent_dim,
im_size=im_size,
downsample=False,
classes=2,
norm=args.norm,
spec_norm=args.spec_norm)
self.res_4b = CondResBlock(args,
filters=4 * filter_dim,
latent_dim=latent_dim,
im_size=im_size,
rescale=True,
classes=2,
norm=args.norm,
spec_norm=args.spec_norm)
self.self_attn = Self_Attn(4 * filter_dim, self.act)
self.energy_map = nn.Linear(filter_dim*8, 1)
def init_mid_model(self):
args = self.args
filter_dim = args.n_f
latent_dim = args.n_f
im_size = args.img_size
self.mid_conv1 = nn.Conv2d(3, filter_dim, kernel_size=3, stride=1, padding=1)
self.mid_res_1a = CondResBlock(args,
filters=filter_dim,
latent_dim=latent_dim,
im_size=im_size,
downsample=True,
rescale=False,
classes=2)
self.mid_res_1b = CondResBlock(args,
filters=filter_dim,
latent_dim=latent_dim,
im_size=im_size,
rescale=False,
classes=2)
self.mid_res_2a = CondResBlock(args,
filters=filter_dim,
latent_dim=latent_dim,
im_size=im_size,
downsample=True,
rescale=False,
classes=2)
self.mid_res_2b = CondResBlock(args,
filters=filter_dim,
latent_dim=latent_dim,
im_size=im_size,
rescale=True,
classes=2)
self.mid_res_3a = CondResBlock(args,
filters=2 * filter_dim,
latent_dim=latent_dim,
im_size=im_size,
downsample=False,
classes=2)
self.mid_res_3b = CondResBlock(args,
filters=2 * filter_dim,
latent_dim=latent_dim,
im_size=im_size,
rescale=True,
classes=2)
self.mid_energy_map = nn.Linear(filter_dim * 4, 1)
self.avg_pool = Downsample(channels=3)
def init_small_model(self):
args = self.args
filter_dim = args.n_f
latent_dim = args.n_f
im_size = args.img_size
self.small_conv1 = nn.Conv2d(3, filter_dim, kernel_size=3, stride=1, padding=1)
self.small_res_1a = CondResBlock(args,
filters=filter_dim,
latent_dim=latent_dim,
im_size=im_size,
downsample=True,
rescale=False,
classes=2)
self.small_res_1b = CondResBlock(args,
filters=filter_dim,
latent_dim=latent_dim,
im_size=im_size,
rescale=False,
classes=2)
self.small_res_2a = CondResBlock(args,
filters=filter_dim,
latent_dim=latent_dim,
im_size=im_size,
downsample=True,
rescale=False,
classes=2)
self.small_res_2b = CondResBlock(args,
filters=filter_dim,
latent_dim=latent_dim,
im_size=im_size,
rescale=True,
classes=2)
self.small_energy_map = nn.Linear(filter_dim * 2, 1)
def main_model(self, x, latent):
x = self.act(self.conv1(x))
x = self.res_1a(x, latent)
x = self.res_1b(x, latent)
x = self.res_2a(x, latent)
x = self.res_2b(x, latent)
x = self.res_3a(x, latent)
x = self.res_3b(x, latent)
if self.args.self_attn:
x, _ = self.self_attn(x)
x = self.res_4a(x, latent)
x = self.res_4b(x, latent)
x = self.act(x)
x = x.mean(dim=2).mean(dim=2)
x = x.view(x.size(0), -1)
energy = self.energy_map(x)
return energy
def mid_model(self, x, latent):
x = F.avg_pool2d(x, 3, stride=2, padding=1)
x = self.act(self.mid_conv1(x))
x = self.mid_res_1a(x, latent)
x = self.mid_res_1b(x, latent)
x = self.mid_res_2a(x, latent)
x = self.mid_res_2b(x, latent)
x = self.mid_res_3a(x, latent)
x = self.mid_res_3b(x, latent)
x = self.act(x)
x = x.mean(dim=2).mean(dim=2)
x = x.view(x.size(0), -1)
energy = self.mid_energy_map(x)
return energy
def small_model(self, x, latent):
x = F.avg_pool2d(x, 3, stride=2, padding=1)
x = F.avg_pool2d(x, 3, stride=2, padding=1)
x = self.act(self.small_conv1(x))
x = self.small_res_1a(x, latent)
x = self.small_res_1b(x, latent)
x = self.small_res_2a(x, latent)
x = self.small_res_2b(x, latent)
x = self.act(x)
x = x.mean(dim=2).mean(dim=2)
x = x.view(x.size(0), -1)
energy = self.small_energy_map(x)
return energy
def label_map(self, latent):
x = self.act(self.map_fc1(latent))
x = self.act(self.map_fc2(x))
x = self.act(self.map_fc3(x))
x = self.act(self.map_fc4(x))
return x
def forward(self, x, latent=None):
assert (latent is None) == (not self.cond)
args = self.args
if not self.cond:
latent = None
energy = self.main_model(x, latent)
if args.multiscale:
large_energy = energy
mid_energy = self.mid_model(x, latent)
small_energy = self.small_model(x, latent)
energy = torch.cat([small_energy, mid_energy, large_energy], dim=-1)
return energy
class CNNCondBigger(nn.Module):
def __init__(self, n_c=1, n_f=8, label_dim=0, uncond=False, cond_mode=None, small_mlp=False, spectral=False):
super(CNNCondBigger, self).__init__()
self.label_dim = label_dim
self.uncond = uncond
self.cond_mode = cond_mode
if uncond:
if spectral:
self.cnn = nn.Sequential(
spectral_norm(nn.Conv2d(n_c, n_f, 3, 1, 1)),
nn.SiLU(inplace=True),
spectral_norm(nn.Conv2d(n_f, n_f * 2, 4, 2, 1)),
nn.SiLU(inplace=True),
spectral_norm(nn.Conv2d(n_f * 2, n_f * 4, 4, 2, 1)),
nn.SiLU(inplace=True),
spectral_norm(nn.Conv2d(n_f * 4, n_f * 8, 4, 2, 1)),
nn.SiLU(inplace=True),
spectral_norm(nn.Conv2d(n_f * 8, 1, 4, 1, 0))
)
else:
self.cnn = nn.Sequential(
nn.Conv2d(n_c, n_f, 3, 1, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f, n_f * 2, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 2, n_f * 4, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 4, n_f * 8, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 8, 1, 4, 1, 0)
)
else:
assert cond_mode is not None
if cond_mode == "dot":
cnn_out_dim = 1024
if n_f == 8:
pass
elif n_f == 16:
cnn_out_dim *= 2
elif n_f == 32:
cnn_out_dim *= 4
elif n_f == 64:
cnn_out_dim *= 8
else:
raise ValueError
if spectral:
self.cnn = nn.Sequential(
spectral_norm(nn.Conv2d(n_c, n_f, 3, 1, 1)),
nn.SiLU(inplace=True),
spectral_norm(nn.Conv2d(n_f, n_f * 2, 4, 2, 1)),
nn.SiLU(inplace=True),
spectral_norm(nn.Conv2d(n_f * 2, n_f * 4, 4, 2, 1)),
nn.SiLU(inplace=True),
spectral_norm(nn.Conv2d(n_f * 4, n_f * 8, 4, 2, 1)),
nn.Flatten(),
)
else:
self.cnn = nn.Sequential(
nn.Conv2d(n_c, n_f, 3, 1, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f, n_f * 2, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 2, n_f * 4, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 4, n_f * 8, 4, 2, 1),
nn.Flatten(),
)
if small_mlp:
self.mlp = small_mlp_ebm(nin=label_dim, nout=cnn_out_dim, spectral=spectral)
else:
self.mlp = smooth_mlp_ebm_bigger('swish', nin=label_dim, nout=cnn_out_dim, spectral=spectral)
elif cond_mode == "cnn-mlp":
cnn_out_dim = 128
if n_f == 8:
pass
elif n_f == 16:
cnn_out_dim *= 2
elif n_f == 32:
cnn_out_dim *= 4
elif n_f == 64:
cnn_out_dim *= 8
else:
raise ValueError
if spectral:
self.cnn = nn.Sequential(
spectral_norm(nn.Conv2d(n_c, n_f, 3, 1, 1)),
nn.SiLU(inplace=True),
spectral_norm(nn.Conv2d(n_f, n_f * 2, 4, 2, 1)),
nn.SiLU(inplace=True),
spectral_norm(nn.Conv2d(n_f * 2, n_f * 4, 4, 2, 1)),
nn.SiLU(inplace=True),
spectral_norm(nn.Conv2d(n_f * 4, n_f * 8, 4, 2, 1)),
nn.SiLU(inplace=True),
spectral_norm(nn.Conv2d(n_f * 8, n_f, 1, 1, 0)),
nn.Flatten(),
)
else:
self.cnn = nn.Sequential(
nn.Conv2d(n_c, n_f, 3, 1, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f, n_f * 2, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 2, n_f * 4, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 4, n_f * 8, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 8, n_f, 1, 1, 0),
nn.Flatten(),
)
if small_mlp:
self.mlp = small_mlp_ebm(nin=label_dim + cnn_out_dim, nout=1, spectral=spectral)
else:
self.mlp = smooth_mlp_ebm_bigger('swish', nin=label_dim + cnn_out_dim, nout=1, spectral=spectral)
else:
raise ValueError
def forward(self, x, label=None):
x = self.cnn(x)
if label is None:
assert self.uncond
return x.squeeze()
else:
label = label.flatten(start_dim=1)
if self.cond_mode == "dot":
label = self.mlp(label)
return (x * label).sum(-1)
elif self.cond_mode == "cnn-mlp":
return self.mlp(torch.cat([x, label], dim=1)).squeeze()
else:
raise ValueError
class MNISTCNNCond(nn.Module):
def __init__(self, n_c=1, n_f=8, label_dim=0, cond_mode=None, small_mlp=False):
super(MNISTCNNCond, self).__init__()
self.label_dim = label_dim
self.cond_mode = cond_mode
assert cond_mode is not None
if cond_mode in ("dot", "cos"):
cnn_out_dim = 1024
assert n_f in (8, 16, 32, 64), f"Unrecognized n_f {n_f}"
cnn_out_dim *= n_f // 8
self.cnn = nn.Sequential(
nn.Conv2d(n_c, n_f, 3, 1, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f, n_f * 2, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 2, n_f * 4, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 4, n_f * 8, 4, 2, 1),
nn.Flatten(),
)
if small_mlp:
self.mlp = small_mlp_ebm(nin=label_dim, nout=cnn_out_dim, spectral=False)
else:
self.mlp = smooth_mlp_ebm_bigger('swish', nin=label_dim, nout=cnn_out_dim, spectral=False)
elif cond_mode == "cnn-mlp":
cnn_out_dim = 128
assert n_f in (8, 16, 32, 64), f"Unrecognized n_f {n_f}"
cnn_out_dim *= n_f // 8
self.cnn = nn.Sequential(
nn.Conv2d(n_c, n_f, 3, 1, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f, n_f * 2, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 2, n_f * 4, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 4, n_f * 8, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 8, n_f, 1, 1, 0),
nn.Flatten(),
)
if small_mlp:
self.mlp = small_mlp_ebm(nin=label_dim + cnn_out_dim, nout=1, spectral=False)
else:
self.mlp = smooth_mlp_ebm_bigger('swish', nin=label_dim + cnn_out_dim, nout=1, spectral=False)
else:
raise ValueError(f"Unrecognized cond_mode {cond_mode}")
def forward(self, x, label):
x = self.cnn(x)
label = label.flatten(start_dim=1)
if self.cond_mode in ("dot", "cos"):
label = self.mlp(label)
if self.cond_mode == "dot":
return (x * label).sum(-1)
else:
return (x * label).sum(-1) / (x.norm(p=2, dim=-1) * label.norm(p=2, dim=-1))
elif self.cond_mode == "cnn-mlp":
return self.mlp(torch.cat([x, label], dim=1)).squeeze()
else:
raise ValueError
class ZapposCNNCond(nn.Module):
def __init__(self, img_size=64, n_c=1, n_f=8, label_dim=0, cond_mode=None,
small_mlp=False, small_mlp_nhidden=256, all_binary=False):
super(ZapposCNNCond, self).__init__()
self.label_dim = label_dim
self.cond_mode = cond_mode
assert cond_mode is not None
assert n_f in (8, 16, 32, 64), f"Unrecognized n_f {n_f}"
cnn_layers = [nn.Conv2d(n_c, n_f, 3, 1, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f, n_f * 2, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 2, n_f * 4, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 4, n_f * 8, 4, 2, 1)]
if img_size == 64:
cnn_layers.extend([nn.SiLU(inplace=True),
nn.Conv2d(n_f * 8, n_f * 8, 4, 2, 1)])
else:
if img_size != 32:
raise ValueError(f"Unrecognized img size {img_size}")
if cond_mode in ("dot", "cos"):
cnn_out_dim = 1024
cnn_out_dim *= n_f // 8
nin, nout = label_dim, cnn_out_dim
# get input features to last layer
cnn_layers = cnn_layers + [nn.Flatten()]
elif cond_mode in ("cnn-mlp", "poj"):
cnn_out_dim = 128
cnn_out_dim *= n_f // 8
if cond_mode == "cnn-mlp":
nin, nout = label_dim + cnn_out_dim, 1
elif cond_mode == "poj":
nin, nout = cnn_out_dim, label_dim
if all_binary:
nout *= 2
else:
raise ValueError(f"Unrecognized cond mode {cond_mode}")
# add 1x1 conv layer
cnn_layers = cnn_layers + [nn.SiLU(inplace=True),
nn.Conv2d(n_f * 8, n_f, 1, 1, 0),
nn.Flatten()]
else:
raise ValueError(f"Unrecognized cond_mode {cond_mode}")
self.cnn = nn.Sequential(*cnn_layers)
if small_mlp:
mlp_ = partial(small_mlp_ebm, spectral=False, nhidden=small_mlp_nhidden)
else:
mlp_ = partial(smooth_mlp_ebm_bigger, 'swish', spectral=False)
self.mlp = mlp_(nin=nin, nout=nout)
def forward(self, x, label=None):
assert implies(label is None, self.cond_mode == "poj")
x = self.cnn(x)
if self.cond_mode == "poj":
return self.mlp(x).squeeze()
else:
label = label.flatten(start_dim=1)
if self.cond_mode in ("dot", "cos"):
label = self.mlp(label)
if self.cond_mode == "dot":
return (x * label).sum(-1)
else:
return (x * label).sum(-1) / (x.norm(p=2, dim=-1) * label.norm(p=2, dim=-1))
elif self.cond_mode == "cnn-mlp":
return self.mlp(torch.cat([x, label], dim=1)).squeeze()
else:
raise ValueError
def small_cnn(n_c=3, n_f=32):
return nn.Sequential(
nn.Conv2d(n_c, n_f, 3, 1, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f, n_f * 2, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 2, n_f * 4, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 4, n_f * 8, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 8, 1, 4, 1, 0)
)
def medium_cnn(n_c=3, n_f=64):
return nn.Sequential(
nn.Conv2d(n_c, n_f, 3, 1, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f, n_f * 2, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 2, n_f * 4, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 4, n_f * 8, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 8, n_f * 8, 4, 2, 1),
nn.SiLU(inplace=True),
nn.Conv2d(n_f * 8, 1, 4, 1, 0)
)
def get_scales(net):
scales = []
for k, v in net.named_children():
if int(k) % 2 == 0:
scales.append(v.scale.item())
return scales
def ema_model(model, model_ema, mu=0.99):
assert 0 <= mu <= 1
if mu != 1: # if mu is 1, the ema parameters stay the same
for param, param_ema in zip(model.parameters(), model_ema.parameters()):
param_ema.data[:] = mu * param_ema.data + (1 - mu) * param.data
def ema_params(model, model_ema):
"""
Check if params are the same.
"""
for param, param_ema in zip(model.parameters(), model_ema.parameters()):
if not torch.eq(param_ema.data, param.data).all():
return False
return True
def get_sample_q(init_x_random, init_b_random, reinit_freq, step_size, sigma, device, transform=None, one_hot_b=None,
only_transform_buffer=False):
def sample_p_0(replay_buffer, bs, y=None, y_replay_buffer=None, y_cond=None):
if len(replay_buffer) == 0 and not isinstance(replay_buffer, ReplayBuffer):
return init_x_random(bs), []
assert implies(y_cond is not None, y_replay_buffer is not None), "Buffer conditional sampling requires buffer"
assert implies(y is not None, y_replay_buffer is not None), "Joint initialization requires buffer"
assert y is None or y_cond is None, "Buffer conditional sampling or joint initialization, but not both"
# conditional buffer sampling
if y_cond is not None:
if not isinstance(y_cond, int):
assert len(y_cond) == 1, "Init conditionally with 1 label only!"
assert len(y_cond.shape) == 1, "Wrong shape"
if isinstance(replay_buffer, ReplayBuffer):
raise NotImplementedError("Condtional yd buffer is not available")
else:
replay_buffer = replay_buffer[y_replay_buffer == y_cond]
buffer_size = len(replay_buffer)
if buffer_size == 0 and not isinstance(replay_buffer, ReplayBuffer):
logger(f"====== WARNING ====== Encountered buffer size 0 for class {y_cond}")
return init_x_random(bs), []
choose_random = (torch.rand(bs) < reinit_freq).float().to(device)
if y is None:
random_samples = init_x_random(bs)
buffer_samples, inds = get_buffer_samples(replay_buffer, buffer_size, bs)
if only_transform_buffer:
buffer_samples = transform(buffer_samples)
samples = get_random_or_buffer_samples(choose_random, random_samples, buffer_samples)
else:
samples = get_random_or_buffer_samples(choose_random, random_samples, buffer_samples)
samples = samples.to(device) # TODO: i'm pretty sure this is redundant, everything's already on device
samples = transform(samples)
else:
random_x_samples, random_y_samples = init_x_random(bs), init_b_random(bs, label_samples=True)
# pass inds when sampling y, so we get the corresponding y buffer samples
buffer_x_samples, inds = get_buffer_samples(replay_buffer, buffer_size, bs)
buffer_y_samples, inds = get_buffer_samples(y_replay_buffer, buffer_size, bs, inds)
if only_transform_buffer:
buffer_x_samples = transform(buffer_x_samples)
x_samples = get_random_or_buffer_samples(choose_random, random_x_samples, buffer_x_samples)
y_samples = get_random_or_buffer_samples(choose_random, random_y_samples, buffer_y_samples)
x_samples, y_samples = x_samples.to(device), y_samples.to(device)
y_samples = one_hot_b(y_samples.type(random_y_samples.dtype))
else:
x_samples = get_random_or_buffer_samples(choose_random, random_x_samples, buffer_x_samples)
y_samples = get_random_or_buffer_samples(choose_random, random_y_samples, buffer_y_samples)
x_samples, y_samples = x_samples.to(device), y_samples.to(device)
x_samples, y_samples = transform(x_samples), one_hot_b(y_samples.type(random_y_samples.dtype))
samples = (x_samples, y_samples)
return samples, inds
def get_buffer_samples(replay_buffer, buffer_size, bs, inds=None):
if inds is None and not isinstance(replay_buffer, ReplayBuffer):
# if yd buffer, let it generate its own inds
inds = torch.randint(0, buffer_size, (bs,))
if isinstance(replay_buffer, ReplayBuffer):
buffer_samples, inds = replay_buffer.sample(bs, inds)
else:
buffer_samples = replay_buffer[inds]
return buffer_samples.to(device), inds
def get_random_or_buffer_samples(choose_random, random_samples, buffer_samples):
assert random_samples.shape == buffer_samples.shape
assert len(choose_random.shape) == 1
assert choose_random.shape[0] == random_samples.shape[0]
choose_random = choose_random[:, None]
structured_shape = random_samples.shape
if len(random_samples.shape) == 2:
pass
elif len(random_samples.shape) == 3:
random_samples = random_samples.view(random_samples.shape[0], -1)
buffer_samples = random_samples.view(buffer_samples.shape[0], -1)
elif len(random_samples.shape) == 4:
choose_random = choose_random[:, None, None]
else:
raise ValueError(f"Unrecognized samples shape {random_samples.shape}")
final_samples = choose_random * random_samples + (1 - choose_random) * buffer_samples
return final_samples.view(structured_shape)
def init_sampling(replay_buffer, x, y=None, y_replay_buffer=None, y_cond=None):
"""
Generate initial samples and buffer inds of those samples (if buffer is used)
"""
if y_replay_buffer is not None:
assert len(replay_buffer) == len(y_replay_buffer)
assert isinstance(replay_buffer, ReplayBuffer) == isinstance(y_replay_buffer, ReplayBuffer)
if len(replay_buffer) == 0 and not isinstance(replay_buffer, ReplayBuffer):
init_x_sample = x
init_y_sample = y
buffer_inds = []
else:
bs = x.size(0)
init_sample, buffer_inds = sample_p_0(replay_buffer, bs=bs,
y=y, y_replay_buffer=y_replay_buffer, y_cond=y_cond)
if y is None:
init_x_sample, init_y_sample = init_sample, None
else:
init_x_sample, init_y_sample = init_sample
init_x_sample = init_x_sample.clone().detach().requires_grad_(True)
if init_y_sample is not None:
init_y_sample = init_y_sample.clone().detach().requires_grad_(True)
init_sample = (init_x_sample, init_y_sample)
else:
init_sample = init_x_sample
return init_sample, buffer_inds
def step_sampling(f, x_k, sigma_=sigma, bp=False):
if bp:
# track changes for autograd so we can do truncated langevin backprop
f_prime = torch.autograd.grad(f(x_k).sum(), [x_k], retain_graph=True, create_graph=True)[0]
x_k = x_k + step_size * f_prime + sigma_ * torch.randn_like(x_k) # += is in-place!!
else:
f_prime = torch.autograd.grad(f(x_k).sum(), [x_k], retain_graph=True)[0]
x_k.data += step_size * f_prime + sigma_ * torch.randn_like(x_k)
return x_k
def set_sampling(x_k, replay_buffer, y_replay_buffer, buffer_inds, update_buffer=True, y=None, y_k=None):
if y_replay_buffer is not None:
assert len(replay_buffer) == len(y_replay_buffer)
assert isinstance(replay_buffer, ReplayBuffer) == isinstance(y_replay_buffer, ReplayBuffer)
assert implies(update_buffer, y_k is not None)
final_samples = x_k.detach()
if y_k is not None:
final_y_samples = y_k.detach()
else:
final_y_samples = None
num_added = None
# update replay buffer
if isinstance(replay_buffer, ReplayBuffer):
if update_buffer:
num_added, which_added = replay_buffer.add(final_samples)
if y_replay_buffer is not None:
y_replay_buffer.add(final_y_samples, which_added)
else:
if len(replay_buffer) > 0 and update_buffer:
replay_buffer[buffer_inds] = final_samples
if y is not None:
# noinspection PyUnresolvedReferences
y_replay_buffer[buffer_inds] = y.squeeze()
if y_k is not None:
final_samples = (final_samples, one_hot_b(final_y_samples).detach())
return final_samples, num_added
return init_sampling, step_sampling, set_sampling
def _plot_pr_curve(save_dir, fn, precision, recall, ap, freq, dset_label_info):
plt.clf()
with open(f"{save_dir}/cache_pr_{fn}.pickle", "wb") as f:
d = {"precision": precision, "recall": recall, "ap": ap, "freq": freq, "dset_label_info": dset_label_info}
pickle.dump(d, f, protocol=4)
plt.plot(recall, precision)
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.05])
plt.xlabel('Recall')
plt.ylabel('Precision')
plt.title(f"Precision-Recall Curve. Average Precision: {ap:.4f} (Freq. {freq:.4f})")
plt.savefig(f"{save_dir}/pr_{fn}.png")
def _plot_roc_curve(save_dir, fn, fpr, tpr, auroc, freq, dset_label_info):
plt.clf()
with open(f"{save_dir}/cache_auroc_{fn}.pickle", "wb") as f:
d = {"fpr": fpr, "tpr": tpr, "auroc": auroc, "freq": freq, "dset_label_info": dset_label_info}
pickle.dump(d, f, protocol=4)
plt.plot(fpr, tpr)
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.05])
plt.xlabel('False-Positive Rate')
plt.ylabel('True-Positive Rate')
plt.title(f"AUROC: {auroc:.4f} (Freq. {freq:.4f})")
plt.savefig(f"{save_dir}/auroc_{fn}.png")
def _plot_ece_hist_no_cache(save_dir, fn, reliability_diag, ece, freq, dset_label_info):
plt.clf()
with open(f"{save_dir}/cache_ece_{fn}.pickle", "wb") as f:
d = {"reliability_diag": reliability_diag, "ece": ece, "freq": freq, "dset_label_info": dset_label_info}
pickle.dump(d, f, protocol=4)
conf, acc = reliability_diag
conf[conf.isnan()] = 0
acc[acc.isnan()] = 0
num_bins = 20
tau_tab = torch.linspace(0, 1, num_bins + 1)
binned_confs = tau_tab[torch.searchsorted(tau_tab, conf)]
font = {'family': 'normal',
'size': 20}
plt.rc('font', **font)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.set_aspect('equal', adjustable='box')
plt.bar(binned_confs, acc, color="lightcoral", linewidth=.1, edgecolor="black", align="edge", width=1 / num_bins)
plt.plot(np.linspace(0, 1, 1000), np.linspace(0, 1, 1000), "--")
plt.annotate(f"ECE: {ece * 100:.2f}%", xy=(140, 240), xycoords='axes points', # TODO: xy=(130, 240) for ebm (140 s)
size=20, ha='right', va='top',
bbox=dict(boxstyle='round', fc="#f6b2b2", color="#f6b2b2"))
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.0])
plt.xticks([.0, .5, 1.])
plt.yticks([.0, .5, 1.])
plt.xlabel('Confidence')
plt.ylabel('Accuracy')
plt.title('')
plt.gcf().subplots_adjust(right=.95, left=.14, bottom=.15)
plt.savefig(f"{save_dir}/ece_{fn}.png")
plt.close(fig)
def _plot_ece_hist(save_dir, fn, reliability_diag=None, ece=None, freq=None, dset_label_info=None,
from_cache=False):
if from_cache:
with open(f"{save_dir}/cache_ece_{fn}.pickle", "rb") as f:
d = pickle.load(f)
else:
d = {"reliability_diag": reliability_diag, "ece": ece, "freq": freq, "dset_label_info": dset_label_info}
_plot_ece_hist_no_cache(save_dir, fn, **d)
def main(args):
zero_shot_tst_dset = zero_shot_combos = tst_dset_len = None
if args.zero_shot:
*_rest, trn_dset_freqs = get_data_batch(args, args.data, args.batch_size, args.device, return_dset=True,
zero_shot=True)
data_batch, data_val_batch, data_test_batch, dset_label_info, dset_lengths = _rest
trn_dset_len = dset_lengths['trn']
else:
if args.data == "mnist" or args.dsprites_test or args.full_test:
if args.data == "celeba" and args.dset_split_type == "zero_shot":
*_rest, trn_dset_freqs, zero_shot_combos, trn_dset_len \
= get_data_batch(args, args.data, args.batch_size, args.device, return_dset=True,
return_trn_len=True, return_tst_dset=True)
else:
*_rest, trn_dset_freqs, trn_dset_len = get_data_batch(args, args.data, args.batch_size, args.device,
return_dset=True, return_trn_len=True)
if args.data in ("utzappos", "celeba", "cub"):
if args.data == "celeba" and args.dset_split_type == "zero_shot":
data_batch, data_test_batch, dset_label_info, tst_dset_len, zero_shot_tst_dset = _rest
else:
data_batch, data_test_batch, dset_label_info, tst_dset_len = _rest
tst_dset_len, zero_shot_tst_dset = None, None
else:
data_batch, data_test_batch = _rest
dset_label_info, tst_dset_len, zero_shot_tst_dset = None, None, None
else:
data_batch = get_data_batch(args, args.data, args.batch_size, args.device)
data_test_batch, trn_dset_freqs, trn_dset_len, tst_dset_len, dset_label_info = None, None, None, None, None
zero_shot_tst_dset = None
data_val_batch = dset_lengths = None
label_shape = (-1,)
all_labels = 0
all_binary = False
unif_label_shape = None
diff_label_axes = None
struct_mask = None
fix_label_axis_mask = None
if args.data == "celeba":
if args.dset_split_type == "zero_shot":
custom_cls_combos = CELEBA_ZERO_SHOT_COMBOS
if args.eval_filter_to_tst_combos:
custom_cls_combos = [combo for combo in CELEBA_ZERO_SHOT_COMBOS if combo in zero_shot_combos]
else:
custom_cls_combos = [{"Male": 1, "No_Beard": 0},
{"Male": 0, "Smiling": 1},
{"Male": 0, "Wearing_Lipstick": 1},
{"Male": 0, "Arched_Eyebrows": 1},
{"Male": 0, "High_Cheekbones": 1},
{"Male": 0, "Bangs": 1},
{"Male": 0, "Young": 1},
{"Male": 0, "Smiling": 1, "Young": 1},
{"Male": 0, "Smiling": 1, "Young": 1, "Wavy_Hair": 1},
{"Male": 1, "No_Beard": 0, "Black_Hair": 1},
{"Male": 1, "No_Beard": 0, "Black_Hair": 1, "Bushy_Eyebrows": 1}]
else:
custom_cls_combos = [{"Gender_Men": 1, "Category_Boots": 1, "Material_Leather": 1},
{"Gender_Men": 1, "Category_Boots": 1, "Closure_Lace up": 1},
{"Gender_Men": 1, "SubCategory_Sneakers and Athletic Shoes": 1, "Closure_Lace up": 1},
{"Gender_Women": 1, "Category_Boots": 1, "Closure_Lace up": 1},
{"Gender_Women": 1, "Category_Boots": 1, "Material_Leather": 1},
{"Gender_Women": 1, "Closure_Slip-On": 1, "SubCategory_Heels": 1},
{"Gender_Women": 1, "Closure_Slip-On": 1, "Material_Leather": 1},
{"Gender_Women": 1, "Closure_Slip-On": 1, "SubCategory_Heels": 1, "Material_Leather": 1}]
if args.data in IMG_DSETS:
if args.data == "dsprites":
data_dim = 32 ** 2 # need to actually set this because using MLP
else:
data_dim = 784
if args.mode == "uncond" and not args.uncond_poj:
label_dim = 0
else:
if args.data == "mwa":
label_shape = (4, 4, 4, 4, 4)
unif_label_shape, = set(label_shape)
label_dim = sum(label_shape)
all_labels = int(np.prod(label_shape))
elif args.data == "celeba":
all_binary = True
if not args.uncond_poj:
label_dim = all_labels = len(dset_label_info)
label_shape = (label_dim,) # set this to reuse the plotting code
else:
label_dim = 0
elif args.data == "cub":
all_binary = True
label_dim = all_labels = len(dset_label_info)
label_shape = (label_dim,) # set this to reuse the plotting code
elif args.data == "utzappos_old":
label_shape = (4, 21, 7, 14, 18, 8, 62, 19)
label_axes = get_label_axes(torch.tensor(label_shape, device=args.device))
diff_label_axes = get_diff_label_axes(label_axes)
struct_mask = get_struct_mask(label_axes)
label_dim = sum(label_shape)
all_labels = int(np.prod(label_shape))
elif args.data == "utzappos":
all_binary = True
if not args.uncond_poj:
label_dim = all_labels = len(dset_label_info)
label_shape = (label_dim,) # set this to reuse the plotting code
else:
label_dim = 0
elif args.data == "dsprites":
label_shape = (16, 16)
unif_label_shape, = set(label_shape)
label_dim = sum(label_shape)
all_labels = int(np.prod(label_shape))
else:
label_dim = 10
all_labels = label_dim
def plot_samples(x, fn):
if x.size(0) > 0:
pad_value = 0
if args.data == "celeba":
img_size = args.img_size
num_channels = 3
# x = (x + 1) / 2 # colours and shit
elif args.data == "utzappos":
img_size = args.img_size
num_channels = 3
elif args.data == "cub":
img_size = args.img_size
num_channels = 3
elif args.data == "mwa":
img_size = args.img_size
num_channels = 3
x = (x + 1) / 2
elif args.data == "dsprites":
img_size = 32
num_channels = 1
x = torch.sigmoid(x)
x = (x - 1e-6) / (1 - 2 * 1e-6)
pad_value = 1
elif args.data == "mnist":
if args.small_cnn:
img_size = args.img_size
else:
img_size = 28
num_channels = 1
if args.logit:
x = torch.sigmoid(x)
x = (x - 1e-6) / (1 - 2 * 1e-6)
else:
img_size = 28
num_channels = 1
save_image(x.view(x.size(0), num_channels, img_size, img_size), fn,
normalize=False, nrow=int(x.size(0) ** .5), pad_value=pad_value)
if args.data == "celeba":
if label_dim == 0 and not args.uncond_poj:
# net_fn = lambda *_: CelebAModel(args)
if args.img_size == 32:
net_fn = lambda *_: small_cnn(n_f=args.n_f)
elif args.img_size == 64:
net_fn = lambda *_: medium_cnn(n_f=args.n_f)
else:
raise ValueError(f"Got img size {args.img_size} for CelebA")
else:
net_fn = lambda *_: ZapposCNNCond(img_size=args.img_size, n_c=3, n_f=args.n_f,
label_dim=len(dset_label_info) if args.uncond_poj else label_dim,
cond_mode="poj" if args.model == "poj" else args.cond_mode,
small_mlp=args.small_mlp,
small_mlp_nhidden=args.small_mlp_nhidden,
all_binary=all_binary)
elif args.data == "cub":
if label_dim == 0:
# net_fn = lambda *_: CelebAModel(args)
if args.img_size == 32:
net_fn = lambda *_: small_cnn(n_f=args.n_f)
elif args.img_size == 64:
net_fn = lambda *_: medium_cnn(n_f=args.n_f)
else:
raise ValueError(f"Got img size {args.img_size} for CelebA")
else:
net_fn = lambda *_: ZapposCNNCond(img_size=args.img_size, n_c=3, n_f=args.n_f,
label_dim=label_dim,
cond_mode="poj" if args.model == "poj" else args.cond_mode,
small_mlp=args.small_mlp,
small_mlp_nhidden=args.small_mlp_nhidden,
all_binary=all_binary)
elif args.data == "utzappos":
if label_dim == 0 and not args.uncond_poj:
# net_fn = lambda *_: CelebAModel(args)
if args.img_size == 32:
net_fn = lambda *_: small_cnn(n_f=args.n_f)
elif args.img_size == 64:
net_fn = lambda *_: medium_cnn(n_f=args.n_f)
else:
raise ValueError(f"Got img size {args.img_size} for UTZappos")
else:
net_fn = lambda *_: ZapposCNNCond(img_size=args.img_size, n_c=3, n_f=args.n_f,
label_dim=len(dset_label_info) if args.uncond_poj else label_dim,
cond_mode="poj" if args.model == "poj" else args.cond_mode,
small_mlp=args.small_mlp,
small_mlp_nhidden=args.small_mlp_nhidden,
all_binary=all_binary)
# net_fn = lambda *_: CNNCond(label_dim=label_dim, uncond=label_dim == 0)
elif args.data == "mwa":
if args.model != "joint":
raise NotImplementedError
if label_dim == 0 and not args.cond_arch:
net_fn = lambda *_: small_cnn()
else:
net_fn = lambda *_: CNNCond(label_dim=label_dim, uncond=label_dim == 0)
elif args.data == "dsprites":
if args.model != "joint":
raise NotImplementedError
if args.cnn:
net_fn = lambda *_: CNNCondBigger(n_c=1, n_f=args.n_f,
label_dim=label_dim,
uncond=label_dim == 0,
cond_mode=args.cond_mode,
small_mlp=args.small_mlp,
spectral=args.spectral)
else:
net_fn = partial(smooth_mlp_ebm_bigger, 'elu')
else:
if args.model != "joint":
raise NotImplementedError
if args.cnn:
net_fn = lambda *_: MNISTModel(args)
elif args.small_cnn:
if label_dim == 0:
net_fn = lambda *_: small_cnn(n_c=1)
else:
net_fn = lambda *_: MNISTCNNCond(n_c=1, n_f=args.n_f,
label_dim=label_dim,
cond_mode=args.cond_mode,
small_mlp=args.small_mlp)
else:
net_fn = partial(smooth_mlp_ebm_bigger, args.mnist_act)
else:
data_dim = 2
if args.mode == "uncond":
label_dim = 0
else:
if args.data == "rings":
label_dim = 4
all_labels = label_dim
elif args.data == "rings_struct":
label_shape = (2, 2)
unif_label_shape, = set(label_shape)
label_dim = sum(label_shape)
all_labels = int(np.prod(label_shape))
elif args.data in ["checkerboard", "8gaussians"]:
label_dim = 8
all_labels = label_dim
elif args.data == "circles":
all_binary = True
label_dim = 1
all_labels = label_dim
elif "8gaussians_struct" in args.data:
label_shape = (2, 4)
label_axes = get_label_axes(torch.tensor(label_shape, device=args.device))
diff_label_axes = get_diff_label_axes(label_axes)
struct_mask = get_struct_mask(label_axes)
label_dim = sum(label_shape)
all_labels = int(np.prod(label_shape))
elif args.data in ["8gaussians_multi", "8gaussians_hierarch", "8gaussians_hierarch_missing"]:
label_shape = (2, 2, 2)
unif_label_shape, = set(label_shape)
label_dim = sum(label_shape)
all_labels = int(np.prod(label_shape))
elif "8gaussians_hierarch_binarized" in args.data:
all_binary = True
label_dim = all_labels = 3
label_shape = (label_dim,) # set this to reuse the plotting code
else:
raise ValueError(f"Unrecognized data {args.data}")
def plot_samples(x, fn):
plt.clf()
plt_samples(x, plt.gca())
plt.savefig(fn)
net_fn = partial(smooth_mlp_ebm, args.spectral)
if args.model == "joint":
net_fn_args = (data_dim + label_dim, 1)
elif args.model == "poj":
if all_binary:
net_fn_args = (data_dim, 2 * label_dim)
else:
net_fn_args = (data_dim, label_dim)
else:
raise ValueError(f"Unrecognized model {args.model}")
logp_net = net_fn(*net_fn_args)
if args.mode == "sup":
ema_logp_net = logp_net
else:
ema_logp_net = net_fn(*net_fn_args)
ema_logp_net.load_state_dict(logp_net.state_dict()) # copy the weights of logp_net
if args.multi_gpu:
logp_net = nn.DataParallel(logp_net).cuda()
ema_logp_net = nn.DataParallel(ema_logp_net).cuda()
elif args.old_multi_gpu:
logp_net = nn.DataParallel(logp_net)
ema_logp_net = nn.DataParallel(ema_logp_net)
logp_net.to(args.device)
ema_logp_net.to(args.device)
else:
# idk if this does anything
logp_net.to(args.device)
ema_logp_net.to(args.device)
logger(logp_net)
if args.log_ema:
logger(f"Params the same: {ema_params(logp_net, ema_logp_net)}")
if label_dim > 1 and not all_binary:
if label_shape != (-1,):
if unif_label_shape is None:
sampler = DiffSamplerMultiDim(n_steps=1, approx=True, temp=args.temp, struct=True,
label_shape=label_shape,
shift_logit=not args.no_shift_logit,
other_reverse_changes=args.other_reverse_changes,
device=args.device)
cond_sampler = sampler
else:
sampler = DiffSamplerMultiDim(n_steps=1, approx=True, temp=args.temp, struct=False,
label_shape=label_shape,
shift_logit=not args.no_shift_logit,
other_reverse_changes=args.other_reverse_changes,
device=args.device)
cond_sampler = sampler
else:
sampler = DiffSamplerMultiDim(n_steps=1, approx=True, temp=args.temp,
shift_logit=not args.no_shift_logit,
other_reverse_changes=args.other_reverse_changes, device=args.device)
cond_sampler = sampler
else:
sampler = DiffSampler(n_steps=1, approx=True, temp=args.temp)
cond_sampler = sampler
def init_x_random(bs=args.batch_size, to_device=True):
init_x_random_samples_ = x_init_dist.sample((bs,))
if to_device:
init_x_random_samples_ = init_x_random_samples_.to(args.device)
return init_x_random_samples_
def init_b_random(bs=args.batch_size, label_samples=False, to_device=True):
samples_ = b_init_dist.sample((bs,))
if to_device:
samples_ = samples_.to(args.device)
if label_samples:
samples_ = label(samples_)
return samples_
def energy(net, x, b=None):
"""
Define tuple interface for energy so we can hold one of them fixed while sampling.
"""
if args.model == "poj":
return logit_logsumexp(net(x)).sum(-1)
if label_dim == 0:
return net(x).squeeze()
else:
assert b is not None
if args.data in ["mwa", "utzappos"]:
return net(x, b.float()).squeeze()
else:
if args.cnn or args.small_cnn:
return net(x, b).squeeze()
else:
if args.data in ["dsprites", "8gaussians_multi",
"8gaussians_hierarch", "8gaussians_hierarch_missing", "rings_struct"]:
return net(torch.cat([x, b.view(-1, label_dim).float()], 1)).squeeze()
else:
return net(torch.cat([x, b.float()], 1)).squeeze()
def format_fix_label_axis(fix_label_axis):
if fix_label_axis is None:
return fix_label_axis
if isinstance(fix_label_axis, int):
fix_label_axis = torch.tensor([fix_label_axis])
elif isinstance(fix_label_axis, list):
assert len(fix_label_axis) > 0
assert len(set(map(type, fix_label_axis))) == 1
assert isinstance(fix_label_axis[0], int)
fix_label_axis = torch.tensor(fix_label_axis)
else:
assert isinstance(fix_label_axis, torch.Tensor)
if unif_label_shape:
assert len(fix_label_axis.shape) == 1
return fix_label_axis.to(args.device)
def init_sample_b(b_init, fix_label_axes=None):
"""
Process b_init for sampling.
Reshape b. If labels need to be fixed, create mask and split labels.
Returns:
b: The labels that need to be resampled.
b_all: The entire label, both those that are fixed and those are resampled.
b_fixed: The labels that are fixed.
axis_mask: The mask from which b and b_fixed can be obtained from b_all.
"""
# reshape b
if label_shape != (-1,) and unif_label_shape is not None:
# in the case of structured labels, we'll want to pass in structured b to the sampler
b = b_init
b = b.view(b.shape[0], len(label_shape), unif_label_shape)
elif all_binary:
b = b_init # don't expand dims
else:
b = b_init[:, None]
if fix_label_axes is not None:
if not all_binary:
assert (fix_label_axes < len(label_shape)).all()
b_all = b
# per example mask (from masking out missing data), in the case of structured labels
if fix_label_axes.shape[0] == b_init.shape[0]:
fix_label_axes_nonzero = fix_label_axes.nonzero()[:, -1][:, None]
set_axis_mask = get_onehot_struct_mask(diff_label_axes, struct_mask, fix_label_axes_nonzero)
axis_mask = torch.zeros_like(b_all).type(torch.bool)
axis_mask[fix_label_axes.any(-1)] = set_axis_mask
b = init_b_random(axis_mask.shape[0])[:, None][axis_mask] # init missing b
b_fixed = b_all[~axis_mask]
# per example mask (from masking out missing data), in the case of simple (unstructured) labels
elif (fix_label_axes == -1).all():
axis_mask = (b_all == 0).all(-1)
b = init_b_random(axis_mask.shape[0])[axis_mask][:, None] # init missing b
b_fixed = b_all[~axis_mask][:, None]
# fixing one label axis everywhere, for conditional sampling
else:
axis_mask = (fix_label_axis_mask[..., None] != fix_label_axes[None]).all(-1)
if unif_label_shape is None and not all_binary:
axis_mask = ~get_onehot_struct_mask(diff_label_axes, struct_mask,
fix_label_axes[:, None]).squeeze()
if len(fix_label_axes) > 1:
axis_mask = axis_mask.all(0)
axis_mask = axis_mask[None]
b = b_all[:, axis_mask]
b_fixed = b_all[:, ~axis_mask]
else:
b_all = None
axis_mask = None
b_fixed = None
return b, b_all, b_fixed, axis_mask
def sample_b(net, x_init, b_init, steps=args.n_steps, verbose=False, fix_label_axis=None):
"""
Sample b from net conditioned on x_init (and b_init).
"""
a_s = np.zeros(steps)
lrs = np.zeros(steps)
lfs = np.zeros(steps)
l_s = np.zeros(steps)
m_s = np.zeros(steps)
p_s = np.zeros(steps)
h_s = np.zeros(steps)
fix_label_axis = format_fix_label_axis(fix_label_axis)
b, b_all, b_fixed, axis_mask = init_sample_b(b_init, fix_label_axis)
for i in range(steps):
b, *_info = step_sample_b(net, x_init, b,
axis_mask=axis_mask, b_fixed=b_fixed, b_all=b_all)
a_s[i], lrs[i], lfs[i], l_s[i], m_s[i], p_s[i], h_s[i] = _info
if fix_label_axis is not None:
if per_example_mask(axis_mask):
b_all[axis_mask] = b.squeeze()
b_all[~axis_mask] = b_fixed.squeeze()
else:
b_all[:, axis_mask] = b
b_all[:, ~axis_mask] = b_fixed
b = b_all
if label_shape != (-1,) and unif_label_shape is not None:
# we'll want to flatten b again in case it wasn't, so that
# concatenation operations work outside the function
b = b.view(b.shape[0], label_dim)
if label_dim > 1:
return_tpl = (b.squeeze(), )
else:
return_tpl = (b, )
if verbose:
log_tpl = (np.mean(a_s), np.mean(lrs), np.mean(lfs), np.mean(l_s), np.mean(m_s), np.mean(p_s), np.mean(h_s))
return return_tpl + log_tpl
else:
return return_tpl[0]
def step_sample_b(net, x_init, b, axis_mask=None, b_fixed=None, b_all=None):
assert (axis_mask is None) == (b_fixed is None) == (b_all is None)
if all_binary:
# remove any added dims if they exist
b = b.squeeze()
if label_shape != (-1,) and unif_label_shape is not None:
# if we have structured b we'll want to shape it here
# if b is already structured then this is a no-op, but this isn't the case when doing interleaved sampling
# if an axis is fixed, the number of labels is reduced, hence -1 instead of len(label_shape)
b = b.view(b.shape[0], -1, unif_label_shape)
if axis_mask is not None:
b_all = torch.zeros_like(b_all)
if per_example_mask(axis_mask):
# the axis mask must be per batch example
assert axis_mask.shape[0] == b_all.shape[0]
if unif_label_shape:
# noinspection PyUnresolvedReferences
b_all[~axis_mask] = b_fixed.squeeze(1)
else:
b_all[~axis_mask] = b_fixed
else:
b_all[:, ~axis_mask] = b_fixed
def energy_(b_):
if unif_label_shape is None:
b_ = b_.squeeze()
if per_example_mask(axis_mask):
if unif_label_shape:
b_all[axis_mask] = b_.squeeze(1)
else:
b_all[axis_mask] = b_
else:
b_all[:, axis_mask] = b_
return energy(net, x_init, b_all.squeeze())
else:
if label_dim > 1:
energy_ = lambda b_: energy(net, x_init, b_.squeeze())
else:
energy_ = lambda b_: energy(net, x_init, b_)
if args.model == "joint":
if axis_mask is not None:
if all_binary:
b = cond_sampler.step(b.detach(), energy_).detach()
else:
b = cond_sampler.step(b.detach(), energy_, axis_mask).detach()
else:
b = sampler.step(b.detach(), energy_).detach()
else:
b_logits = shape_logits(net(x_init))
if axis_mask is not None:
if all_binary:
# just resample the ones which aren't fixed
# need a categorical since logits parameterize a softmax over two categories
b = torch.distributions.Categorical(logits=b_logits[:, axis_mask]).sample().float()
else:
raise NotImplementedError
else:
if all_binary:
b = torch.distributions.Categorical(logits=b_logits).sample().float()
else:
raise NotImplementedError
return b, sampler._ar, sampler._lr, sampler._lf, sampler._la, sampler._mt, sampler._pt, sampler._hops
def sample_x_b(net, x_init, b_init, steps=args.k,
gibbs_steps=args.gibbs_steps, gibbs_k_steps=args.gibbs_k_steps, gibbs_n_steps=args.gibbs_n_steps,
verbose=False, fix_label_axis=None, update_buffer=True,
new_replay_buffer=None, new_y_replay_buffer=None, return_steps=0, steps_batch_ind=0,
temp=False, anneal=False, truncated_bp=False, full_bp=False, return_num_added=False,
transform_every=None, marginalize_free_b=False):
assert (new_replay_buffer is None) == (new_y_replay_buffer is None)
assert not (anneal and temp)
if new_replay_buffer is None:
new_replay_buffer = replay_buffer
if new_y_replay_buffer is None:
new_y_replay_buffer = y_replay_buffer
assert (new_replay_buffer is None) == (new_y_replay_buffer is None)
assert implies(update_buffer and (args.yd_buffer is None), len(new_replay_buffer) > 0)
x, b = x_init, b_init
assert implies(fix_label_axis is not None, label_shape != (-1,))
fix_label_axis = format_fix_label_axis(fix_label_axis)
if label_dim == 1:
# need to expand dims if we do conditional sampling first, one-hot already has 2 dims
b = b[:, None]
if anneal:
betas = torch.linspace(0., 1., gibbs_steps * gibbs_k_steps)
else:
betas = None
if temp:
start_, end_ = args.plot_temp_sigma_start, args.sigma
assert start_ > end_, "Untempered should have larger noise!"
sigmas = torch.linspace(start_, end_, gibbs_steps * gibbs_k_steps)
else:
sigmas = None
a_s = np.zeros(gibbs_steps)
lrs = np.zeros(gibbs_steps)
lfs = np.zeros(gibbs_steps)
l_s = np.zeros(gibbs_steps)
m_s = np.zeros(gibbs_steps)
p_s = np.zeros(gibbs_steps)
h_s = np.zeros(gibbs_steps)
if args.interleave:
if args.sampling == "pcd":
(x, b), buffer_inds = init_sampling(new_replay_buffer, x,
y=b, y_replay_buffer=new_y_replay_buffer)
if args.clamp_samples:
x = clamp_x(x)
else:
buffer_inds = None
b, b_all, b_fixed, axis_mask = init_sample_b(b.squeeze(), fix_label_axis)
else:
buffer_inds = None
b_all, b_fixed, axis_mask = None, None, None
x_steps = []
x_kl = None
num_added = None
for i in range(gibbs_steps):
if args.interleave:
if args.first_gibbs == "dis":
for _ in range(gibbs_n_steps):
b, *_info = step_sample_b(net, x, b.squeeze()[:, None],
b_all=b_all, b_fixed=b_fixed, axis_mask=axis_mask)
a_s[i], lrs[i], lfs[i], l_s[i], m_s[i], p_s[i], h_s[i] = _info
for k in range(gibbs_k_steps):
if return_steps > 0 and (i * gibbs_k_steps + k) % return_steps == 0:
if steps_batch_ind is None:
x_steps.append(x.clone().detach()[None])
else:
x_steps.append(x.clone().detach()[steps_batch_ind][None])
if transform_every is not None and (i * gibbs_k_steps + k) % transform_every == 0 \
and (i * gibbs_k_steps + k) != 0:
# don't transform at first iteration since buffer sampling does that already
x = transform(x)
if fix_label_axis is not None:
if unif_label_shape is None and not all_binary:
b_all[:, axis_mask] = b.squeeze()
b_all[:, ~axis_mask] = b_fixed.squeeze()
else:
b_all[:, axis_mask] = b
b_all[:, ~axis_mask] = b_fixed
b = b_all
if args.model == "joint":
if label_dim > 1:
if temp:
x = step_sampling(lambda x_: energy(net, x_, b.squeeze()), x,
sigmas[i * gibbs_k_steps + k])
elif anneal:
net_ = AISModel(lambda x_: energy(net, x_, b.squeeze()), normal_x_init_dist)
x = step_sampling(lambda x_: net_(x_, betas[i * gibbs_k_steps + k]), x)
elif truncated_bp and i == gibbs_steps - 1 and k == gibbs_k_steps - 1:
x_kl = step_sampling(lambda x_: energy(net, x_, b.squeeze()), x, bp=True)
if args.clamp_samples:
x_kl = clamp_x(x_kl)
x = x_kl.detach()
elif full_bp:
x = step_sampling(lambda x_: energy(net, x_, b.squeeze()), x, bp=True)
else:
x = step_sampling(lambda x_: energy(net, x_, b.squeeze()), x)
else:
if temp:
x = step_sampling(lambda x_: energy(net, x_, b), x,
sigmas[i * gibbs_k_steps + k])
elif anneal:
net_ = AISModel(lambda x_: energy(net, x_, b), normal_x_init_dist)
x = step_sampling(lambda x_: net_(x_, betas[i * gibbs_k_steps + k]), x)
elif truncated_bp and i == gibbs_steps - 1 and k == gibbs_k_steps - 1:
x_kl = step_sampling(lambda x_: energy(net, x_, b), x, bp=True)
if args.clamp_samples:
x_kl = clamp_x(x_kl)
x = x_kl.detach()
elif full_bp:
x = step_sampling(lambda x_: energy(net, x_, b), x, bp=True)
else:
x = step_sampling(lambda x_: energy(net, x_, b), x)
else:
if all_binary:
if marginalize_free_b:
def cond_energy_x_(x_):
logits_neg_ = net(x_)
fixed_log_probs = logit_log_prob_ind_subset(shape_logits(logits_neg_),
b.long(),
list(fix_label_axis.cpu().numpy()))
marginalized_log_probs = logit_logsumexp(logits_neg_)[:, axis_mask]
return fixed_log_probs.sum(-1) + marginalized_log_probs.sum(-1)
else:
def cond_energy_x_(x_):
logits_neg_ = net(x_)
# index the logits according to the sampled classes
return logit_log_prob_ind(shape_logits(logits_neg_), b.long()).sum(-1)
if temp:
x = step_sampling(cond_energy_x_, x, sigmas[i * gibbs_k_steps + k])
elif anneal:
raise NotImplementedError
elif truncated_bp and i == gibbs_steps - 1 and k == gibbs_k_steps - 1:
x_kl = step_sampling(cond_energy_x_, x, bp=True)
if args.clamp_samples:
x_kl = clamp_x(x_kl)
x = x_kl.detach()
elif full_bp:
raise NotImplementedError
else:
x = step_sampling(cond_energy_x_, x)
else:
raise NotImplementedError
if args.clamp_samples:
x = clamp_x(x)
if fix_label_axis is not None:
b = b_all[:, axis_mask]
else:
for k in range(gibbs_k_steps):
if return_steps > 0 and (i * gibbs_k_steps + k) % return_steps == 0:
if steps_batch_ind is None:
x_steps.append(x.clone().detach()[None])
else:
x_steps.append(x.clone().detach()[steps_batch_ind][None])
if transform_every is not None and (i * gibbs_k_steps + k) % transform_every == 0 \
and (i * gibbs_k_steps + k) != 0:
# don't transform at first iteration since buffer sampling does that already
x = transform(x)
if fix_label_axis is not None:
if unif_label_shape is None and not all_binary:
b_all[:, axis_mask] = b.squeeze()
b_all[:, ~axis_mask] = b_fixed.squeeze()
else:
b_all[:, axis_mask] = b
b_all[:, ~axis_mask] = b_fixed
b = b_all
if args.model == "joint":
if label_dim > 1:
if temp:
x = step_sampling(lambda x_: energy(net, x_, b.squeeze()), x,
sigmas[i * gibbs_k_steps + k])
elif anneal:
net_ = AISModel(lambda x_: energy(net, x_, b.squeeze()), normal_x_init_dist)
x = step_sampling(lambda x_: net_(x_, betas[i * gibbs_k_steps + k]), x)
elif truncated_bp and i == gibbs_steps - 1 and k == gibbs_k_steps - 1:
x_kl = step_sampling(lambda x_: energy(net, x_, b.squeeze()), x, bp=True)
if args.clamp_samples:
x_kl = clamp_x(x_kl)
x = x_kl.detach()
elif full_bp:
x = step_sampling(lambda x_: energy(net, x_, b.squeeze()), x, bp=True)
else:
x = step_sampling(lambda x_: energy(net, x_, b.squeeze()), x)
else:
if temp:
x = step_sampling(lambda x_: energy(net, x_, b), x,
sigmas[i * gibbs_k_steps + k])
elif anneal:
net_ = AISModel(lambda x_: energy(net, x_, b), normal_x_init_dist)
x = step_sampling(lambda x_: net_(x_, betas[i * gibbs_k_steps + k]), x)
elif truncated_bp and i == gibbs_steps - 1 and k == gibbs_k_steps - 1:
x_kl = step_sampling(lambda x_: energy(net, x_, b), x, bp=True)
if args.clamp_samples:
x_kl = clamp_x(x_kl)
x = x_kl.detach()
elif full_bp:
x = step_sampling(lambda x_: energy(net, x_, b), x, bp=True)
else:
x = step_sampling(lambda x_: energy(net, x_, b), x)
else:
if all_binary:
if marginalize_free_b:
def cond_energy_x_(x_):
logits_neg_ = net(x_)
fixed_log_probs = logit_log_prob_ind_subset(shape_logits(logits_neg_),
b.long(),
list(fix_label_axis.cpu().numpy()))
marginalized_log_probs = logit_logsumexp(logits_neg_)[:, axis_mask]
return fixed_log_probs.sum(-1) + marginalized_log_probs.sum(-1)
else:
def cond_energy_x_(x_):
logits_neg_ = net(x_)
# index the logits according to the sampled classes
return logit_log_prob_ind(shape_logits(logits_neg_), b.long()).sum(-1)
if temp:
x = step_sampling(cond_energy_x_, x, sigmas[i * gibbs_k_steps + k])
elif anneal:
raise NotImplementedError
elif truncated_bp and i == gibbs_steps - 1 and k == gibbs_k_steps - 1:
x_kl = step_sampling(cond_energy_x_, x, bp=True)
if args.clamp_samples:
x_kl = clamp_x(x_kl)
x = x_kl.detach()
elif full_bp:
raise NotImplementedError
else:
x = step_sampling(cond_energy_x_, x)
else:
raise NotImplementedError
if args.clamp_samples:
x = clamp_x(x)
if fix_label_axis is not None:
b = b_all[:, axis_mask]
for _ in range(gibbs_n_steps):
b, *_info = step_sample_b(net, x, b.squeeze()[:, None],
b_all=b_all, b_fixed=b_fixed, axis_mask=axis_mask)
a_s[i], lrs[i], lfs[i], l_s[i], m_s[i], p_s[i], h_s[i] = _info
else:
if args.first_gibbs == "dis":
# sample discrete
if verbose:
b, *_info = sample_b(net, x, b.squeeze(), verbose=verbose, fix_label_axis=fix_label_axis,
steps=gibbs_n_steps)
a_s[i], lrs[i], lfs[i], l_s[i], m_s[i], p_s[i], h_s[i] = _info
else:
b = sample_b(net, x, b.squeeze(), verbose=verbose, fix_label_axis=fix_label_axis,
steps=gibbs_n_steps)
# sample cts
x = uncond_sample_x(lambda x_: energy(net, x_, b), x, steps=steps,
update_buffer=update_buffer,
new_replay_buffer=new_replay_buffer, new_y_replay_buffer=new_y_replay_buffer,
return_steps=return_steps, steps_batch_ind=steps_batch_ind, temp=temp,
anneal=anneal, truncated_bp=truncated_bp, full_bp=full_bp,
return_num_added=return_num_added, transform_every=transform_every)
if return_num_added:
*x, num_added = x
if return_steps > 0:
x, x_steps = x
else:
# sample cts
x = uncond_sample_x(lambda x_: energy(net, x_, b), x, steps=steps,
update_buffer=update_buffer,
new_replay_buffer=new_replay_buffer, new_y_replay_buffer=new_y_replay_buffer,
return_steps=return_steps, steps_batch_ind=steps_batch_ind, temp=temp,
anneal=anneal, truncated_bp=truncated_bp, full_bp=full_bp,
return_num_added=return_num_added, transform_every=transform_every)
if return_num_added:
*x, num_added = x
if return_steps > 0:
x, x_steps = x
# sample discrete
if verbose:
b, *_info = sample_b(net, x, b.squeeze(), verbose=verbose, fix_label_axis=fix_label_axis,
steps=gibbs_n_steps)
a_s[i], lrs[i], lfs[i], l_s[i], m_s[i], p_s[i], h_s[i] = _info
else:
b = sample_b(net, x, b.squeeze(), verbose=verbose, fix_label_axis=fix_label_axis,
steps=gibbs_n_steps)
if args.interleave:
if fix_label_axis is not None:
b_all[:, axis_mask] = b
b_all[:, ~axis_mask] = b_fixed
b = b_all
if label_dim > 1:
b = b.squeeze()
if label_shape != (-1,) and unif_label_shape is not None:
b = b.view(b.shape[0], label_dim)
if args.sampling == "pcd":
(x, b), num_added = set_sampling(x, new_replay_buffer, new_y_replay_buffer, buffer_inds,
update_buffer=update_buffer, y_k=label(b))
if return_steps > 0:
x_steps = torch.cat(x_steps, dim=0)
if return_steps > 0 or truncated_bp or full_bp or return_num_added:
x = (x,)
if return_steps > 0:
x += (x_steps,)
if truncated_bp or full_bp:
x += (x_kl,)
if return_num_added:
x += (num_added,)
if verbose:
return x, b, \
np.mean(a_s), np.mean(lrs), np.mean(lfs), | np.mean(l_s) | numpy.mean |
import cv2
import numpy as np
import BboxToolkit as bt
import pycocotools.mask as maskUtils
from mmdet.core import PolygonMasks, BitmapMasks
pi = 3.141592
def bbox2mask(bboxes, w, h, mask_type='polygon'):
polys = bt.bbox2type(bboxes, 'poly')
assert mask_type in ['polygon', 'bitmap']
if mask_type == 'bitmap':
masks = []
for poly in polys:
rles = maskUtils.frPyObjects([poly.tolist()], h, w)
masks.append(maskUtils.decode(rles[0]))
gt_masks = BitmapMasks(masks, h, w)
else:
gt_masks = PolygonMasks([[poly] for poly in polys], h, w)
return gt_masks
def switch_mask_type(masks, mtype='bitmap'):
if isinstance(masks, PolygonMasks) and mtype == 'bitmap':
width, height = masks.width, masks.height
bitmap_masks = []
for poly_per_obj in masks.masks:
rles = maskUtils.frPyObjects(poly_per_obj, height, width)
rle = maskUtils.merge(rles)
bitmap_masks.append(maskUtils.decode(rle).astype(np.uint8))
masks = BitmapMasks(bitmap_masks, height, width)
elif isinstance(masks, BitmapMasks) and mtype == 'polygon':
width, height = masks.width, masks.height
polygons = []
for bitmask in masks.masks:
try:
contours, _ = cv2.findContours(
bitmask, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
except ValueError:
_, contours, _ = cv2.findContours(
bitmask, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
polygons.append(list(contours))
masks = PolygonMasks(polygons, width, height)
return masks
def rotate_polygonmask(masks, matrix, width, height):
if len(masks) == 0:
return masks
points, sections, instances = [], [], []
for i, polys_per_obj in enumerate(masks):
for j, poly in enumerate(polys_per_obj):
poly_points = poly.reshape(-1, 2)
num_points = poly_points.shape[0]
points.append(poly_points)
sections.append(np.full((num_points, ), j))
instances.append(np.full((num_points, ), i))
points = np.concatenate(points, axis=0)
sections = np.concatenate(sections, axis=0)
instances = np.concatenate(instances, axis=0)
points = cv2.transform(points[:, None, :], matrix)[:, 0, :]
warpped_polygons = []
for i in range(len(masks)):
_points = points[instances == i]
_sections = sections[instances == i]
warpped_polygons.append(
[_points[_sections == j].reshape(-1)
for j in np.unique(_sections)])
return PolygonMasks(warpped_polygons, height, width)
def polymask2hbb(masks):
hbbs = []
for mask in masks:
all_mask_points = np.concatenate(mask, axis=0).reshape(-1, 2)
min_points = all_mask_points.min(axis=0)
max_points = all_mask_points.max(axis=0)
hbbs.append(np.concatenate([min_points, max_points], axis=0))
hbbs = np.array(hbbs, dtype=np.float32) if hbbs else \
np.zeros((0, 4), dtype=np.float32)
return hbbs
def polymask2obb(masks):
obbs = []
for mask in masks:
all_mask_points = np.concatenate(mask, axis=0).reshape(-1, 2)
all_mask_points = all_mask_points.astype(np.float32)
(x, y), (w, h), angle = cv2.minAreaRect(all_mask_points)
angle = -angle
theta = angle / 180 * pi
obbs.append([x, y, w, h, theta])
if not obbs:
obbs = np.zeros((0, 5), dtype=np.float32)
else:
obbs = np.array(obbs, dtype=np.float32)
obbs = bt.regular_obb(obbs)
return obbs
def polymask2poly(masks):
polys = []
for mask in masks:
all_mask_points = np.concatenate(mask, axis=0)[None, :]
if all_mask_points.size != 8:
all_mask_points = bt.bbox2type(all_mask_points, 'obb')
all_mask_points = bt.bbox2type(all_mask_points, 'poly')
polys.append(all_mask_points)
if not polys:
polys = np.zeros((0, 8), dtype=np.float32)
else:
polys = np.concatenate(polys, axis=0)
return polys
def bitmapmask2hbb(masks):
if len(masks) == 0:
return np.zeros((0, 4), dtype=np.float32)
bitmaps = masks.masks
height, width = masks.height, masks.width
num = bitmaps.shape[0]
x, y = np.arange(width), np.arange(height)
xx, yy = np.meshgrid(x, y)
coors = np.stack([xx, yy], axis=-1)
coors = coors[None, ...].repeat(num, axis=0)
coors_ = coors.copy()
coors_[bitmaps == 0] = -1
max_points = np.max(coors_, axis=(1, 2)) + 1
coors_ = coors.copy()
coors_[bitmaps == 0] = 99999
min_points = | np.min(coors_, axis=(1, 2)) | numpy.min |
import copy
import torch
import numpy as np
from torch import optim
def collect_optimized_episode(env, agent, random=False, eval=False,
semi_am=True, ngs=50):
"""
Collects an episode of experience using the model and environment. The
policy distribution is optimized using gradient descent at each step.
Args:
env (gym.env): the environment
agent (Agent): the agent
random (bool): whether to use random actions
eval (bool): whether to evaluate the agent
semi_am (bool): whether to first use direct inference
ngs (int): number of gradient steps to perform
Returns episode (dict), n_steps (int), and env_states (dict).
"""
agent.reset(); agent.eval()
state = env.reset()
reward = 0.
done = False
n_steps = 0
env_states = {'qpos': [], 'qvel': []}
optimized_actions = []
gaps = []
while not done:
if n_steps > 1000:
break
if 'sim' in dir(env.unwrapped):
env_states['qpos'].append(copy.deepcopy(env.sim.data.qpos))
env_states['qvel'].append(copy.deepcopy(env.sim.data.qvel))
action = env.action_space.sample() if random else None
agent.act(state, reward, done, action, eval=eval)
## SEMI - AMORTIZATION #################################################
state = state.to(agent.device)
actions = agent.approx_post.sample(agent.n_action_samples)
obj = agent.estimate_objective(state, actions)
direct_obj = obj.view(agent.n_action_samples, -1, 1).mean(dim=0).detach()
agent.n_action_samples = 100
grad_obj = []
dist_params = {k: v.data.requires_grad_() for k, v in agent.approx_post.get_dist_params().items()}
agent.approx_post.reset(dist_params=dist_params)
dist_param_list = [param for _, param in dist_params.items()]
optimizer = optim.Adam(dist_param_list, lr=5e-3)
optimizer.zero_grad()
# initial estimate
agent.approx_post._sample = None
actions = agent.approx_post.sample(agent.n_action_samples)
obj = agent.estimate_objective(state, actions)
obj = - obj.view(agent.n_action_samples, -1, 1).mean(dim=0)
grad_obj.append(-obj.detach())
for it_inf in range(ngs):
obj.sum().backward(retain_graph=True)
optimizer.step()
optimizer.zero_grad()
# clear the sample to force resampling
agent.approx_post._sample = None
actions = agent.approx_post.sample(agent.n_action_samples)
obj = agent.estimate_objective(state, actions)
obj = - obj.view(agent.n_action_samples, -1, 1).mean(dim=0)
grad_obj.append(-obj.detach())
# gradient_obj = np.array([obj.numpy() for obj in grad_obj]).reshape(-1)
gaps.append((grad_obj[-1] - grad_obj[0]).cpu().numpy().item())
# sample from the optimized distribution
action = agent.approx_post.sample(n_samples=1, argmax=eval)
action = action.tanh() if agent.postprocess_action else action
action = action.detach().cpu().numpy()
optimized_actions.append(action)
########################################################################
# step the environment with the optimized action
state, reward, done, _ = env.step(action)
n_steps += 1
print(' Average Improvement: ' + str(np.mean(gaps)))
if 'sim' in dir(env.unwrapped):
env_states['qpos'].append(copy.deepcopy(env.sim.data.qpos))
env_states['qvel'].append(copy.deepcopy(env.sim.data.qvel))
env_states['qpos'] = np.stack(env_states['qpos'])
env_states['qvel'] = np.stack(env_states['qvel'])
agent.act(state, reward, done)
episode = agent.collector.get_episode()
if not random:
# replace the collector's actions with optimized actions
final_action = np.zeros(optimized_actions[-1].shape)
optimized_actions.append(final_action)
optimized_actions = | np.concatenate(optimized_actions, axis=0) | numpy.concatenate |
# This module has been generated automatically from space group information
# obtained from the Computational Crystallography Toolbox
#
"""
Space groups
This module contains a list of all the 230 space groups that can occur in
a crystal. The variable space_groups contains a dictionary that maps
space group numbers and space group names to the corresponding space
group objects.
.. moduleauthor:: <NAME> <<EMAIL>>
"""
#-----------------------------------------------------------------------------
# Copyright (C) 2013 The Mosaic Development Team
#
# Distributed under the terms of the BSD License. The full license is in
# the file LICENSE.txt, distributed as part of this software.
#-----------------------------------------------------------------------------
import numpy as N
class SpaceGroup(object):
"""
Space group
All possible space group objects are created in this module. Other
modules should access these objects through the dictionary
space_groups rather than create their own space group objects.
"""
def __init__(self, number, symbol, transformations):
"""
:param number: the number assigned to the space group by
international convention
:type number: int
:param symbol: the Hermann-Mauguin space-group symbol as used
in PDB and mmCIF files
:type symbol: str
:param transformations: a list of space group transformations,
each consisting of a tuple of three
integer arrays (rot, tn, td), where
rot is the rotation matrix and tn/td
are the numerator and denominator of the
translation vector. The transformations
are defined in fractional coordinates.
:type transformations: list
"""
self.number = number
self.symbol = symbol
self.transformations = transformations
self.transposed_rotations = N.array([N.transpose(t[0])
for t in transformations])
self.phase_factors = N.exp(N.array([(-2j*N.pi*t[1])/t[2]
for t in transformations]))
def __repr__(self):
return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol))
def __len__(self):
"""
:return: the number of space group transformations
:rtype: int
"""
return len(self.transformations)
def symmetryEquivalentMillerIndices(self, hkl):
"""
:param hkl: a set of Miller indices
:type hkl: Scientific.N.array_type
:return: a tuple (miller_indices, phase_factor) of two arrays
of length equal to the number of space group
transformations. miller_indices contains the Miller
indices of each reflection equivalent by symmetry to the
reflection hkl (including hkl itself as the first element).
phase_factor contains the phase factors that must be applied
to the structure factor of reflection hkl to obtain the
structure factor of the symmetry equivalent reflection.
:rtype: tuple
"""
hkls = N.dot(self.transposed_rotations, hkl)
p = N.multiply.reduce(self.phase_factors**hkl, -1)
return hkls, p
space_groups = {}
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(1, 'P 1', transformations)
space_groups[1] = sg
space_groups['P 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(2, 'P -1', transformations)
space_groups[2] = sg
space_groups['P -1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(3, 'P 1 2 1', transformations)
space_groups[3] = sg
space_groups['P 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(4, 'P 1 21 1', transformations)
space_groups[4] = sg
space_groups['P 1 21 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(5, 'C 1 2 1', transformations)
space_groups[5] = sg
space_groups['C 1 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(6, 'P 1 m 1', transformations)
space_groups[6] = sg
space_groups['P 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(7, 'P 1 c 1', transformations)
space_groups[7] = sg
space_groups['P 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(8, 'C 1 m 1', transformations)
space_groups[8] = sg
space_groups['C 1 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(9, 'C 1 c 1', transformations)
space_groups[9] = sg
space_groups['C 1 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(10, 'P 1 2/m 1', transformations)
space_groups[10] = sg
space_groups['P 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(11, 'P 1 21/m 1', transformations)
space_groups[11] = sg
space_groups['P 1 21/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(12, 'C 1 2/m 1', transformations)
space_groups[12] = sg
space_groups['C 1 2/m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(13, 'P 1 2/c 1', transformations)
space_groups[13] = sg
space_groups['P 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(14, 'P 1 21/c 1', transformations)
space_groups[14] = sg
space_groups['P 1 21/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(15, 'C 1 2/c 1', transformations)
space_groups[15] = sg
space_groups['C 1 2/c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(16, 'P 2 2 2', transformations)
space_groups[16] = sg
space_groups['P 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(17, 'P 2 2 21', transformations)
space_groups[17] = sg
space_groups['P 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(18, 'P 21 21 2', transformations)
space_groups[18] = sg
space_groups['P 21 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(19, 'P 21 21 21', transformations)
space_groups[19] = sg
space_groups['P 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(20, 'C 2 2 21', transformations)
space_groups[20] = sg
space_groups['C 2 2 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(21, 'C 2 2 2', transformations)
space_groups[21] = sg
space_groups['C 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(22, 'F 2 2 2', transformations)
space_groups[22] = sg
space_groups['F 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(23, 'I 2 2 2', transformations)
space_groups[23] = sg
space_groups['I 2 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(24, 'I 21 21 21', transformations)
space_groups[24] = sg
space_groups['I 21 21 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(25, 'P m m 2', transformations)
space_groups[25] = sg
space_groups['P m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(26, 'P m c 21', transformations)
space_groups[26] = sg
space_groups['P m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(27, 'P c c 2', transformations)
space_groups[27] = sg
space_groups['P c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(28, 'P m a 2', transformations)
space_groups[28] = sg
space_groups['P m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(29, 'P c a 21', transformations)
space_groups[29] = sg
space_groups['P c a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(30, 'P n c 2', transformations)
space_groups[30] = sg
space_groups['P n c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(31, 'P m n 21', transformations)
space_groups[31] = sg
space_groups['P m n 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(32, 'P b a 2', transformations)
space_groups[32] = sg
space_groups['P b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(33, 'P n a 21', transformations)
space_groups[33] = sg
space_groups['P n a 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(34, 'P n n 2', transformations)
space_groups[34] = sg
space_groups['P n n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(35, 'C m m 2', transformations)
space_groups[35] = sg
space_groups['C m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(36, 'C m c 21', transformations)
space_groups[36] = sg
space_groups['C m c 21'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(37, 'C c c 2', transformations)
space_groups[37] = sg
space_groups['C c c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(38, 'A m m 2', transformations)
space_groups[38] = sg
space_groups['A m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(39, 'A b m 2', transformations)
space_groups[39] = sg
space_groups['A b m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(40, 'A m a 2', transformations)
space_groups[40] = sg
space_groups['A m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(41, 'A b a 2', transformations)
space_groups[41] = sg
space_groups['A b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(42, 'F m m 2', transformations)
space_groups[42] = sg
space_groups['F m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(43, 'F d d 2', transformations)
space_groups[43] = sg
space_groups['F d d 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(44, 'I m m 2', transformations)
space_groups[44] = sg
space_groups['I m m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(45, 'I b a 2', transformations)
space_groups[45] = sg
space_groups['I b a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(46, 'I m a 2', transformations)
space_groups[46] = sg
space_groups['I m a 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(47, 'P m m m', transformations)
space_groups[47] = sg
space_groups['P m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(48, 'P n n n :2', transformations)
space_groups[48] = sg
space_groups['P n n n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(49, 'P c c m', transformations)
space_groups[49] = sg
space_groups['P c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(50, 'P b a n :2', transformations)
space_groups[50] = sg
space_groups['P b a n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(51, 'P m m a', transformations)
space_groups[51] = sg
space_groups['P m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(52, 'P n n a', transformations)
space_groups[52] = sg
space_groups['P n n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(53, 'P m n a', transformations)
space_groups[53] = sg
space_groups['P m n a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(54, 'P c c a', transformations)
space_groups[54] = sg
space_groups['P c c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(55, 'P b a m', transformations)
space_groups[55] = sg
space_groups['P b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(56, 'P c c n', transformations)
space_groups[56] = sg
space_groups['P c c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(57, 'P b c m', transformations)
space_groups[57] = sg
space_groups['P b c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(58, 'P n n m', transformations)
space_groups[58] = sg
space_groups['P n n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(59, 'P m m n :2', transformations)
space_groups[59] = sg
space_groups['P m m n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(60, 'P b c n', transformations)
space_groups[60] = sg
space_groups['P b c n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(61, 'P b c a', transformations)
space_groups[61] = sg
space_groups['P b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(62, 'P n m a', transformations)
space_groups[62] = sg
space_groups['P n m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(63, 'C m c m', transformations)
space_groups[63] = sg
space_groups['C m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(64, 'C m c a', transformations)
space_groups[64] = sg
space_groups['C m c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(65, 'C m m m', transformations)
space_groups[65] = sg
space_groups['C m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(66, 'C c c m', transformations)
space_groups[66] = sg
space_groups['C c c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(67, 'C m m a', transformations)
space_groups[67] = sg
space_groups['C m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(68, 'C c c a :2', transformations)
space_groups[68] = sg
space_groups['C c c a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(69, 'F m m m', transformations)
space_groups[69] = sg
space_groups['F m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(70, 'F d d d :2', transformations)
space_groups[70] = sg
space_groups['F d d d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(71, 'I m m m', transformations)
space_groups[71] = sg
space_groups['I m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(72, 'I b a m', transformations)
space_groups[72] = sg
space_groups['I b a m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(73, 'I b c a', transformations)
space_groups[73] = sg
space_groups['I b c a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(74, 'I m m a', transformations)
space_groups[74] = sg
space_groups['I m m a'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(75, 'P 4', transformations)
space_groups[75] = sg
space_groups['P 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(76, 'P 41', transformations)
space_groups[76] = sg
space_groups['P 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(77, 'P 42', transformations)
space_groups[77] = sg
space_groups['P 42'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(78, 'P 43', transformations)
space_groups[78] = sg
space_groups['P 43'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(79, 'I 4', transformations)
space_groups[79] = sg
space_groups['I 4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(80, 'I 41', transformations)
space_groups[80] = sg
space_groups['I 41'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(81, 'P -4', transformations)
space_groups[81] = sg
space_groups['P -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(82, 'I -4', transformations)
space_groups[82] = sg
space_groups['I -4'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(83, 'P 4/m', transformations)
space_groups[83] = sg
space_groups['P 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(84, 'P 42/m', transformations)
space_groups[84] = sg
space_groups['P 42/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(85, 'P 4/n :2', transformations)
space_groups[85] = sg
space_groups['P 4/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(86, 'P 42/n :2', transformations)
space_groups[86] = sg
space_groups['P 42/n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(87, 'I 4/m', transformations)
space_groups[87] = sg
space_groups['I 4/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(88, 'I 41/a :2', transformations)
space_groups[88] = sg
space_groups['I 41/a :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(89, 'P 4 2 2', transformations)
space_groups[89] = sg
space_groups['P 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(90, 'P 4 21 2', transformations)
space_groups[90] = sg
space_groups['P 4 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(91, 'P 41 2 2', transformations)
space_groups[91] = sg
space_groups['P 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(92, 'P 41 21 2', transformations)
space_groups[92] = sg
space_groups['P 41 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(93, 'P 42 2 2', transformations)
space_groups[93] = sg
space_groups['P 42 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(94, 'P 42 21 2', transformations)
space_groups[94] = sg
space_groups['P 42 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,3])
trans_den = N.array([1,1,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(95, 'P 43 2 2', transformations)
space_groups[95] = sg
space_groups['P 43 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(96, 'P 43 21 2', transformations)
space_groups[96] = sg
space_groups['P 43 21 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(97, 'I 4 2 2', transformations)
space_groups[97] = sg
space_groups['I 4 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(98, 'I 41 2 2', transformations)
space_groups[98] = sg
space_groups['I 41 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(99, 'P 4 m m', transformations)
space_groups[99] = sg
space_groups['P 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(100, 'P 4 b m', transformations)
space_groups[100] = sg
space_groups['P 4 b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(101, 'P 42 c m', transformations)
space_groups[101] = sg
space_groups['P 42 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(102, 'P 42 n m', transformations)
space_groups[102] = sg
space_groups['P 42 n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(103, 'P 4 c c', transformations)
space_groups[103] = sg
space_groups['P 4 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(104, 'P 4 n c', transformations)
space_groups[104] = sg
space_groups['P 4 n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(105, 'P 42 m c', transformations)
space_groups[105] = sg
space_groups['P 42 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(106, 'P 42 b c', transformations)
space_groups[106] = sg
space_groups['P 42 b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(107, 'I 4 m m', transformations)
space_groups[107] = sg
space_groups['I 4 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(108, 'I 4 c m', transformations)
space_groups[108] = sg
space_groups['I 4 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(109, 'I 41 m d', transformations)
space_groups[109] = sg
space_groups['I 41 m d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(110, 'I 41 c d', transformations)
space_groups[110] = sg
space_groups['I 41 c d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(111, 'P -4 2 m', transformations)
space_groups[111] = sg
space_groups['P -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(112, 'P -4 2 c', transformations)
space_groups[112] = sg
space_groups['P -4 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(113, 'P -4 21 m', transformations)
space_groups[113] = sg
space_groups['P -4 21 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(114, 'P -4 21 c', transformations)
space_groups[114] = sg
space_groups['P -4 21 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(115, 'P -4 m 2', transformations)
space_groups[115] = sg
space_groups['P -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(116, 'P -4 c 2', transformations)
space_groups[116] = sg
space_groups['P -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(117, 'P -4 b 2', transformations)
space_groups[117] = sg
space_groups['P -4 b 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(118, 'P -4 n 2', transformations)
space_groups[118] = sg
space_groups['P -4 n 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(119, 'I -4 m 2', transformations)
space_groups[119] = sg
space_groups['I -4 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(120, 'I -4 c 2', transformations)
space_groups[120] = sg
space_groups['I -4 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(121, 'I -4 2 m', transformations)
space_groups[121] = sg
space_groups['I -4 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,3])
trans_den = N.array([2,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,5])
trans_den = N.array([1,2,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(122, 'I -4 2 d', transformations)
space_groups[122] = sg
space_groups['I -4 2 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(123, 'P 4/m m m', transformations)
space_groups[123] = sg
space_groups['P 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(124, 'P 4/m c c', transformations)
space_groups[124] = sg
space_groups['P 4/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(125, 'P 4/n b m :2', transformations)
space_groups[125] = sg
space_groups['P 4/n b m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(126, 'P 4/n n c :2', transformations)
space_groups[126] = sg
space_groups['P 4/n n c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(127, 'P 4/m b m', transformations)
space_groups[127] = sg
space_groups['P 4/m b m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(128, 'P 4/m n c', transformations)
space_groups[128] = sg
space_groups['P 4/m n c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(129, 'P 4/n m m :2', transformations)
space_groups[129] = sg
space_groups['P 4/n m m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(130, 'P 4/n c c :2', transformations)
space_groups[130] = sg
space_groups['P 4/n c c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(131, 'P 42/m m c', transformations)
space_groups[131] = sg
space_groups['P 42/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(132, 'P 42/m c m', transformations)
space_groups[132] = sg
space_groups['P 42/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(133, 'P 42/n b c :2', transformations)
space_groups[133] = sg
space_groups['P 42/n b c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(134, 'P 42/n n m :2', transformations)
space_groups[134] = sg
space_groups['P 42/n n m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(135, 'P 42/m b c', transformations)
space_groups[135] = sg
space_groups['P 42/m b c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(136, 'P 42/m n m', transformations)
space_groups[136] = sg
space_groups['P 42/m n m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(137, 'P 42/n m c :2', transformations)
space_groups[137] = sg
space_groups['P 42/n m c :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(138, 'P 42/n c m :2', transformations)
space_groups[138] = sg
space_groups['P 42/n c m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(139, 'I 4/m m m', transformations)
space_groups[139] = sg
space_groups['I 4/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(140, 'I 4/m c m', transformations)
space_groups[140] = sg
space_groups['I 4/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(141, 'I 41/a m d :2', transformations)
space_groups[141] = sg
space_groups['I 41/a m d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-3,-3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,-1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(142, 'I 41/a c d :2', transformations)
space_groups[142] = sg
space_groups['I 41/a c d :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(143, 'P 3', transformations)
space_groups[143] = sg
space_groups['P 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(144, 'P 31', transformations)
space_groups[144] = sg
space_groups['P 31'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(145, 'P 32', transformations)
space_groups[145] = sg
space_groups['P 32'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(146, 'R 3 :H', transformations)
space_groups[146] = sg
space_groups['R 3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(147, 'P -3', transformations)
space_groups[147] = sg
space_groups['P -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(148, 'R -3 :H', transformations)
space_groups[148] = sg
space_groups['R -3 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(149, 'P 3 1 2', transformations)
space_groups[149] = sg
space_groups['P 3 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(150, 'P 3 2 1', transformations)
space_groups[150] = sg
space_groups['P 3 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(151, 'P 31 1 2', transformations)
space_groups[151] = sg
space_groups['P 31 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(152, 'P 31 2 1', transformations)
space_groups[152] = sg
space_groups['P 31 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(153, 'P 32 1 2', transformations)
space_groups[153] = sg
space_groups['P 32 1 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(154, 'P 32 2 1', transformations)
space_groups[154] = sg
space_groups['P 32 2 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(155, 'R 3 2 :H', transformations)
space_groups[155] = sg
space_groups['R 3 2 :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(156, 'P 3 m 1', transformations)
space_groups[156] = sg
space_groups['P 3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(157, 'P 3 1 m', transformations)
space_groups[157] = sg
space_groups['P 3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(158, 'P 3 c 1', transformations)
space_groups[158] = sg
space_groups['P 3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(159, 'P 3 1 c', transformations)
space_groups[159] = sg
space_groups['P 3 1 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(160, 'R 3 m :H', transformations)
space_groups[160] = sg
space_groups['R 3 m :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(161, 'R 3 c :H', transformations)
space_groups[161] = sg
space_groups['R 3 c :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(162, 'P -3 1 m', transformations)
space_groups[162] = sg
space_groups['P -3 1 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(163, 'P -3 1 c', transformations)
space_groups[163] = sg
space_groups['P -3 1 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(164, 'P -3 m 1', transformations)
space_groups[164] = sg
space_groups['P -3 m 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(165, 'P -3 c 1', transformations)
space_groups[165] = sg
space_groups['P -3 c 1'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(166, 'R -3 m :H', transformations)
space_groups[166] = sg
space_groups['R -3 m :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,7])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,2,2])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,2,1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,5])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([2,1,1])
trans_den = N.array([3,3,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([2,1,-1])
trans_den = N.array([3,3,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(167, 'R -3 c :H', transformations)
space_groups[167] = sg
space_groups['R -3 c :H'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(168, 'P 6', transformations)
space_groups[168] = sg
space_groups['P 6'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(169, 'P 61', transformations)
space_groups[169] = sg
space_groups['P 61'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(170, 'P 65', transformations)
space_groups[170] = sg
space_groups['P 65'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(171, 'P 62', transformations)
space_groups[171] = sg
space_groups['P 62'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(172, 'P 64', transformations)
space_groups[172] = sg
space_groups['P 64'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(173, 'P 63', transformations)
space_groups[173] = sg
space_groups['P 63'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(174, 'P -6', transformations)
space_groups[174] = sg
space_groups['P -6'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(175, 'P 6/m', transformations)
space_groups[175] = sg
space_groups['P 6/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(176, 'P 63/m', transformations)
space_groups[176] = sg
space_groups['P 63/m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(177, 'P 6 2 2', transformations)
space_groups[177] = sg
space_groups['P 6 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(178, 'P 61 2 2', transformations)
space_groups[178] = sg
space_groups['P 61 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,5])
trans_den = N.array([1,1,6])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(179, 'P 65 2 2', transformations)
space_groups[179] = sg
space_groups['P 65 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(180, 'P 62 2 2', transformations)
space_groups[180] = sg
space_groups['P 62 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,2])
trans_den = N.array([1,1,3])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(181, 'P 64 2 2', transformations)
space_groups[181] = sg
space_groups['P 64 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(182, 'P 63 2 2', transformations)
space_groups[182] = sg
space_groups['P 63 2 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(183, 'P 6 m m', transformations)
space_groups[183] = sg
space_groups['P 6 m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(184, 'P 6 c c', transformations)
space_groups[184] = sg
space_groups['P 6 c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(185, 'P 63 c m', transformations)
space_groups[185] = sg
space_groups['P 63 c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(186, 'P 63 m c', transformations)
space_groups[186] = sg
space_groups['P 63 m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(187, 'P -6 m 2', transformations)
space_groups[187] = sg
space_groups['P -6 m 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(188, 'P -6 c 2', transformations)
space_groups[188] = sg
space_groups['P -6 c 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(189, 'P -6 2 m', transformations)
space_groups[189] = sg
space_groups['P -6 2 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(190, 'P -6 2 c', transformations)
space_groups[190] = sg
space_groups['P -6 2 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(191, 'P 6/m m m', transformations)
space_groups[191] = sg
space_groups['P 6/m m m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(192, 'P 6/m c c', transformations)
space_groups[192] = sg
space_groups['P 6/m c c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(193, 'P 63/m c m', transformations)
space_groups[193] = sg
space_groups['P 63/m c m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,1,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,1,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,-1,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,-1,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(194, 'P 63/m m c', transformations)
space_groups[194] = sg
space_groups['P 63/m m c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(195, 'P 2 3', transformations)
space_groups[195] = sg
space_groups['P 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(196, 'F 2 3', transformations)
space_groups[196] = sg
space_groups['F 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(197, 'I 2 3', transformations)
space_groups[197] = sg
space_groups['I 2 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(198, 'P 21 3', transformations)
space_groups[198] = sg
space_groups['P 21 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(199, 'I 21 3', transformations)
space_groups[199] = sg
space_groups['I 21 3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(200, 'P m -3', transformations)
space_groups[200] = sg
space_groups['P m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(201, 'P n -3 :2', transformations)
space_groups[201] = sg
space_groups['P n -3 :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(202, 'F m -3', transformations)
space_groups[202] = sg
space_groups['F m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,-1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(203, 'F d -3 :2', transformations)
space_groups[203] = sg
space_groups['F d -3 :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(204, 'I m -3', transformations)
space_groups[204] = sg
space_groups['I m -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(205, 'P a -3', transformations)
space_groups[205] = sg
space_groups['P a -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(206, 'I a -3', transformations)
space_groups[206] = sg
space_groups['I a -3'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(207, 'P 4 3 2', transformations)
space_groups[207] = sg
space_groups['P 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(208, 'P 42 3 2', transformations)
space_groups[208] = sg
space_groups['P 42 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(209, 'F 4 3 2', transformations)
space_groups[209] = sg
space_groups['F 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(210, 'F 41 3 2', transformations)
space_groups[210] = sg
space_groups['F 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(211, 'I 4 3 2', transformations)
space_groups[211] = sg
space_groups['I 4 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(212, 'P 43 3 2', transformations)
space_groups[212] = sg
space_groups['P 43 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(213, 'P 41 3 2', transformations)
space_groups[213] = sg
space_groups['P 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(214, 'I 41 3 2', transformations)
space_groups[214] = sg
space_groups['I 41 3 2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(215, 'P -4 3 m', transformations)
space_groups[215] = sg
space_groups['P -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(216, 'F -4 3 m', transformations)
space_groups[216] = sg
space_groups['F -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(217, 'I -4 3 m', transformations)
space_groups[217] = sg
space_groups['I -4 3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(218, 'P -4 3 n', transformations)
space_groups[218] = sg
space_groups['P -4 3 n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(219, 'F -4 3 c', transformations)
space_groups[219] = sg
space_groups['F -4 3 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,5,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,5])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,5,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,3,3])
trans_den = N.array([4,4,4])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(220, 'I -4 3 d', transformations)
space_groups[220] = sg
space_groups['I -4 3 d'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(221, 'P m -3 m', transformations)
space_groups[221] = sg
space_groups['P m -3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,-1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(222, 'P n -3 n :2', transformations)
space_groups[222] = sg
space_groups['P n -3 n :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,-1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(223, 'P m -3 n', transformations)
space_groups[223] = sg
space_groups['P m -3 n'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(224, 'P n -3 m :2', transformations)
space_groups[224] = sg
space_groups['P n -3 m :2'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(225, 'F m -3 m', transformations)
space_groups[225] = sg
space_groups['F m -3 m'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,0])
trans_den = N.array([2,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([2,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,1])
trans_den = N.array([1,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([2,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,0])
trans_den = N.array([1,2,1])
transformations.append((rot, trans_num, trans_den))
sg = SpaceGroup(226, 'F m -3 c', transformations)
space_groups[226] = sg
space_groups['F m -3 c'] = sg
transformations = []
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,-1,0])
trans_den = N.array([4,4,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,0,-1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,-1,-1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,3,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,3,3])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([-1,1,1])
trans_den = N.array([4,2,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,1,1])
trans_den = N.array([1,2,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([3,1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([3,0,3])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,1,3])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,1,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,0,-1,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,-1,0,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,0,-1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,-1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,1,0,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([2,1,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,1,0,0])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([2,4,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,0,1])
trans_den = N.array([4,1,4])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([1,-1,1])
trans_den = N.array([4,4,2])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
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])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,-1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,1,0,0,0,0,1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,0,1,0,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = | N.array([0,0,1,0,1,0,1,0,0]) | numpy.array |
__all__ = ['multigaussian', 'multigaussian_deviates']
import sys
import numpy as np
# -----------------------------------------------------------------
# model for fitting EIS line profiles using mpfit.py
# -----------------------------------------------------------------
# series of Guassian model functions with polynomial background
def multigaussian(param, x, n_gauss=1, n_poly=0):
"""Multigaussian model with a polynomial background
Parameters
----------
param : array_like
Model fit parameters. There must be 3*n_gauss + n_poly param values.
For each Gaussian component, the parameters are assumed to have the
following order: [peak, centroid, width]
x : array_like
Independent variable values to evaluate the function at. For EIS data,
this will usually correspond to wavelength values.
n_gauss : int, optional
Number of Gaussian components. Default is "1"
n_poly : int, optional
Number of background polynomial terms. Common values are:
o (no background), 1 (constant), and 2 (linear). Default is "0"
Returns
-------
f : array_like
Function evaluated at each x value
"""
# check inputs
n_param = len(param)
if n_param != 3*n_gauss+n_poly:
print(' ! input parameter sizes do not match ... stopping')
sys.exit()
# compute Gaussians
nx = len(x)
f = | np.zeros(nx) | numpy.zeros |
import numpy as np
from numpy.testing import assert_equal, assert_, run_module_suite
import unittest
from qutip import *
import qutip.settings as qset
if qset.has_openmp:
from qutip.cy.openmp.benchmark import _spmvpy, _spmvpy_openmp
@unittest.skipIf(qset.has_openmp == False, 'OPENMP not available.')
def test_openmp_spmv():
"OPENMP : spmvpy_openmp == spmvpy"
for k in range(100):
L = rand_herm(10,0.25).data
vec = rand_ket(L.shape[0],0.25).full().ravel()
out = np.zeros_like(vec)
out_openmp = np.zeros_like(vec)
_spmvpy(L.data, L.indices, L.indptr, vec, 1, out)
_spmvpy_openmp(L.data, L.indices, L.indptr, vec, 1, out_openmp, 2)
assert_(np.allclose(out, out_openmp, 1e-15))
@unittest.skipIf(qset.has_openmp == False, 'OPENMP not available.')
def test_openmp_mesolve():
"OPENMP : mesolve"
N = 100
wc = 1.0 * 2 * np.pi # cavity frequency
wa = 1.0 * 2 * np.pi # atom frequency
g = 0.05 * 2 * np.pi # coupling strength
kappa = 0.005 # cavity dissipation rate
gamma = 0.05 # atom dissipation rate
n_th_a = 1 # temperature in frequency units
use_rwa = 0
# operators
a = tensor(destroy(N), qeye(2))
sm = tensor(qeye(N), destroy(2))
# Hamiltonian
if use_rwa:
H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())
else:
H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() + a) * (sm + sm.dag())
c_op_list = []
rate = kappa * (1 + n_th_a)
if rate > 0.0:
c_op_list.append(np.sqrt(rate) * a)
rate = kappa * n_th_a
if rate > 0.0:
c_op_list.append( | np.sqrt(rate) | numpy.sqrt |
#!/usr/bin/env python
u"""
ncdf_read.py
Written by <NAME> (11/2021)
Reads spatial data from COARDS-compliant netCDF4 files
CALLING SEQUENCE:
dinput = ncdf_read(filename, DATE=False, VERBOSE=False)
INPUTS:
filename: netCDF4 file to be opened and read
OUTPUTS:
data: z value of dataset
lon: longitudinal array
lat: latitudinal array
time: time value of dataset (if specified by DATE)
attributes: netCDF4 attributes (for variables and title)
OPTIONS:
DATE: netCDF4 file has date information
VERBOSE: will print to screen the netCDF4 structure parameters
VARNAME: z variable name in netCDF4 file
LONNAME: longitude variable name in netCDF4 file
LATNAME: latitude variable name in netCDF4 file
TIMENAME: time variable name in netCDF4 file
COMPRESSION: netCDF4 file is compressed or streaming as bytes
gzip
zip
bytes
PYTHON DEPENDENCIES:
numpy: Scientific Computing Tools For Python (https://numpy.org)
netCDF4: Python interface to the netCDF C library
(https://unidata.github.io/netcdf4-python/netCDF4/index.html)
UPDATE HISTORY:
Updated 11/2021: try to get more global attributes. use kwargs
Updated 10/2021: using python logging for handling verbose output
Updated 02/2021: prevent warnings with python3 compatible regex strings
Updated 12/2020: try/except for getting variable unit attributes
attempt to get a standard set of attributes from each variable
add fallback for finding netCDF4 file within from zip files
added bytes option for COMPRESSION if streaming from memory
Updated 08/2020: flake8 compatible regular expression strings
add options to read from gzip or zip compressed files
Updated 07/2020: added function docstrings
Updated 06/2020: output data as lat/lon following spatial module
attempt to read fill value attribute and set to None if not present
Updated 10/2019: changing Y/N flags to True/False
Updated 03/2019: print variables keys in list for Python3 compatibility
Updated 06/2018: extract fill_value and title without variable attributes
Updated 07-09/2016: using netCDF4-python
Updated 06/2016: using __future__ print, output filename if VERBOSE
Updated 05/2016: will only transpose if data is 2 dimensional (not 3)
added parameter to read the TITLE variable
Updated 07/2015: updated read title for different cases with regex
Updated 05/2015: added parameter TIMENAME for time variable name
Updated 04/2015: fix attribute outputs (forgot to copy to new dictionary)
Updated 02/2015: added copy for variable outputs
fixes new error flag from mmap=True
Updated 11/2014: new parameters for variable names and attributes
all variables in a single python dictionary
Updated 05/2014: new parameter for missing value
new outputs: all attributes, fill value
added try for TITLE attribute
converting time to numpy array
Updated 02/2014: minor update to if statements
Updated 07/2013: switched from Scientific Python to Scipy
Updated 01/2013: adding time variable
Written 07/2012
"""
from __future__ import print_function
import os
import re
import uuid
import gzip
import logging
import netCDF4
import zipfile
import numpy as np
def ncdf_read(filename, **kwargs):
"""
Reads spatial data from COARDS-compliant netCDF4 files
Arguments
---------
filename: netCDF4 file to be opened and read
Keyword arguments
-----------------
DATE: netCDF4 file has date information
VERBOSE: will print to screen the netCDF4 structure parameters
VARNAME: z variable name in netCDF4 file
LONNAME: longitude variable name in netCDF4 file
LATNAME: latitude variable name in netCDF4 file
TIMENAME: time variable name in netCDF4 file
COMPRESSION: netCDF4 file is compressed or streaming as bytes
gzip
zip
bytes
Returns
-------
data: z value of dataset
lon: longitudinal array
lat: latitudinal array
time: time value of dataset
attributes: netCDF4 attributes
"""
#-- set default keyword arguments
kwargs.setdefault('DATE',False)
kwargs.setdefault('VARNAME','z')
kwargs.setdefault('LONNAME','lon')
kwargs.setdefault('LATNAME','lat')
kwargs.setdefault('TIMENAME','time')
kwargs.setdefault('COMPRESSION',None)
#-- Open the NetCDF4 file for reading
if (kwargs['COMPRESSION'] == 'gzip'):
#-- read as in-memory (diskless) netCDF4 dataset
with gzip.open(os.path.expanduser(filename),'r') as f:
fileID = netCDF4.Dataset(os.path.basename(filename),memory=f.read())
elif (kwargs['COMPRESSION'] == 'zip'):
#-- read zipped file and extract file into in-memory file object
fileBasename,_ = os.path.splitext(os.path.basename(filename))
with zipfile.ZipFile(os.path.expanduser(filename)) as z:
#-- first try finding a netCDF4 file with same base filename
#-- if none found simply try searching for a netCDF4 file
try:
f,=[f for f in z.namelist() if re.match(fileBasename,f,re.I)]
except:
f,=[f for f in z.namelist() if re.search(r'\.nc(4)?$',f)]
#-- read bytes from zipfile as in-memory (diskless) netCDF4 dataset
fileID = netCDF4.Dataset(uuid.uuid4().hex, memory=z.read(f))
elif (kwargs['COMPRESSION'] == 'bytes'):
#-- read as in-memory (diskless) netCDF4 dataset
fileID = netCDF4.Dataset(uuid.uuid4().hex, memory=filename.read())
else:
#-- read netCDF4 dataset
fileID = netCDF4.Dataset(os.path.expanduser(filename), 'r')
#-- create python dictionary for output variables
dinput = {}
dinput['attributes'] = {}
#-- Output NetCDF file information
logging.info(fileID.filepath())
logging.info(list(fileID.variables.keys()))
#-- mapping between output keys and netCDF4 variable names
keys = ['lon','lat','data']
nckeys = [kwargs['LONNAME'],kwargs['LATNAME'],kwargs['VARNAME']]
if kwargs['DATE']:
keys.append('time')
nckeys.append(kwargs['TIMENAME'])
#-- list of variable attributes
attributes_list = ['description','units','long_name','calendar',
'standard_name','_FillValue','missing_value']
#-- for each variable
for key,nckey in zip(keys,nckeys):
#-- Getting the data from each NetCDF variable
dinput[key] = | np.squeeze(fileID.variables[nckey][:].data) | numpy.squeeze |
import numpy as np
import matplotlib.pyplot as plt
import copy
import torch
from torch import nn
from torchsummary import summary
from sklearn.metrics import confusion_matrix
import torchvision
from . import constants
from sklearn.metrics import roc_curve
from sklearn.metrics import auc
from sklearn.metrics import roc_auc_score
# import scikitplot as skplt
def evaluate_acc_par(args, model, param_G, dataloader, cf_mat=False, roc=False, preds=False):
model.eval()
param_G.eval()
valid_batch_acc_1, valid_batch_acc_2 = [], []
y_true_1, y_pred_1, y_prob_1 = [], [], []
y_true_2, y_pred_2, y_prob_2 = [], [], []
auc_scores_1 = []
n_samples = 0
for batch_id, (images, labels) in enumerate(dataloader):
images, labels = images.to(args.device), labels.to(args.device)
output_valid_1 = model(images)
output_valid_2 = param_G(output_valid_1)
auc_scores_1.append(roc_auc_score(labels[:, 0].cpu().detach(), output_valid_1.max(1)[1].cpu().detach()))
# auc_scores_2 = roc_auc_score(labels[:, 1], output_valid_2)
predictions_1 = output_valid_1.max(1)[1]
predictions_2 = output_valid_2.max(1)[1]
current_acc_1 = torch.sum((predictions_1 == labels[:, 0]).float())
current_acc_2 = torch.sum((predictions_2 == labels[:, 1]).float())
valid_batch_acc_1.append(current_acc_1)
valid_batch_acc_2.append(current_acc_2)
n_samples += len(labels)
y_true_1 = y_true_1 + labels[:, 0].tolist()
y_pred_1 = y_pred_1 + predictions_1.tolist()
if constants.SOFTMAX:
y_prob_1 = y_prob_1 + ((output_valid_1).detach().cpu().numpy()).tolist()
else:
y_prob_1 = y_prob_1 + (nn.Softmax(dim=1)(output_valid_1).detach().cpu().numpy()).tolist()
y_true_2 = y_true_2 + labels[:, 1].tolist()
y_pred_2 = y_pred_2 + predictions_2.tolist()
y_prob_2 = y_prob_2 + (nn.Softmax(dim=1)(output_valid_2).detach().cpu().numpy()).tolist()
acc_1 = (sum(valid_batch_acc_1) / n_samples) * 100
acc_2 = (sum(valid_batch_acc_2) / n_samples) * 100
if preds:
return y_prob_1
if roc:
plt.figure(figsize=(5, 5))
# skplt.metrics.
plot_roc(y_true_1, y_prob_1,
plot_micro=False, plot_macro=False,
title=None,
cmap='prism',
figsize=(5, 5),
text_fontsize="large",
title_fontsize="large",
line_color=['r', 'b'],
line_labels=["y=0", "y=1"])
plt.show()
plt.figure(figsize=(5, 5))
# skplt.metrics.
plot_roc(y_true_2, y_prob_2,
plot_micro=False, plot_macro=False,
title=None,
cmap='prism',
figsize=(5, 5),
text_fontsize="large",
title_fontsize="large",
line_color=['m', 'g', 'y'],
line_labels=["s=0", "s=1", "s=2"])
plt.show()
if cf_mat:
cf_1 = confusion_matrix(y_true_1, y_pred_1, normalize='true')
cf_2 = confusion_matrix(y_true_2, y_pred_2, normalize='true')
return acc_1, acc_2, cf_1, cf_2
return acc_1, acc_2
def evaluate_acc_reg(args, model, dataloader, cf_mat=False, roc=False, preds=False, beTau=constants.REGTAU):
model.eval()
valid_batch_acc_1, valid_batch_acc_2 = [], []
y_true_1, y_pred_1, y_prob_1 = [], [], []
y_true_2, y_pred_2, y_prob_2 = [], [], []
n_samples = 0
for batch_id, (images, labels) in enumerate(dataloader):
images, labels = images.to(args.device), labels.to(args.device)
output_valid_1 = model(images)
predictions_1 = output_valid_1.max(1)[1]
if constants.SOFTMAX:
output_valid_2 = output_valid_1
else:
output_valid_2 = nn.Softmax(dim=1)(output_valid_1)
output_valid_2 = output_valid_2 + 1e-16
entropies = -(torch.sum(output_valid_2 * torch.log(output_valid_2), dim=1))
predictions_2 = torch.where(entropies >= beTau, torch.tensor(1.).to(args.device),
torch.tensor(0.).to(args.device))
current_acc_1 = torch.sum((predictions_1 == labels[:, 0]).float())
current_acc_2 = torch.sum((predictions_2 == labels[:, 1]).float())
valid_batch_acc_1.append(current_acc_1)
valid_batch_acc_2.append(current_acc_2)
n_samples += len(labels)
y_true_1 = y_true_1 + labels[:, 0].tolist()
y_pred_1 = y_pred_1 + predictions_1.tolist()
y_prob_1 = y_prob_1 + output_valid_2.detach().cpu().numpy().tolist()
y_true_2 = y_true_2 + labels[:, 1].tolist()
y_pred_2 = y_pred_2 + predictions_2.tolist()
entropies = entropies.detach().cpu().numpy()
y_prob_2 = y_prob_2 + np.concatenate((1 - entropies[:, np.newaxis], entropies[:, np.newaxis]), axis=1).tolist()
acc_1 = (sum(valid_batch_acc_1) / n_samples) * 100
acc_2 = (sum(valid_batch_acc_2) / n_samples) * 100
y_true_2 = [int(x) for x in y_true_2]
if roc:
plt.figure(figsize=(5, 5))
# skplt.metrics.
plot_roc(y_true_1, y_prob_1,
plot_micro=False, plot_macro=False,
title=None,
cmap='prism',
figsize=(5, 5),
text_fontsize=14,
title_fontsize="large",
line_color=['r', 'b', 'g'],
line_labels=["label 0", "label 1", "label 2"],
line_style=["-", "--", ":"])
plt.show()
plt.figure(figsize=(5, 5))
# skplt.metrics.
plot_roc(y_true_2, y_prob_2,
plot_micro=False, plot_macro=False,
title=None,
cmap='prism',
figsize=(5, 5),
text_fontsize=14,
title_fontsize="large",
line_color=['m', 'g', 'y'],
line_labels=["male", "female"],
line_style=["-.", ":"])
plt.show()
if cf_mat:
cf_1 = confusion_matrix(y_true_1, y_pred_1, normalize='true')
cf_2 = confusion_matrix(y_true_2, y_pred_2, normalize='true')
return acc_1, acc_2, cf_1, cf_2
return acc_1, acc_2
def evaluate_acc_get_preds(args, model, param_G, dataloader):
model.eval()
param_G.eval()
preds = []
n_samples = 0
for batch_id, (images, labels) in enumerate(dataloader):
images, labels = images.to(args.device), labels.to(args.device)
preds = preds + ((model(images)).detach().cpu().numpy()).tolist()
return preds
def log_sum_exp(x, axis=1):
m = torch.max(x, dim=1)[0]
return m + torch.log(torch.sum(torch.exp(x - m.unsqueeze(1)), dim=axis))
def print_dataset_info(dataset):
print("Data Dimensions: ", dataset[0].shape)
labels = np.array(dataset[1]).astype(int)
_unique, _counts = np.unique(labels[:, 0], return_counts=True)
print("Honest:\n", np.asarray((_unique, _counts)).T)
_unique, _counts = | np.unique(labels[:, 1], return_counts=True) | numpy.unique |
import numpy as np
import scipy.optimize
import scipy.linalg
from scipy.stats import unitary_group as UG
###############
### Matrix Operations
###############
def dag(A):
return 1.*np.conjugate(np.transpose(A))
def dot(A,B):
return np.trace(dag(A)@B)
def norm(A):
return np.sqrt(np.abs(dot(A,A)))
def kprod(A,B):
return np.kron(A,B)
def ksum(A,B):
return np.kron(A,one) + np.kron(one,B)
def eig(A):
vals, vecs = np.linalg.eigh(A)
vecs = np.transpose(vecs) ## so vecs[0] is an eigenvector
return 1.*vals, 1.*vecs
def couter(psi):
return 1.*np.outer(psi, np.conjugate(psi))
###############
### Multipartite Matrix Operations
###############
## basis dictionaries
d22 = {'00':0, '01':1, '10':2, '11':3}
d23 = {'00':0, '01':1, '02':2, '10':3, '11':4, '12':5}
d33 = {'00':0, '01':1, '02':2, '10':3, '11':4, '12':5, '20':6, '21':7, '22':8}
d222 = {'000':0, '001':1, '010':2, '011':3, '100':4, '101':5, '110':6, '111':7}
d223 = {'000':0, '001':1, '002':2, '010':3, '011':4, '012':5, '100':6, '101':7, '102':8, '110':9, '111':10, '112':11}
d2222 = {format(i,'04b'):i for i in range(16)}
dxx = {'22':d22, '23':d23, '222':d222, '223':d223, '33':d33, '2222':d2222}
## dictionary lookup from n=(nA,nB,...)
def ndict(n):
return dxx[''.join([str(nn) for nn in n])]
## generate list of basis index labels for system of type n=(nA,nB,...), possibly holding some index values fixed
## sums over all index values which are 'x' in the hold argument
## "mind" = "multipartite indices"
def mind(n=[2,2], hold='xxxxx'):
ss = [''.join([str(i) for i in range(nn)]) for nn in n]
for i in range(len(n)):
if not hold[i] == 'x':
ss[i] = hold[i]
ijk= [x for x in ss[0]]
for s in ss[1:]:
ijk = [x+y for x in ijk for y in s]
return tuple(ijk)
## "rind" = "rho indices"
def rind(n=[2,2], hold='xxxxx'):
dd = ndict(n)
return np.array([dd[idx] for idx in mind(n,hold)], dtype=int)
## compute reduced density matrices given n=(nA,nB,...) and rho
def REDUCE(rho, n):
## check dims match
if len(rho)==np.prod(n):
if len(n)==1:
red = [1.*rho]
if len(n)>1:
red = [np.zeros((nn,nn), dtype=complex) for nn in n]
## iterate over subspaces
for m in range(len(n)):
## iterate over reduced density matrix elements
for i in range(n[m]):
for j in range(n[m]):
## indices to sum over
hold = len(n)*'x'
hold = hold[:m]+str(i)+hold[m+1:]
mi, ri = mind(n,hold), rind(n,hold)
mj, rj = mind(n,hold.replace(str(i),str(j))), rind(n,hold.replace(str(i),str(j)))
## fill rho
red[m][i,j] = np.sum([rho[ri[k],rj[k]] for k in range(len(ri))], axis=0, dtype=complex)
## return
return tuple([1.*rr for rr in red])
###############
### Generate Arbitrary 2 or 3 dimensional rank-1 coarse-graining
###############
## function used in parameterizing SU3
def FF(v,w,x,y,z):
v,w,x,y,z = 1.*v,1.*w,1.*x,1.*y,1.*z
return -np.cos(v)*np.cos(w)*np.cos(x)*np.exp(1j*y) - np.sin(w)*np.sin(x)*np.exp(-1j*z)
## arbitrary SU matrix parameterized by real vector x in (0,1)
def SU(x):
if len(x)==3:
return SU2(x)
if len(x)==8:
return SU3(x)
## SU2 parameterized by real vector x
def SU2(x=np.zeros(3)):
## identity is at x = np.array([0.,0.,0.])
## periodic as each x=x+1, so use x in (0,1)
th = 2.*np.pi*x
su = np.array(
[
[ np.cos(th[0])*np.exp( 1j*th[1]), np.sin(th[0])*np.exp( 1j*th[2])],
[-np.sin(th[0])*np.exp(-1j*th[2]), np.cos(th[0])*np.exp(-1j*th[1])],
], dtype=complex)
return 1.*su
## SU3 parameterized by real vector x
def SU3(x=np.array([.5,.5,.5,0.,0.,0.,0.,0.])):
## https://arxiv.org/abs/1303.5904
## identity is at x = np.array([.5,.5,.5,0.,0.,0.,0.,0.])
## periodic as each x=x+1, so use x in (0,1)
x = 2.*np.pi*x
pi = np.pi
ph31, th31, th32, ph32, ch32, th21, ch21, ph21 = 1.*x
su = np.zeros((3,3), dtype=complex)
## top row
su[0,0] = FF(th31,0,0,ph31+pi,0)
su[0,1] = FF(th31-pi/2.,th32,pi,ph32,0)
su[0,2] = FF(th31-pi/2.,th32-pi/2.,pi,ch32,0)
## middle row
su[1,0] = FF(th31-pi/2.,pi,th21,ph21,0)
su[1,1] = FF(th31,th32,th21,-ph31+ph32+ph21,ch32+ch21)
su[1,2] = FF(th31,th32-pi/2.,th21,-ph31+ch32+ph21,ph32+ch21)
## bottom row
su[2,0] = FF(th31-pi/2.,pi,th21-pi/2.,ch21,0)
su[2,1] = FF(th31,th32,th21-pi/2,-ph31+ph32+ch21,ch32+ph21)
su[2,2] = FF(th31,th32-pi/2,th21-pi/2,-ph31+ch32+ch21,ph32+ph21)
## return
return 1.*su
## make a set of projectors from the columns of a unitary matrix
def PROJ(U):
proj = np.array([couter(U[i]) for i in range(len(U))], dtype=complex)
return 1.*proj
## combine two sets of projectors by tensor product
def PROJPROD(PA,PB):
return 1.*np.array([kprod(pa,pb) for pa in PA for pb in PB], dtype=complex)
## combine a list of sets of projectors by tensor product
def PROJMP(PX):
proj = PX[0]
for j in range(1,len(PX)):
proj = PROJPROD(proj,PX[j])
return 1.*proj
## product projectors parameterized by real vector x
## n=(nA,nB,...) dictates how dimensions split into product
def PROJN(x=np.zeros(6), n=[2,2], factors_out=False):
n = | np.array(n, dtype=int) | numpy.array |
import os
import numpy as np
import pydensecrf.densecrf as dcrf
from pydensecrf.utils import unary_from_softmax
import matplotlib
matplotlib.use("TkAgg")
import matplotlib.pyplot as plt
class DenseCRF:
def __init__(self):
# self.gauss_sxy = 3
# self.gauss_compat = 30
# self.bilat_sxy = 10
# self.bilat_srgb = 20
# self.bilat_compat = 50
# self.n_infer = 5
self.gauss_sxy = 3
self.gauss_compat = 30
self.bilat_sxy = 10
self.bilat_srgb = 20
self.bilat_compat = 50
self.n_infer = 5
def load_config(self, path):
if os.path.exists(path):
config = np.load(path)
self.gauss_sxy, self.gauss_compat, self.bilat_sxy, self.bilat_srgb, self.bilat_compat, self.n_config = \
config[0]
else:
print('Warning: dense CRF config file ' + path + ' does not exist - using defaults')
def process(self, probs, images):
# Set up variable sizes
num_input_images = probs.shape[0]
num_classes = probs.shape[1]
size = images.shape[1:3]
crf = np.zeros((num_input_images, num_classes, size[0], size[1]))
for iter_input_image in range(num_input_images):
pass_class_inds = np.where(np.sum(np.sum(probs[iter_input_image], axis=1), axis=1) > 0)
# Set up dense CRF 2D
d = dcrf.DenseCRF2D(size[1], size[0], len(pass_class_inds[0]))
if len(pass_class_inds[0]) > 0:
cur_probs = probs[iter_input_image, pass_class_inds[0]]
# Unary energy
U = np.ascontiguousarray(unary_from_softmax(cur_probs))
d.setUnaryEnergy(U)
# Penalize small, isolated segments
# (sxy are PosXStd, PosYStd)
d.addPairwiseGaussian(sxy=self.gauss_sxy, compat=self.gauss_compat)
# Incorporate local colour-dependent features
# (sxy are Bi_X_Std and Bi_Y_Std,
# srgb are Bi_R_Std, Bi_G_Std, Bi_B_Std)
d.addPairwiseBilateral(sxy=self.bilat_sxy, srgb=self.bilat_srgb, rgbim= | np.uint8(images[iter_input_image]) | numpy.uint8 |
from torch import nn
import numpy as np
import torch
import sys
# import torch.nn.functional as F # Deprecated
# 因果卷积，哪里体现了因果呢？dilation吗？
# 因为是逐层递推的，所以是因果卷积
# 假设seq=8, 则layer=0,1,2, 经过三层CausalConv单词维度划分为：
# [embedding0, 0, 0, 0]
# [embedding3, 3, 23, 0123]
# [embedding7, 67, 4567, 01234567]
# 不断汇聚前文信息
class CausalConv1d(nn.Module):
# dilation: 膨胀
# kernel_size始终为2
def __init__(self, in_channels, out_channels, kernel_size=2, dilation=2):
super().__init__()
self.padding = dilation
self.causal_conv = nn.Conv1d(in_channels, out_channels, kernel_size, padding=self.padding, dilation=dilation)
def forward(self, minibatch):
# 保持序列长度不变
return self.causal_conv(minibatch)[:, :, :-self.padding]
class DenseBlock(nn.Module):
"""卷积后拼接在一起"""
def __init__(self, in_channels, filters, dilation=2):
super().__init__()
self.causal_conv1 = CausalConv1d(in_channels, out_channels=filters, dilation=dilation)
self.causal_conv2 = CausalConv1d(in_channels, out_channels=filters, dilation=dilation)
def forward(self, minibatch):
tanh = torch.tanh(self.causal_conv1(minibatch))
sig = torch.sigmoid(self.causal_conv2(minibatch))
# element-wise product
return torch.cat([minibatch, tanh * sig], dim=1)
class TCBlock(nn.Module):
def __init__(self, in_channels, filters, seq_len):
"""
不能处理变长数据，可能需要save then load
"""
super().__init__()
layer_count = np.ceil(np.log2(seq_len)).astype(np.int) # 取对数，上取整
blocks = []
channel_count = in_channels
for layer in range(layer_count):
# 序列长度：
# L_out = L_in + 2 * padding - dilation
# 经过DenseBlock序列长度是不变的
block = DenseBlock(channel_count, filters, dilation=2**layer)
blocks.append(block)
channel_count += filters
self.tcblock = nn.Sequential(*blocks)
self._dim = channel_count
def forward(self, minibatch):
return self.tcblock(minibatch)
@property
def dim(self): # 向量维度
return self._dim
class AttentionBlock(nn.Module):
def __init__(self, dims, k_size, v_size):
"""
self-attention
:param dims: 输入维度
:param k_size: key维度
:param v_size: value维度
"""
super().__init__()
self.key_layer = nn.Linear(dims, k_size)
self.query_layer = nn.Linear(dims, k_size)
self.value_layer = nn.Linear(dims, v_size)
self.sqrt_k = | np.sqrt(k_size) | numpy.sqrt |
from moviepy.editor import VideoFileClip
from camera_calibration import camera_calibration
import cv2
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
from pipeline import pipeline
ret, mtx, dist, rvecs, tvecs = camera_calibration()
# straight_lines1.jpg
src = np.float32([[209, 719], [1095, 719], [538, 492], [751, 492]])
dst = np.float32([[209, 719], [1095, 719], [209, 0], [1095, 0]])
M1 = cv2.getPerspectiveTransform(src, dst)
Minv1 = cv2.getPerspectiveTransform(dst, src)
# print(M1)
# straight_lines2.jpg
src = np.float32([[228, 719], [1109, 719], [537, 492], [757, 492]])
dst = np.float32([[228, 719], [1109, 719], [228, 0], [1109, 0]])
M2 = cv2.getPerspectiveTransform(src, dst)
Minv2 = cv2.getPerspectiveTransform(dst, src)
# print(M2)
M = (M1 + M2) / 2
Minv = (Minv1 + Minv2) / 2
print(M)
def process_image(img):
img = cv2.undistort(img, mtx, dist, None, mtx)
threshed = pipeline(img)
height, width, channels = img.shape
binary_warped = cv2.warpPerspective(threshed, M, (width, height), flags=cv2.INTER_LINEAR)
# Assuming you have created a warped binary image called "binary_warped"
# Take a histogram of the bottom half of the image
histogram = np.sum(binary_warped[binary_warped.shape[0] // 2:, :], axis=0)
# Create an output image to draw on and visualize the result
out_img = np.dstack((binary_warped, binary_warped, binary_warped)) * 255
# Find the peak of the left and right halves of the histogram
# These will be the starting point for the left and right lines
midpoint = | np.int(histogram.shape[0] // 2) | numpy.int |
import numpy as np
from allocmodel.topics.OptimizerRhoOmegaBetter import kvec
from util import NumericUtil
from util import digamma, gammaln
from util.StickBreakUtil import rho2beta
from util.NumericUtil import calcRlogRdotv_allpairs
from util.NumericUtil import calcRlogRdotv_specificpairs
from util.NumericUtil import calcRlogR_allpairs, calcRlogR_specificpairs
from util.NumericUtil import calcRlogR, calcRlogRdotv
from util.SparseRespStatsUtil import calcSparseRlogR, calcSparseRlogRdotv
from util.SparseRespStatsUtil \
import calcSparseMergeRlogR, calcSparseMergeRlogRdotv
ELBOTermDimMap = dict(
slackTheta='K',
slackThetaRem=None,
gammalnTheta='K',
gammalnThetaRem=None,
gammalnSumTheta=None,
Hresp=None,
)
def calcELBO(**kwargs):
""" Calculate ELBO objective for provided model state.
Returns
-------
L : scalar float
L is the value of the objective function at provided state.
"""
Llinear = calcELBO_LinearTerms(**kwargs)
Lnon = calcELBO_NonlinearTerms(**kwargs)
if isinstance(Lnon, dict):
Llinear.update(Lnon)
return Llinear
return Lnon + Llinear
def calcELBO_LinearTerms(SS=None, LP=None,
nDoc=None,
rho=None, omega=None, Ebeta=None,
alpha=0, gamma=None,
afterGlobalStep=0, todict=0, **kwargs):
""" Calculate ELBO objective terms that are linear in suff stats.
Returns
-------
L : scalar float
L is sum of any term in ELBO that is const/linear wrt suff stats.
"""
if LP is not None:
nDoc = LP['theta'].shape[0]
elif SS is not None:
nDoc = SS.nDoc
return L_alloc(
nDoc=nDoc, rho=rho, omega=omega, Ebeta=Ebeta,
alpha=alpha, gamma=gamma, todict=todict)
def calcELBO_NonlinearTerms(Data=None, SS=None, LP=None, todict=0,
rho=None, Ebeta=None, alpha=None,
resp=None,
nDoc=None, DocTopicCount=None,
theta=None, thetaRem=None,
ElogPi=None, ElogPiRem=None,
sumLogPi=None,
sumLogPiRem=None, sumLogPiRemVec=None,
Hresp=None, slackTheta=None, slackThetaRem=None,
gammalnTheta=None, gammalnSumTheta=None,
gammalnThetaRem=None,
thetaEmptyComp=None, ElogPiEmptyComp=None,
ElogPiOrigComp=None,
gammalnThetaOrigComp=None, slackThetaOrigComp=None,
returnMemoizedDict=0, **kwargs):
""" Calculate ELBO objective terms non-linear in suff stats.
"""
if resp is not None:
N, K = resp.shape
elif LP is not None:
if 'resp' in LP:
N, K = LP['resp'].shape
else:
N, K = LP['spR'].shape
if Ebeta is None:
Ebeta = rho2beta(rho, returnSize='K+1')
if LP is not None:
DocTopicCount = LP['DocTopicCount']
nDoc = DocTopicCount.shape[0]
theta = LP['theta']
thetaRem = LP['thetaRem']
ElogPi = LP['ElogPi']
ElogPiRem = LP['ElogPiRem']
sumLogPi = np.sum(ElogPi, axis=0)
sumLogPiRem = | np.sum(ElogPiRem) | numpy.sum |
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
from perlin import generate_perlin
def gaussian_2d_fast(size, amp, mu_x, mu_y, sigma):
x = np.arange(0, 1, 1/size[0])
y = np.arange(0, 1, 1/size[1])
xs, ys = np.meshgrid(x,y)
dxs = np.minimum(np.abs(xs-mu_x), 1-np.abs(xs-mu_x))
dys = np.minimum(np.abs(ys-mu_y), 1-np.abs(ys-mu_y))
heat_map = amp*np.exp(-(dxs**2+dys**2)/(2*sigma**2))
return heat_map
def excitability_matrix(sigma_e, sigma_i, perlin_scale, grid_offset,
p_e=0.05, p_i=0.05, we=0.22, g=4,
n_row_e=120, n_row_i=60, mu_gwn=0, multiple_connections=True,
expected_connectivity=True, is_plot=True):
n_pop_e = n_row_e**2
n_pop_i = n_row_i**2
gL = 25 * 1e-9 # Siemens
p_max_e = p_e / (2 * np.pi * sigma_e**2)
p_max_i = p_i / (2 * np.pi * sigma_i**2)
# Two landscapes: e and i. The contribution of each neuron is stored separately in the n_row_e**2 matrices
e_landscape = np.zeros((n_row_e**2, n_row_e, n_row_e))
i_landscape = np.zeros((n_row_i**2, n_row_e, n_row_e))
perlin = generate_perlin(n_row_e, perlin_scale, seed_value=0)
x = np.arange(0,1,1/n_row_e)
y = np.arange(0,1,1/n_row_e)
X, Y = np.meshgrid(x,y)
U = np.cos(perlin)
V = np.sin(perlin)
# Excitatory
mu_xs = np.arange(0,1,1/n_row_e)
mu_ys = np.arange(0,1,1/n_row_e)
counter = 0
for i, mu_x in enumerate(mu_xs):
for j, mu_y in enumerate(mu_ys):
x_offset = grid_offset / n_row_e * np.cos(perlin[i,j])
y_offset = grid_offset / n_row_e * np.sin(perlin[i,j])
mh = gaussian_2d_fast((n_row_e, n_row_e), p_max_e, mu_x+x_offset, mu_y+y_offset, sigma_e)
if not multiple_connections:
#clip probabilities at 1
e_landscape[counter] = np.minimum(mh, np.ones(mh.shape))
else:
e_landscape[counter] = mh
counter += 1
# Inhibitory
mu_xs = np.arange(1/n_row_e,1+1/n_row_e,1/n_row_i)
mu_ys = np.arange(1/n_row_e,1+1/n_row_e,1/n_row_i)
counter = 0
for mu_x in mu_xs:
for mu_y in mu_ys:
mh = gaussian_2d_fast((n_row_e, n_row_e), p_max_i, mu_x, mu_y, sigma_i)
if not multiple_connections:
#clip probabilities at 1
i_landscape[counter] = np.minimum(mh, | np.ones(mh.shape) | numpy.ones |
from __future__ import print_function
import argparse
import numpy as np
import cv2
ap = argparse.ArgumentParser()
ap.add_argument("-i", "--image", required = True,
help = "path to the image")
args = vars(ap.parse_args())
image = cv2.imread(args["image"])
image = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
cv2.imshow("Image", image)
cv2.waitKey(0)
lap = cv2.Laplacian(image,cv2.CV_64F)
lap = np.uint8(np.absolute(lap))
cv2.imshow("Laplacian", lap)
cv2.waitKey(0)
sobelX = cv2.Sobel(image, cv2.CV_64F, 1, 0)
sobelY = cv2.Sobel(image, cv2.CV_64F, 0, 1)
sobelX = np.uint8(np.absolute(sobelX))
sobelY = np.uint8(np.absolute(sobelY))
sobelCombined = cv2.bitwise_or(sobelX, sobelY)
cv2.imshow("three", | np.hstack([sobelX, sobelY, sobelCombined]) | numpy.hstack |
"""@package etddf
Shares the N most recent measurements of an agent into the buffer
"""
__author__ = "<NAME>"
__copyright__ = "Copyright 2020, COHRINT Lab"
__email__ = "<EMAIL>"
__status__ = "Development"
__license__ = "MIT"
__maintainer__ = "<NAME>"
from copy import deepcopy
from etddf.etfilter import ETFilter, ETFilter_Main
from etddf.ros2python import get_internal_meas_from_ros_meas
from etddf_minau.msg import Measurement
import time
from pdb import set_trace as st
import numpy as np
import scipy
import scipy.optimize
import rospy
# Just used for debugging
# class Measurement:
# def __init__(self, meas_type, stamp, src_asset, measured_asset, data, variance, global_pose):
# self.meas_type = meas_type
# self.stamp = stamp
# self.src_asset = src_asset
# self.measured_asset = measured_asset
# self.data = data
# self.variance = variance
# self.global_pose = global_pose
class MostRecent:
"""Windowed Communication Event Triggered Communication
Provides a buffer that can be pulled and received from another. Just shares the N most recent measurements of another agent
"""
def __init__(self, num_ownship_states, x0, P0, buffer_capacity, meas_space_table, delta_codebook_table, delta_multipliers, asset2id, my_name, default_meas_variance):
"""Constructor
Arguments:
num_ownship_states {int} -- Number of ownship states for each asset
x0 {np.ndarray} -- initial states
P0 {np.ndarray} -- initial uncertainty
buffer_capacity {int} -- capacity of measurement buffer
meas_space_table {dict} -- Hash that stores how much buffer space a measurement takes up. Str (meas type) -> int (buffer space)
delta_codebook_table {dict} -- Hash that stores delta trigger for each measurement type. Str(meas type) -> float (delta trigger)
delta_multipliers {list} -- List of delta trigger multipliers
asset2id {dict} -- Hash to get the id number of an asset from the string name
my_name {str} -- Name to loopkup in asset2id the current asset's ID#
default_meas_variance {dict} -- Hash to get measurement variance
"""
self.meas_ledger = []
self.asset2id = asset2id
self.my_name = my_name
self.default_meas_variance = default_meas_variance
self.filter = ETFilter(asset2id[my_name], num_ownship_states, 3, x0, P0, True)
# Remember for instantiating new LedgerFilters
self.num_ownship_states = num_ownship_states
self.buffer_capacity = buffer_capacity
self.meas_space_table = meas_space_table
self.last_update_time = None
def add_meas(self, ros_meas, common=False):
"""Adds a measurement to filter
Arguments:
ros_meas {etddf.Measurement.msg} -- Measurement taken
Keyword Arguments:
delta_multiplier {int} -- not used (left to keep consistent interface)
force_fuse {bool} -- not used
"""
src_id = self.asset2id[ros_meas.src_asset]
if ros_meas.measured_asset in self.asset2id.keys():
measured_id = self.asset2id[ros_meas.measured_asset]
elif ros_meas.measured_asset == "":
measured_id = -1 #self.asset2id["surface"]
else:
rospy.logerr("ETDDF doesn't recognize: " + ros_meas.measured_asset + " ... ignoring")
return
meas = get_internal_meas_from_ros_meas(ros_meas, src_id, measured_id)
self.filter.add_meas(meas)
self.meas_ledger.append(ros_meas)
@staticmethod
def run_covariance_intersection(xa, Pa, xb, Pb):
"""Runs covariance intersection on the two estimates A and B
Arguments:
xa {np.ndarray} -- mean of A
Pa {np.ndarray} -- covariance of A
xb {np.ndarray} -- mean of B
Pb {np.ndarray} -- covariance of B
Returns:
c_bar {np.ndarray} -- intersected estimate
Pcc {np.ndarray} -- intersected covariance
"""
Pa_inv = np.linalg.inv(Pa)
Pb_inv = np.linalg.inv(Pb)
fxn = lambda omega: np.trace(np.linalg.inv(omega*Pa_inv + (1-omega)*Pb_inv))
omega_optimal = scipy.optimize.minimize_scalar(fxn, bounds=(0,1), method="bounded").x
# print("Omega: {}".format(omega_optimal)) # We'd expect a value of 1
Pcc = np.linalg.inv(omega_optimal*Pa_inv + (1-omega_optimal)*Pb_inv)
c_bar = Pcc.dot( omega_optimal*Pa_inv.dot(xa) + (1-omega_optimal)*Pb_inv.dot(xb))
jump = max( [np.linalg.norm(c_bar - xa), np.linalg.norm(c_bar - xb)] )
if jump > 10: # Think this is due to a floating point error in the inversion
print("!!!!!!!!!!! BIG JUMP!!!!!!!")
print(xa)
print(xb)
print(c_bar)
print(omega_optimal)
print(Pa)
print(Pb)
print(Pcc)
return c_bar.reshape(-1,1), Pcc
def psci(self, x_prior, P_prior, c_bar, Pcc):
""" Partial State Update all other states of the filter using the result of CI
Arguments:
x_prior {np.ndarray} -- This filter's prior estimate (over common states)
P_prior {np.ndarray} -- This filter's prior covariance
c_bar {np.ndarray} -- intersected estimate
Pcc {np.ndarray} -- intersected covariance
Returns:
None
Updates self.main_filter.filter.x_hat and P, the delta tier's primary estimate
"""
# Full state estimates
x = self.filter.x_hat
P = self.filter.P
D_inv = | np.linalg.inv(Pcc) | numpy.linalg.inv |
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