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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])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,-1,0,0,0,1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,-1,0,0,0,1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,0,-1,1,0,0,0,-1,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([0,1,0,0,0,-1,-1,0,0])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([1,0,0,0,-1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,1,0,0,0,-1])
rot.shape = (3, 3)
trans_num = N.array([0,0,0])
trans_den = N.array([1,1,1])
transformations.append((rot, trans_num, trans_den))
rot = N.array([-1,0,0,0,-1,0,0,0,1])
rot.shape = (3, 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]) | numpy.array |
'''
Created on Mar 23, 2012
@author: <NAME> (<EMAIL>)
'''
from run_rmhd2d import rmhd2d
import numpy as np
from numpy import abs
import time
from petsc4py import PETSc
from rmhd.solvers.common.PETScDerivatives import PETScDerivatives
from rmhd.solvers.linear.PETScPoissonCFD2 import PETScPoisson
from rmhd.solvers.nonlinear.PETScNonlinearSolverArakawaJ1CFD2 import PETScSolver
from rmhd.solvers.nonlinear.PETScNonlinearSolverArakawaJ1CFD2DB import PETScSolverDB
from rmhd.solvers.preconditioner.PETScPreconditionerArakawaJ1CFD2DOF2Vec import PETScPreconditioner
class rmhd2d_ppc(rmhd2d):
'''
PETSc/Python Reduced MHD Solver in 2D using physics based preconditioner.
'''
def __init__(self, cfgfile):
'''
Constructor
'''
super().__init__(cfgfile, mode = "ppc")
OptDB = PETSc.Options()
# OptDB.setValue('ksp_monitor', '')
# OptDB.setValue('snes_monitor', '')
#
# OptDB.setValue('log_info', '')
# OptDB.setValue('log_summary', '')
#
# OptDB.setValue('ksp_initial_guess_nonzero', 1)
# OptDB.setValue('pc_type', 'hypre')
# OptDB.setValue('pc_hypre_type', 'boomeramg')
OptDB.setValue('pc_hypre_boomeramg_max_iter', 2)
# OptDB.setValue('pc_hypre_boomeramg_max_levels', 6)
# OptDB.setValue('pc_hypre_boomeramg_tol', 1e-7)
# create Jacobian, Function, and linear Matrix objects
if self.cfg["solver"]["preconditioner"] == 'none' or self.cfg["solver"]["preconditioner"] == None:
self.petsc_precon = None
else:
self.petsc_precon = PETScPreconditioner(self.da1, self.da4, self.nx, self.ny, self.ht, self.hx, self.hy)#, self.de)
self.petsc_precon.set_tolerances(poisson_rtol=self.cfg['solver']['pc_poisson_rtol'],
poisson_atol=self.cfg['solver']['pc_poisson_atol'],
poisson_max_it=self.cfg['solver']['pc_poisson_max_iter'],
parabol_rtol=self.cfg['solver']['pc_parabol_rtol'],
parabol_atol=self.cfg['solver']['pc_parabol_atol'],
parabol_max_it=self.cfg['solver']['pc_parabol_max_iter'],
jacobi_max_it=self.cfg['solver']['pc_jacobi_max_iter'])
if self.nu != 0.:
self.petsc_solver = PETScSolverDB(self.da1, self.da4, self.nx, self.ny, self.ht, self.hx, self.hy, self.de, self.petsc_precon, self.nu)
else:
self.petsc_solver = PETScSolver(self.da1, self.da4, self.nx, self.ny, self.ht, self.hx, self.hy, self.de, self.petsc_precon)
# initialise matrixfree Jacobian
self.Jmf = PETSc.Mat().createPython([self.x.getSizes(), self.b.getSizes()],
context=self.petsc_solver,
comm=PETSc.COMM_WORLD)
self.Jmf.setUp()
# self.Jmf.setNullSpace(self.solver_nullspace)
# create PC shell
# self.pc = PETSc.PC().createPython(context=self.petsc_precon,
# comm=PETSc.COMM_WORLD)
# self.pc.setFromOptions()
# self.pc.setUp()
# create linear solver
self.ksp = PETSc.KSP().create()
self.ksp.setFromOptions()
self.ksp.setOperators(self.Jmf)
self.ksp.setInitialGuessNonzero(True)
self.ksp.setType('fgmres')
self.ksp.getPC().setType('none')
# self.ksp.getPC().setType(PETSc.PC.Type.SHELL)
# self.ksp.setPC(PETSc.PCShell(self.petsc_precon))
# self.ksp.setPC(self.pc)
# self.ksp.setPC(self.ksp.getPC().createPython(context=self.petsc_precon, comm=PETSc.COMM_WORLD))
# self.ksp.setPCSide(PETSc.KSP.PCSide.RIGHT)
self.ksp.setUp()
# update solution history
self.petsc_solver.update_previous(self.x)
def __del__(self):
self.ksp.destroy()
self.Jmf.destroy()
def run(self):
run_time = time.time()
alpha = 1.5
gamma = 0.9
ksp_rtol_max = 1E-3
for itime in range(1, self.nt+1):
if PETSc.COMM_WORLD.getRank() == 0:
localtime = time.asctime( time.localtime(time.time()) )
print("\nit = %4d, t = %10.4f, %s" % (itime, self.ht*itime, localtime) )
print
# calculate initial guess
if self.cfg['solver']['petsc_snes_initial_guess']:
self.calculate_initial_guess(initial=itime==1)
# self.calculate_initial_guess(initial=True)
# update history
self.petsc_solver.update_history()
# copy initial guess to x
if self.cfg['solver']['petsc_snes_initial_guess']:
self.copy_x_from_da1_to_da4()
# solve
i = 0
self.petsc_solver.update_previous(self.x)
self.petsc_solver.function(self.f)
pred_norm = self.f.norm()
prev_norm = pred_norm
tolerance = self.tolerance + self.cfg['solver']['petsc_snes_rtol'] * pred_norm
if PETSc.COMM_WORLD.getRank() == 0:
print(" Nonlinear Solver Iteration %i: residual = %22.16E" % (i, pred_norm))
while True:
i+=1
self.f.copy(self.b)
self.b.scale(-1.)
if self.petsc_precon == None:
self.dx.set(0.)
else:
self.b.copy(self.dy)
if self.cfg['solver']['petsc_ksp_adapt_rtol']:
if i == 1:
zeta_A = 0.
zeta_B = 0.
zeta_C = 0.
zeta_D = 0.
ksp_tol = self.cfg['solver']['petsc_ksp_rtol']
else:
zeta_A = gamma * np.power(pred_norm / prev_norm , alpha)
zeta_B = np.power(ksp_tol, alpha)
zeta_C = np.min([ksp_rtol_max, np.max(zeta_A, zeta_B)])
zeta_D = gamma * tolerance / pred_norm
ksp_tol = np.min([ksp_rtol_max, | np.max(zeta_C, zeta_D) | numpy.max |
#!/usr/bin/env python
"""
Copyright 2010-2018 University Of Southern California
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.
# This is PYTHON port of Walter Imperatori GeoBB_srf.m matlab code
# Function to calculate stations position in CompSyn geometry convention.
# It also calculates stations and hypocenter positions in BBTool geometry.
# Then it provides some parameters useful for subsequent analysis, such
# as different type of station-to-fault distances.
# INPUT:
#
# stat_file - file with coordinates (lon/lat) of the stations
# flag - flag for plots ('y' or 'n')
# Note: Plotting feature is not implemented in this version.
# filename - srf input filename
# extended - flag for extended fault computations ('y' or 'n')
#
# OUTPUT:
# par - array with several parameters:
# par.bbextent - "far-side" for the BBTool code
# par.hypo - hypocentral coordinates for BBTool
# par.Mw - moment magnitude
# par.mecha - general mechanism
# par.subfault - subfaults coordinates
#
#
# Remarks: current version work only with positive dip
"""
from __future__ import division, print_function
# Import Python modules
import os
import sys
import math
import numpy as np
import pyproj
# Import Broadband modules
import bband_utils
from station_list import StationList
class GeoBBSRF(object):
def __init__(self, sim_id=0):
"""
Initialize class variables
"""
self.station_file = ''
self.sim_id = sim_id
self.mw = 0.0
self.mecha = ''
self.f_len = 0.0
self.f_width = 0.0
self.f_dip = 0.0
self.f_strike = 0.0
self.depth = 0.0
self.rake = 0.0
self.hyp = []
self.fault_maxlon = 0.0
self.fault_minlon = 0.0
self.fault_maxlat = 0.0
self.fault_minlat = 0.0
self.corn = []
self.projobj = None
self.extended = 'n'
def geo2cart(self, lon, lat, lonmin=0, latmin=0):
"""
# Function to convert geographic coordinates into cartesian ones
# Transversal Mercator projection is used
#
# INPUT:
# lon,lat -> input vectors with geographic coordinates
# lonmin,latmin -> lower-left-corner (on x-y plane)
# of plot box (used for shifting)
# OUTPUT:
# [x,y] -> computed cartesian coordinates (in meters)
"""
# m.geoid= [6378135 0.08181881]
# print "proj obj in geo2cart", self.projobj
[a, b] = self.projobj(lon, lat)
# print "[a,b] = self.projobj(lat,lon)", a,b
if lonmin == 0:
a0 = 0
b0 = 0
else:
[a0, b0] = self.projobj(lonmin, latmin)
# shift of [a0,b0]
x = (a - a0)
y = (b - b0)
return [x, y]
def translation_matrix(self, direction):
T = np.identity(4)
T[:3, 3] = direction[:3]
return T
def read_srf(self, srffile):
if os.path.exists(srffile):
srff = open(srffile, 'r')
else:
raise bband_utils.ParameterError("Missing SRF file (%s)!" %
(srffile))
# Check number of planes
version = float(srff.readline().strip().split()[0])
tokens = srff.readline().strip().split()
# Make sure we have a valid SRF file
if len(tokens) != 2:
raise bband_utils.ProcessingError("Invalid SRF file (%s)!" %
(srffile))
planes = int(tokens[1])
# Make sure we have only 1 plane
if planes > 1:
raise bband_utils.ProcessingError("Only one plane is supported!" +
" Found %d planes in SRF file!" %
(planes))
# Read Fault Data
tokens = srff.readline().strip().split()
if len(tokens) != 6:
raise bband_utils.ProcessingError("Invalid SRF file (%s)!" %
(srffile))
self.f_len = float(tokens[4])
self.f_width = float(tokens[5])
tokens = srff.readline().strip().split()
if len(tokens) != 5:
raise bband_utils.ProcessingError("Invalid SRF file (%s)!" %
(srffile))
self.f_strike = float(tokens[0])
self.f_dip = float(tokens[1])
self.f_depth = float(tokens[2])
tokens = srff.readline().strip().split()
if len(tokens) != 2:
raise bband_utils.ProcessingError("Invalid SRF file (%s)!" %
(srffile))
n_cels = int(tokens[1])
# print ("F_len: %f, F_width: %f, F_Strike: %f" %
# (self.f_len, self.f_width, self.f_strike))
# print ("F_dip: %f, F_depth: %f, n_cells: %d" %
# (self.f_dip, self.f_depth, n_cels))
M0 = 0.0
lon = []
lat = []
dep = []
tinit = []
rake = []
for i in range(0, n_cels):
tokens = srff.readline().strip().split()
if version == 1.0 and len(tokens) != 8:
raise bband_utils.ProcessingError("Invalid SRF version 1 "
"file (%s)!" %
(srffile))
if version == 2.0 and len(tokens) != 10:
raise bband_utils.ProcessingError("Invalid SRF version 2 "
"file (%s)!" %
(srffile))
lon.append(float(tokens[0]))
lat.append(float(tokens[1]))
dep.append(float(tokens[2]))
area = float(tokens[5])
tinit.append(float(tokens[6]))
tokens = srff.readline().strip().split()
if len(tokens) != 7:
raise bband_utils.ProcessingError("Invalid SRF file (%s)!" %
(srffile))
rake.append(float(tokens[0]))
slip1 = float(tokens[1])
slip2 = float(tokens[3])
slip3 = float(tokens[5])
nt1 = float(tokens[2])
nt2 = float(tokens[4])
nt3 = float(tokens[6])
if nt1 > 0:
for k in range(0, int(math.ceil(nt1 / 6.0))):
token = srff.readline()
if token == "":
raise bband_utils.ProcessingError("Invalid SRF "
"file (%s)!" %
(srffile))
if nt2 > 0:
for k in range(0, int(math.ceil(nt2 / 6.0))):
token = srff.readline()
if token == "":
raise bband_utils.ProcessingError("Invalid SRF "
"file (%s)!" %
(srffile))
if nt3 > 0:
for k in range(0, int(math.ceil(nt3 / 6.0))):
token = srff.readline()
if token == "":
raise bband_utils.ProcessingError("Invalid SRF "
"file (%s)!" %
(srffile))
M0 = M0 + (area *
(math.sqrt(slip1**2 + slip2**2 + slip3**2))*3)*(10**11)
srff.close()
np_tinit = np.array(tinit)
tinit_index = []
[tinit_index] = np.nonzero(np_tinit == np.min(np_tinit))
# Find hypocenter
hyp = []
hyp.append(lon[tinit_index[0]])
hyp.append(lat[tinit_index[0]])
hyp.append(dep[tinit_index[0]])
self.hyp = hyp
# Find mw
mw = (math.log10(M0)) / 1.5 - 10.73
self.mw = mw
# Find rake (i.e. mechanism)
rake_ave = np.mean(np.array(rake))
self.rake = rake_ave
if rake_ave > 45 and rake_ave < 135:
mecha = 'rs'
if rake_ave >= 135 and rake_ave < 225:
mecha = 'ss'
if rake_ave >= 225 and rake_ave < 315:
mecha = 'ns'
if rake_ave <= 45 or rake_ave >= 315:
mecha = 'ss'
self.mecha = mecha
# print "mw: %f, rake_ave: %f, mecha:%s"%(mw, rake_ave, mecha)
if self.extended == 'y':
# Find fault corners
i = []
j = []
k = []
np_dep = np.array(dep)
# print np.min(np_dep), len(np_dep)
[i] = np.nonzero(np_dep == min(dep))
if len(i) < 1:
raise bband_utils.ProcessingError("Invalid SRF file: %s\n" %
(srffile) +
"len(i)=%d Failed to " %
len(i) + "calculate " +
"extended fault data!")
np_lon = np.array(lon)
[j] = np.nonzero(np_lon[i] == np.min(np_lon[i]))
if len(j) < 1:
raise bband_utils.ProcessingError("Invalid SRF file: %s\n" %
(srffile) +
"len(j)=%d Failed to " %
len(j) + "calculate " +
"extended fault data!")
np_lat = np.array(lat)
[k] = np.nonzero(np_lat[j] == np.min(np_lat[j]))
if len(k) == 1:
lat_index = k[0]
self.corn = [lon[lat_index], lat[lat_index]]
# print "Corner:", self.corn
else:
raise bband_utils.ProcessingError("Invalid SRF file: %s\n" %
(srffile) +
"len(k)=%d Failed to " %
len(k) + "calculate " +
"extended fault data!")
self.fault_maxlon = np.max(np_lon)
self.fault_minlon = np.min(np_lon)
self.fault_maxlat = np.max(np_lat)
self.fault_minlat = np.min(np_lat)
#print ("fault_maxlon: %f, fault_minlon: %f, fault_maxlat: %f, " %
# (self.fault_maxlon,self.fault_minlon,self.fault_maxlat) +
# "fault_minlat: %f" % (self.fault_minlat))
# par.mw = mw; par.mecha = mecha;
return 0
def write_xyz_srf(self, srf_file, xyz_srf_file, T3M):
"""
Reads the SRF file and converts its lat/lon to XYZ format
using self.latmin and self.lonmin as reference points. The T3M
matrix is used to shift the coordinates to the new reference
point calculated in the run function.
"""
# Open files
infile = open(srf_file, 'r')
outfile = open(xyz_srf_file, 'w')
# Pick up version number from SRF file
version = float(infile.readline().strip().split()[0])
# Now go back to the start
infile.seek(0)
# Copy lines
while True:
line = infile.readline()
# Cannot mix for line in infile with readline...
if line is None:
break
outfile.write(line)
# Until we find the plane line
if line.find("PLANE") >= 0:
break
tokens = line.strip().split()
# Make sure we have a valid SRF file
if len(tokens) != 2:
raise bband_utils.ProcessingError("Invalid SRF file (%s)!" %
(srf_file))
planes = int(tokens[1])
# Make sure we have only 1 plane
if planes > 1:
raise bband_utils.ProcessingError("Only one plane is " +
"supported!" +
" Found %d " % (planes) +
" in SRF file!")
line = infile.readline()
tokens = line.strip().split()
if len(tokens) != 6:
raise bband_utils.ProcessingError("Invalid SRF file (%s)!" %
(srf_file))
# Convert to XYZ
lon = float(tokens[0])
lat = float(tokens[1])
[x_cart, y_cart] = self.geo2cart(lon, lat, self.min_lon, self.min_lat)
tmp = T3M * np.mat([x_cart, y_cart, 0, 1]).transpose()
tokens[0] = str(float(tmp[0]))
tokens[1] = str(float(tmp[1]))
outfile.write(" %s\n" % " ".join(tokens))
# Continue copying
while True:
line = infile.readline()
# Cannot mix for line in infile with readline...
if line is None:
break
outfile.write(line)
if line.find("POINTS") >= 0:
break
# Figure out how many cells
tokens = line.strip().split()
if len(tokens) != 2:
raise bband_utils.ProcessingError("Invalid SRF file (%s)!" %
(srf_file))
n_cels = int(tokens[1])
# Go through each cell
for i in range(0, n_cels):
tokens = infile.readline().strip().split()
if version == 1.0 and len(tokens) != 8:
raise bband_utils.ProcessingError("Invalid SRF version 1 "
"file (%s)!" %
(srffile))
if version == 2.0 and len(tokens) != 10:
raise bband_utils.ProcessingError("Invalid SRF version 2 "
"file (%s)!" %
(srffile))
lon = float(tokens[0])
lat = float(tokens[1])
[x_cart, y_cart] = self.geo2cart(lon, lat,
self.min_lon, self.min_lat)
tmp = T3M * | np.mat([x_cart, y_cart, 0, 1]) | numpy.mat |
import math
import os
import random
import numpy as np
import torch
import torch.utils.data as data
from PIL import Image
from lib.utils.functional import read_mat, mapping_function
from ..utils.transforms import fliplr_joints, crop, generate_target, transform_pixel
class AFLW2000(data.Dataset):
def __init__(self, cfg, ds_type="train", transform=None, return_pose=False):
# specify annotation file for dataset
if ds_type == "train":
self.filenames = cfg.DATASET.TRAINSET
elif ds_type == "val":
self.filenames = cfg.DATASET.VALSET
elif ds_type == "test":
self.filenames = cfg.DATASET.TESTSET
else:
raise NotImplementedError("Dataset type %s is not implemented!" % ds_type)
self.is_train = (ds_type == "train")
self.transform = transform
self.return_pose = return_pose
self.data_root = cfg.DATASET.ROOT
self.input_size = cfg.MODEL.IMAGE_SIZE
self.output_size = cfg.MODEL.HEATMAP_SIZE
self.sigma = cfg.MODEL.SIGMA
self.scale_factor = cfg.DATASET.SCALE_FACTOR
self.rot_factor = cfg.DATASET.ROT_FACTOR
self.label_type = cfg.MODEL.TARGET_TYPE
self.flip = cfg.DATASET.FLIP
self.num_joints = cfg.MODEL.NUM_JOINTS
# load annotations
self.images = []
self.landmarks = []
if self.return_pose:
self.pose = []
for filename in open(self.filenames, "r").read().splitlines():
file_path = os.path.join(self.data_root, filename)
mat_path = file_path.replace("jpg", "mat")
landmarks, pose, _ = read_mat(mat_path, pt3d=True)
self.images.append(file_path)
self.landmarks.append(landmarks)
if self.return_pose:
self.pose.append(pose)
self.mean = np.array([0.485, 0.456, 0.406], dtype=np.float32)
self.std = np.array([0.229, 0.224, 0.225], dtype=np.float32)
def __len__(self):
return len(self.images)
def __getitem__(self, idx):
image_path = self.images[idx]
if self.return_pose:
pose = self.pose[idx]
x_min = math.floor( | np.min(self.landmarks[idx][:, 0]) | numpy.min |
#!/usr/bin/python3
# -*- coding: utf-8 -*-
import sys
import os
from PyQt5.QtGui import *
from PyQt5.QtCore import *
from PyQt5.QtWidgets import *
from PyQt5 import QtCore, QtGui, QtWidgets
import cv2
import imutils
import numpy as np
import torch
from PIL import ImageDraw, ImageFont
from PIL import Image
from torch import nn
from data_tool.custom_dataset import CustomImageDataset
from torch.utils.data import DataLoader
from nets.mobilenet import MobileNet
from torchvision.io import read_image
from mainWindowLayout import MainLayout
# import cv2
# import numpy as np
from scipy import ndimage
from matplotlib import pyplot as plt
class MainWindow(QMainWindow, MainLayout):
imagePaths = []
originImages=[]
imageList = [] #二维的图像列表
hideLayoutTag=-1
def __init__(self,parent=None):
super(MainWindow, self).__init__(parent)
self.setupUi(self)
self.signalSlots()
#button与具体方法关联
def signalSlots(self):
#文件按钮相关方法
#打开
self.openAct.triggered.connect(lambda : importImage(self))
#保存
self.saveAct.triggered.connect(lambda : importImage(self))
#退出
self.exitAct.triggered.connect(self.close)
#编辑按钮相关方法
#放大
self.largeAct.triggered.connect(lambda : largeImage(self))
#缩小
self.smallAct.triggered.connect(lambda : smallImage(self))
#灰度
self.grayAct.triggered.connect(lambda : grayImage(self))
#亮度
self.brightAct.triggered.connect(lambda : brightImage(self))
#旋转
self.rotateAct.triggered.connect(lambda : rotateImage(self))
#截图
self.screenshotAct.triggered.connect(lambda : screenshotImage(self))
#变换按钮相关方法
#傅里叶变换
self.change1Act.triggered.connect(lambda : change1Image(self))
#离散余弦变换
self.change2Act.triggered.connect(lambda : change2Image(self))
#Radon变换
self.change3Act.triggered.connect(lambda : change3Image(self))
#噪声按钮相关方法
#高斯噪声
self.noise1Act.triggered.connect(lambda : noise1Image(self))
#椒盐噪声
self.noise2Act.triggered.connect(lambda : noise2Image(self))
#斑点噪声
self.noise3Act.triggered.connect(lambda : importImage(self))
#泊松噪声
self.noise4Act.triggered.connect(lambda : importImage(self))
#滤波按钮相关方法
#高通滤波
self.smoothing1Act.triggered.connect(lambda : smoothing1Image(self))
#低通滤波
self.smoothing2Act.triggered.connect(lambda : smoothing2Image(self))
#平滑滤波
self.smoothing3Act.triggered.connect(lambda : smoothing3Image(self))
#锐化滤波
self.smoothing4Act.triggered.connect(lambda : smoothing4Image(self))
#直方图统计按钮相关方法
#R直方图
self.hist1Act.triggered.connect(lambda : hist1Image(self))
#G直方图
self.hist2Act.triggered.connect(lambda : importImage(self))
#B直方图
self.hist3Act.triggered.connect(lambda : importImage(self))
#图像增强按钮相关方法
#伪彩色增强
self.enhance1Act.triggered.connect(lambda : enhance1Image(self))
#真彩色增强
self.enhance2Act.triggered.connect(lambda : enhance2Image(self))
#直方图均衡
self.enhance3Act.triggered.connect(lambda : histNormalized(self))
#NTSC颜色模型
self.enhance4Act.triggered.connect(lambda : enhance4Image(self))
#YCbCr颜色模型
self.enhance5Act.triggered.connect(lambda : enhance5Image(self))
#HSV颜色模型
self.enhance6Act.triggered.connect(lambda : enhance6Image(self))
#阈值分割方法
self.threButton.clicked.connect(lambda : threImage(self))
#形态学处理方法
self.morphologyProcessButton.clicked.connect(lambda : morphologyProcessImage(self))
#特征提取方法
self.featureButton.clicked.connect(lambda : featureImage(self))
#图像分类与识别方法
self.imgButton.clicked.connect(lambda : layoutChange(self))
self.cla_button.clicked.connect(lambda: cla(self))
#底部
#上一张
self.preButton.clicked.connect(lambda : preImage(self))
#下一张
self.nextButton.clicked.connect(lambda : nextImage(self))
#退出
self.exitButton.clicked.connect(self.close)
#编辑按钮相关方法
#放大
def largeImage(window):
imageList=[]
for img in window.originImages:
imgs=[]
img_info=img[0].shape
image_height=img_info[0]
image_weight=img_info[1]
dstHeight=int(2*image_height)
dstWeight=int(2*image_weight)
result=cv2.resize(img[0],(dstHeight,dstWeight))
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','放大后'])
#缩小
def smallImage(window):
imageList=[]
for img in window.originImages:
imgs=[]
img_info=img[0].shape
image_height=img_info[0]
image_weight=img_info[1]
dstHeight=int(0.5*image_height)
dstWeight=int(0.5*image_weight)
result=cv2.resize(img[0],(dstHeight,dstWeight))
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','缩小后'])
#灰度
def grayImage(window):
imageList=[]
for img in window.originImages:
imgs=[]
result = cv2.cvtColor(img[0], cv2.COLOR_BGR2RGB)
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','灰度处理后'])
#亮度
def brightImage(window):
imageList=[]
for img in window.originImages:
imgs=[]
rows, cols, chunnel = img[0].shape
blank = np.zeros([rows, cols, chunnel], img[0].dtype)
result = cv2.addWeighted(img[0], 1.3, blank, 1-1.3, 3)
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','调整亮度后'])
#旋转
def rotateImage(window):
imageList=[]
for img in window.originImages:
imgs=[]
img_info=img[0].shape
image_height=img_info[0]
image_weight=img_info[1]
mat_rotate=cv2.getRotationMatrix2D((image_height*0.5,image_weight*0.5),90,1) #center angle 3scale
result=cv2.warpAffine(img[0],mat_rotate,(image_height,image_weight))
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','旋转后'])
#截图
def screenshotImage(window):
imageList=[]
for img in window.originImages:
imgs=[]
result = img[0][70:170, 440:540]
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','截图后'])
#变换按钮相关方法
#傅里叶变换
def change1Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
b,g,r=cv2.split(img[0])
b_freImg,b_recImg=oneChannelDft(b)
g_freImg, g_recImg = oneChannelDft(g)
r_freImg, r_recImg = oneChannelDft(r)
freImg=cv2.merge([b_freImg,g_freImg,r_freImg])
imgs.extend([img[0],freImg])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','傅里叶变换后'])
def oneChannelDft(img):
width, height = img.shape
nwidth = cv2.getOptimalDFTSize(width)
nheigth = cv2.getOptimalDFTSize(height)
nimg = np.zeros((nwidth, nheigth))
nimg[:width, :height] = img
dft = cv2.dft(np.float32(nimg), flags=cv2.DFT_COMPLEX_OUTPUT)
ndft = dft[:width, :height]
ndshift = np.fft.fftshift(ndft)
magnitude = np.log(cv2.magnitude(ndshift[:, :, 0], ndshift[:, :, 1]))
result = (magnitude - magnitude.min()) / (magnitude.max() - magnitude.min()) * 255
frequencyImg = result.astype('uint8')
ilmg = cv2.idft(dft)
ilmg = cv2.magnitude(ilmg[:, :, 0], ilmg[:, :, 1])[:width, :height]
ilmg = np.floor((ilmg - ilmg.min()) / (ilmg.max() - ilmg.min()) * 255)
recoveredImg = ilmg.astype('uint8')
return frequencyImg,recoveredImg
#离散余弦变换
def change2Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
img1 = cv2.cvtColor(img[0], cv2.COLOR_BGR2RGB)
img_dct = cv2.dct(img1) #进行离散余弦变换
imgs.extend([img[0],img_dct])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','离散余弦变换后'])
#Radon变换
def change3Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
img_dct = cv2.dct(img[0])
result = np.log(abs(img_dct))
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','Radon变换后'])
#噪声按钮相关方法
#高斯噪声
#定义添加高斯噪声的函数
def addGaussianNoise(image,percetage):
G_Noiseimg = image
G_NoiseNum=int(percetage*image.shape[0]*image.shape[1])
for i in range(G_NoiseNum):
temp_x = np.random.randint(20,40)
temp_y = np.random.randint(20,40)
G_Noiseimg[temp_x][temp_y] = 255
return G_Noiseimg
def noise1Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
grayImage = cv2.cvtColor(img[0], cv2.COLOR_BGR2RGB) #灰度变换
result = addGaussianNoise(grayImage,0.01) #添加10%的高斯噪声
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','高斯噪声后'])
#椒盐噪声
#定义添加椒盐噪声的函数
def saltpepper(img,n):
m=int((img.shape[0]*img.shape[1])*n)
for a in range(m):
i=int(np.random.random()*img.shape[1])
j=int(np.random.random()*img.shape[0])
if img.ndim==2:
img[j,i]=255
elif img.ndim==3:
img[j,i,0]=255
img[j,i,1]=255
img[j,i,2]=255
for b in range(m):
i=int(np.random.random()*img.shape[1])
j=int(np.random.random()*img.shape[0])
if img.ndim==2:
img[j,i]=0
elif img.ndim==3:
img[j,i,0]=0
img[j,i,1]=0
img[j,i,2]=0
return img
def noise2Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
grayImage = cv2.cvtColor(img[0], cv2.COLOR_BGR2RGB) #灰度变换
result = saltpepper(grayImage,0.02)
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','椒盐噪声后'])
#滤波按钮相关方法
#高通滤波
def smoothing1Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
x=cv2.Sobel(img[0],cv2.CV_16S,1,0)
y=cv2.Sobel(img[0],cv2.CV_16S,0,1)
absx=cv2.convertScaleAbs(x)
absy=cv2.convertScaleAbs(y)
result = cv2.addWeighted(absx,0.5,absy,0.5,0)
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','高通滤波后'])
#低通滤波
def smoothing2Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
result = cv2.medianBlur(img[0],5)
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','低通滤波后'])
#平滑滤波
def smoothing3Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
result = cv2.blur(img[0], (5, 5))
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','平滑滤波后'])
#锐化滤波
def smoothing4Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
result = cv2.bilateralFilter(img[0],9,75,75)
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','锐化滤波后'])
#直方图统计按钮相关方法
#R直方图
def hist1Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
color = ('b','g','r')
for i,col in enumerate(color):
histr = cv2.calcHist([img[0]],[i],None,[256],[0,256])
plt.plot(histr,color = col)
plt.xlim([0,256])
plt.savefig("hist1.jpg")
result = cv2.imread("hist1.jpg")
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','R直方图后'])
#图像增强按钮相关方法
#伪彩色增强
def enhance1Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
grayImage = cv2.cvtColor(img[0], cv2.COLOR_BGR2RGB) #灰度变换
result = cv2.applyColorMap(grayImage, cv2.COLORMAP_JET)
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','伪彩色增强后'])
#真彩色增强
def enhance2Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
grayImage = cv2.cvtColor(img[0], cv2.COLOR_BGR2RGB) #灰度变换
result = cv2.applyColorMap(grayImage, cv2.COLORMAP_JET)
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','真彩色增强后'])
#直方图均衡
def histNormalized(window):
imageList=[]
for img in window.originImages:
imgs=[]
b, g, r = cv2.split(img[0])
b_equal = cv2.equalizeHist(b)
g_equal = cv2.equalizeHist(g)
r_equal = cv2.equalizeHist(r)
result = cv2.merge([b_equal, g_equal, r_equal])
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','直方图均衡化后'])
#NTSC颜色模型
def enhance4Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
result = cv2.cvtColor(img[0], cv2.COLOR_BGR2RGB)
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','NTSC颜色模型后'])
#YCbCr颜色模型
def enhance5Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
result = cv2.cvtColor(img[0], cv2.COLOR_BGR2YCR_CB)
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','YCbCr颜色模型后'])
#HSV颜色模型
def enhance6Image(window):
imageList=[]
for img in window.originImages:
imgs=[]
result = cv2.cvtColor(img[0],cv2.COLOR_BGR2HSV)
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','HSV颜色模型后'])
#阈值分割方法
def threImage(window):
imageList=[]
for img in window.originImages:
print(img.size)
imgs=[]
grayImage = cv2.cvtColor(img[0], cv2.COLOR_BGR2RGB) #灰度变换
result = cv2.threshold(grayImage, 127, 255, cv2.THRESH_BINARY)
imgs.extend([img[0],result])
imageList.append(imgs)
# resizeFromList(window, imageList)
showImage(window,['原图','阈值分割后'])
#形态学处理方法
def morphologyProcessImage(window):
imageList=[]
for img in window.originImages:
imgs=[]
kernel = cv2.getStructuringElement(cv2.MORPH_RECT,(3, 3))
result = cv2.erode(img[0],kernel)
imgs.extend([img[0],result])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','形态学处理后'])
#特征提取方法
def featureImage(window):
imageList=[]
for img in window.originImages:
imgs=[]
img1 = img[0].copy()
gray=cv2.cvtColor(img[0],cv2.COLOR_BGR2GRAY)
gray=np.float32(gray)
dst=cv2.cornerHarris(gray,2,3,0.04)
img[0][dst>0.01*dst.max()]=[0,0,255]
imgs.extend([img1,img[0]])
imageList.append(imgs)
resizeFromList(window, imageList)
showImage(window,['原图','特征提取后'])
def resizeFromList(imageList):
width=256
height=256
for x_pos in range(len(imageList)):
image=cv2.resize(imageList[x_pos], (width, height))
imageList[x_pos]=image
#打开图像
def importImage(window):
fnames, _ = QFileDialog.getOpenFileNames(window, 'Open file', '.', 'Image Files(*.jpg *.bmp *.png *.jpeg *.rgb *.tif)')
window.imagePaths = []
for fname in fnames:
if fname!='':
window.imagePaths.append(fname)
if window.imagePaths!=[]:
readIamge(window)
resizeFromList(window.originImages)
# print(len(window.originImages))
showImage(window)
def readIamge(window):
window.originImages=[]
for path in window.imagePaths:
img=cv2.imread(path)
window.originImages.append(img)
#显示图像
def showImage(window,headers=[]):
window.showImageView.clear()
window.showImageView.setColumnCount(3)
ent=len(window.originImages)//3
dul=len(window.originImages)%3
echo=ent+1 #if dul else ent
window.showImageView.setRowCount(echo)
window.showImageView.setShowGrid(True)
window.showImageView.setEditTriggers(QAbstractItemView.NoEditTriggers)
window.showImageView.setHorizontalHeaderLabels(headers)
# print(len(window.originImages))
for x in range(echo):
circle=3 if x<echo-1 else dul
if circle:
for y in range(circle):
imageView=QGraphicsView()
imageView.setHorizontalScrollBarPolicy(Qt.ScrollBarAlwaysOff)
imageView.setVerticalScrollBarPolicy(Qt.ScrollBarAlwaysOff)
img=window.originImages[3*x+y]
img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)
width=img.shape[1]
height=img.shape[0]
window.showImageView.setColumnWidth(y, width)
window.showImageView.setRowHeight(x, height)
frame = QImage(img, width, height, QImage.Format_RGB888)
#调用QPixmap命令，建立一个图像存放框
pix = QPixmap.fromImage(frame)
item = QGraphicsPixmapItem(pix)
scene = QGraphicsScene() # 创建场景
scene.addItem(item)
imageView.setScene(scene)
window.showImageView.setCellWidget(x, y, imageView)
else:
break
device = "cuda"
test_mode = 0
test_mode_list = ['ori', 'gen', 'comb']
#
model = MobileNet().to(device)
model.eval()
def change_cv2_draw(image, strs, local, sizes, colour):
cv2img = cv2.cvtColor(image, cv2.COLOR_BGR2RGB)
pilimg = Image.fromarray(cv2img)
draw = ImageDraw.Draw(pilimg)
font = ImageFont.truetype("SIMYOU.TTF", sizes, encoding="utf-8")
draw.text(local, strs, colour, font=font)
image = cv2.cvtColor( | np.array(pilimg) | numpy.array |
#==============================================================================
# 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])*10)+' -ot Float32 '+shpname+' '+fullpath+'/temp.tiff'
os.system(rasterizecmd)
if gdalpath!=False:
warpcmd=gdalpath+'/gdalwarp -r average -te '+"%.9f"%(rainprop.subextent[0])+' '+"%.9f"%(rainprop.subextent[2])+' '+"%.9f"%(rainprop.subextent[1])+' '+"%.9f"%(rainprop.subextent[3])+' -ts '+"%.9f"%(np.int(rainprop.subdimensions[1]))+' '+"%.9f"%(np.int(rainprop.subdimensions[0]))+' -overwrite '+fullpath+'/temp.tiff '+fullpath+'/tempAGG.tiff'
else:
warpcmd='gdalwarp -r average -te '+"%.9f"%(rainprop.subextent[0])+' '+"%.9f"%(rainprop.subextent[2])+' '+"%.9f"%(rainprop.subextent[1])+' '+"%.9f"%(rainprop.subextent[3])+' -ts '+"%.9f"%(np.int(rainprop.subdimensions[1]))+' '+"%.9f"%(np.int(rainprop.subdimensions[0]))+' -overwrite '+fullpath+'/temp.tiff '+fullpath+'/tempAGG.tiff'
os.system(warpcmd)
ds=rasterio.open(fullpath+'/tempAGG.tiff')
rastertemplate=ds.read(1)
os.system('rm '+fullpath+'/temp.tiff')
os.system('rm '+fullpath+'/tempAGG.tiff')
else:
sys.exit("You entered an incorrect mask type, options are 'simple' or 'fraction'")
rastertemplate=np.array(rastertemplate[:])
return rastertemplate
#==============================================================================
# WRITE SCENARIOS TO NETCDF ONE REALIZATION AT A TIME
#==============================================================================
def writerealization(rlz,nrealizations,writename,outrain,writemax,writestorm,writeperiod,writex,writey,writetimes,latrange,lonrange,whichorigstorm):
# SAVE outrain AS NETCDF FILE
dataset=Dataset(writename, 'w', format='NETCDF4')
# create dimensions
outlats=dataset.createDimension('outlat',len(latrange))
outlons=dataset.createDimension('outlon',len(lonrange))
time=dataset.createDimension('time',writetimes.shape[1])
nyears=dataset.createDimension('nyears',len(writeperiod))
# create variables
times=dataset.createVariable('time',np.float64, ('nyears','time'))
latitudes=dataset.createVariable('latitude',np.float32, ('outlat'))
longitudes=dataset.createVariable('longitude',np.float32, ('outlon'))
rainrate=dataset.createVariable('rainrate',np.float32,('nyears','time','outlat','outlon'),zlib=True,complevel=4,least_significant_digit=2)
basinrainfall=dataset.createVariable('basinrainfall',np.float32,('nyears'))
xlocation=dataset.createVariable('xlocation',np.int32,('nyears'))
ylocation=dataset.createVariable('ylocation',np.int32,('nyears'))
returnperiod=dataset.createVariable('returnperiod',np.float32,('nyears'))
stormnumber=dataset.createVariable('stormnumber',np.int32,('nyears'))
original_stormnumber=dataset.createVariable('original_stormnumber',np.int32,('nyears'))
#stormtimes=dataset.createVariable('stormtimes',np.float64,('nyears'))
# Global Attributes
dataset.description = 'SST Rainfall Scenarios Realization: '+str(rlz+1)+' of '+str(nrealizations)
dataset.history = 'Created ' + str(datetime.now())
dataset.source = 'Storm Catalog for (FILL IN THE BLANK)'
# Variable Attributes (time since 1970-01-01 00:00:00.0 in numpys)
latitudes.units = 'degrees north'
longitudes.units = 'degrees east'
rainrate.units = 'mm/h'
times.units = 'minutes since 1970-01-01 00:00.0'
times.calendar = 'gregorian'
#print dataset.description
#print dataset.history
# fill the netcdf file
latitudes[:]=latrange
longitudes[:]=lonrange
rainrate[:]=outrain
basinrainfall[:]=writemax
times[:]=writetimes
xlocation[:]=writex
ylocation[:]=writey
stormnumber[:]=writestorm
returnperiod[:]=writeperiod
original_stormnumber[:]=whichorigstorm
#stormtimes[:]=writetimes
dataset.close()
#==============================================================================
# WRITE The maximized storm
#==============================================================================
def writemaximized(writename,outrain,writemax,write_ts,writex,writey,writetimes,latrange,lonrange):
# SAVE outrain AS NETCDF FILE
dataset=Dataset(writename, 'w', format='NETCDF4')
# create dimensions
outlats=dataset.createDimension('outlat',len(latrange))
outlons=dataset.createDimension('outlon',len(lonrange))
time=dataset.createDimension('time',len(writetimes))
# create variables
times=dataset.createVariable('time',np.float64, ('time'))
latitudes=dataset.createVariable('latitude',np.float32, ('outlat'))
longitudes=dataset.createVariable('longitude',np.float32, ('outlon'))
rainrate=dataset.createVariable('rainrate',np.float32,('time','outlat','outlon'),zlib=True,complevel=4,least_significant_digit=2)
basinrainfall=dataset.createVariable('basinrainfall',np.float32)
xlocation=dataset.createVariable('xlocation',np.int32)
ylocation=dataset.createVariable('ylocation',np.int32)
#stormtimes=dataset.createVariable('stormtimes',np.float64,('nyears'))
# Global Attributes
dataset.description = 'SST Rainfall Maximum Storm'
dataset.history = 'Created ' + str(datetime.now())
dataset.source = 'Storm Catalog for (FILL IN THE BLANK)'
# Variable Attributes (time since 1970-01-01 00:00:00.0 in numpys)
latitudes.units = 'degrees north'
longitudes.units = 'degrees east'
rainrate.units = 'mm/h'
times.units = 'minutes since 1970-01-01 00:00.0'
times.calendar = 'gregorian'
#print dataset.description
#print dataset.history
# fill the netcdf file
latitudes[:]=latrange
longitudes[:]=lonrange
rainrate[:]=outrain
basinrainfall[:]=writemax
times[:]=writetimes
xlocation[:]=writex
ylocation[:]=writey
dataset.close()
#==============================================================================
# READ RAINFALL FILE FROM NETCDF
#==============================================================================
def readnetcdf(rfile,inbounds=False):
infile=Dataset(rfile,'r')
if np.any(inbounds!=False):
outrain=np.array(infile.variables['rainrate'][:,inbounds[3]:inbounds[2]+1,inbounds[0]:inbounds[1]+1])
outlatitude=np.array(infile.variables['latitude'][inbounds[3]:inbounds[2]+1])
outlongitude=np.array(infile.variables['longitude'][inbounds[0]:inbounds[1]+1])
else:
outrain=np.array(infile.variables['rainrate'][:])
outlatitude=np.array(infile.variables['latitude'][:])
outlongitude=np.array(infile.variables['longitude'][:])
outtime=np.array(infile.variables['time'][:],dtype='datetime64[m]')
infile.close()
return outrain,outtime,outlatitude,outlongitude
#==============================================================================
# READ RAINFALL FILE FROM NETCDF
#==============================================================================
def readcatalog(rfile):
infile=Dataset(rfile,'r')
outrain=np.array(infile.variables['rainrate'][:])
outtime=np.array(infile.variables['time'][:],dtype='datetime64[m]')
outlatitude=np.array(infile.variables['latitude'][:])
outlongitude=np.array(infile.variables['longitude'][:])
outlocx=np.array(infile.variables['xlocation'][:])
outlocy=np.array(infile.variables['ylocation'][:])
outmax=np.array(infile.variables['basinrainfall'][:])
outmask=np.array(infile.variables['gridmask'][:])
domainmask=np.array(infile.variables['domainmask'][:])
try:
timeresolution=np.int(infile.variables['timeresolution'])
resexists=True
except:
resexists=False
infile.close()
if resexists:
return outrain,outtime,outlatitude,outlongitude,outlocx,outlocy,outmax,outmask,domainmask,timeresolution
return outrain,outtime,outlatitude,outlongitude,outlocx,outlocy,outmax,outmask,domainmask
def readtimeresolution(rfile):
infile=Dataset(rfile,'r')
try:
timeresolution=np.int(infile.variables['timeresolution'])
except:
sys.exit("The time resolution of your storm catalog is ambiguous. This only appears in very specific circumstances. You can contact Dr. <NAME> if you need help!")
return timeresolution
#==============================================================================
# READ RAINFALL FILE FROM NETCDF: LEGACY VERSION! ONLY NEEDED IF READING AN OLDER DATASET
#==============================================================================
def readcatalog_LEGACY(rfile):
infile=Dataset(rfile,'r')
outrain=np.array(infile.variables['rainrate'][:])
outtime=np.array(infile.variables['time'][:],dtype='datetime64[m]')
outlatitude=np.array(infile.variables['latitude'][:])
outlongitude=np.array(infile.variables['longitude'][:])
outlocx=np.array(infile.variables['xlocation'][:])
outlocy=np.array(infile.variables['ylocation'][:])
outmax=np.array(infile.variables['basinrainfall'][:])
outmask=np.array(infile.variables['gridmask'][:])
#domainmask=np.array(infile.variables['domainmask'][:])
infile.close()
return outrain,outtime,outlatitude,outlongitude,outlocx,outlocy,outmax,outmask
#==============================================================================
# WRITE RAINFALL FILE TO NETCDF
#==============================================================================
def writecatalog(catrain,catmax,catx,caty,cattime,latrange,lonrange,catalogname,nstorms,gridmask,parameterfile,dmask,timeresolution=False):
# SAVE outrain AS NETCDF FILE
dataset=Dataset(catalogname, 'w', format='NETCDF4')
# create dimensions
outlats=dataset.createDimension('outlat',len(latrange))
outlons=dataset.createDimension('outlon',len(lonrange))
time=dataset.createDimension('time',cattime.shape[1])
nstorms=dataset.createDimension('nstorms',nstorms)
# create variables
times=dataset.createVariable('time',np.float64, ('nstorms','time',))
latitudes=dataset.createVariable('latitude',np.float32, ('outlat',))
longitudes=dataset.createVariable('longitude',np.float32, ('outlon',))
rainrate=dataset.createVariable('rainrate',np.float32,('nstorms','time','outlat','outlon',),zlib=True,complevel=4,least_significant_digit=2)
basinrainfall=dataset.createVariable('basinrainfall',np.float32,('nstorms'))
xlocation=dataset.createVariable('xlocation',np.int32,('nstorms'))
ylocation=dataset.createVariable('ylocation',np.int32,('nstorms'))
gmask=dataset.createVariable('gridmask',np.float32,('outlat','outlon',))
domainmask=dataset.createVariable('domainmask',np.float32,('outlat','outlon',))
# Global Attributes
with open(parameterfile, "r") as myfile:
params=myfile.read()
myfile.close
dataset.description=params
if timeresolution!=False:
dataset.timeresolution=timeresolution
dataset.history = 'Created ' + str(datetime.now())
dataset.source = 'RainyDay Storm Catalog'
# Variable Attributes (time since 1970-01-01 00:00:00.0 in numpys)
latitudes.units = 'degrees north'
longitudes.units = 'degrees east'
rainrate.units = 'mm/h'
times.units = 'minutes since 1970-01-01 00:00.0'
times.calendar = 'gregorian'
gmask.units="N/A"
# fill the netcdf file
latitudes[:]=latrange
longitudes[:]=lonrange
rainrate[:]=catrain
basinrainfall[:]=catmax
times[:]=cattime
xlocation[:]=catx
ylocation[:]=caty
gmask[:]=gridmask
domainmask[:]=dmask
dataset.close()
def writeintensityfile(intenserain,filename,latrange,lonrange,intensetime):
# SAVE outrain AS NETCDF FILE
dataset=Dataset(filename, 'w', format='NETCDF4')
# create dimensions
outlats=dataset.createDimension('outlat',intenserain.shape[1])
outlons=dataset.createDimension('outlon',intenserain.shape[2])
nstorms=dataset.createDimension('nstorms',intenserain.shape[0])
# create variables
latitudes=dataset.createVariable('latitude',np.float32, ('outlat',))
longitudes=dataset.createVariable('longitude',np.float32, ('outlon',))
stormtotals=dataset.createVariable('stormtotals',np.float32,('nstorms','outlat','outlon',))
times=dataset.createVariable('time',np.float64, ('nstorms','outlat','outlon',))
dataset.history = 'Created ' + str(datetime.now())
dataset.source = 'RainyDay Storm Intensity File'
# Variable Attributes (time since 1970-01-01 00:00:00.0 in numpys)
latitudes.units = 'degrees north'
longitudes.units = 'degrees east'
stormtotals.units = 'mm'
times.units = 'minutes since 1970-01-01 00:00.0'
# fill the netcdf file
latitudes[:]=latrange
longitudes[:]=lonrange
stormtotals[:]=intenserain
times[:]=intensetime
dataset.close()
def readintensityfile(rfile,inbounds=False):
infile=Dataset(rfile,'r')
if np.any(inbounds!=False):
outrain=np.array(infile.variables['stormtotals'][:,inbounds[3]:inbounds[2]+1,inbounds[0]:inbounds[1]+1])
outtime=np.array(infile.variables['time'][:,inbounds[3]:inbounds[2]+1,inbounds[0]:inbounds[1]+1],dtype='datetime64[m]')
outlat=np.array(infile.variables['latitude'][inbounds[3]:inbounds[2]+1])
outlon=np.array(infile.variables['longitude'][inbounds[0]:inbounds[1]+1])
else:
outrain=np.array(infile.variables['stormtotals'][:])
outtime=np.array(infile.variables['time'][:],dtype='datetime64[m]')
outlat=np.array(infile.variables['latitude'][:])
outlon=np.array(infile.variables['longitude'][:])
infile.close()
return outrain,outtime,outlat,outlon
def readmeanfile(rfile,inbounds=False):
infile=Dataset(rfile,'r')
if np.any(inbounds!=False):
outrain=np.array(infile.variables['stormtotals'][inbounds[3]:inbounds[2]+1,inbounds[0]:inbounds[1]+1])
outlat= | np.array(infile.variables['latitude'][inbounds[3]:inbounds[2]+1]) | numpy.array |
"""
Bayesian network implementation
API inspired by SciKit-learn.
"""
import numpy as np
from sklearn.base import BaseEstimator, ClassifierMixin
from sklearn.utils.validation import check_X_y, check_array, check_is_fitted ### Checks if the estimator is fitted by verifying the presence of fitted attributes (ending with a trailing underscore)
#from sklearn.utils.multiclass import unique_labels, not necessary, can be replaced by array(list(set()))
from __future__ import division ###for float operation
from collections import Counter
import numpy as np
from sklearn.metrics import accuracy_score
from sklearn.metrics import recall_score ##tp / (tp + fn)
from sklearn.metrics import precision_score #tp / (tp + fp)
from sklearn.preprocessing import MultiLabelBinarizer
from sklearn.model_selection import KFold, StratifiedKFold
from pyitlib import discrete_random_variable as drv
import time
import timeit
class Bayes_net(BaseEstimator, ClassifierMixin):
def fit(self,X,y):
raise NotImplementedError
def predict_proba(self, X): ### key prediction methods, all other prediction methods will use it first.
raise NotImplementedError
def predict_binary(self,X):
"""
Perform classification on an array of test vectors X, predict P(C1|X), works only for binary classifcation
Parameters
----------
X : array-like of shape (n_samples, n_features)
Returns
-------
C : ndarray of shape (n_samples,)
Predicted P(C1|X)
"""
Prob_C = self.predict_proba(X) ### Prob_C is n*|C| np.array
return(Prob_C[:,0])
def predict(self, X):
"""
Perform classification on an array of test vectors X.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Returns
-------
C : ndarray of shape (n_samples,)
Predicted target values for X
"""
Prob_C = self.predict_proba(X) ## Prob_C is |C|*n np.array ,C is self.C
return( np.array([self.classes_[ele] for ele in np.argmax(Prob_C, axis=1)] ) )
def Conditional_log_likelihood_general(self,y_true,y_pred_prob,C):
"""Calculate the conditional log likelihood.
:param y_true: The true class labels. e.g ['1','1',.....'0','0']
:param y_pred_prob: np.array shows prob of each class for each instance. ith column is the predicted prob for class C[i]
:param C: Class labels e.x ['1','0'], C has to use same labels as y_true.
:return: CLL. A scalar.
"""
cll = []
for i in range(len(y_true)):
cll.append( y_pred_prob[i,C.index(y_true[i])] ) ## \hat p(c_true|c_true)
cll = [np.log2(ele) for ele in cll]
cll = | np.array(cll) | numpy.array |
# -*- coding: utf-8 -*-
"""
docstring goes here.
:copyright: Copyright 2014 by the Elephant team, see AUTHORS.txt.
:license: Modified BSD, see LICENSE.txt for details.
"""
from __future__ import division, print_function
import unittest
from itertools import chain
from neo.test.generate_datasets import fake_neo
import numpy as np
from numpy.testing.utils import assert_array_equal
import quantities as pq
try:
import pandas as pd
from pandas.util.testing import assert_frame_equal, assert_index_equal
except ImportError:
HAVE_PANDAS = False
else:
import elephant.pandas_bridge as ep
HAVE_PANDAS = True
@unittest.skipUnless(HAVE_PANDAS, 'requires pandas')
class MultiindexFromDictTestCase(unittest.TestCase):
def test__multiindex_from_dict(self):
inds = {'test1': 6.5,
'test2': 5,
'test3': 'test'}
targ = pd.MultiIndex(levels=[[6.5], [5], ['test']],
labels=[[0], [0], [0]],
names=['test1', 'test2', 'test3'])
res0 = ep._multiindex_from_dict(inds)
self.assertEqual(targ.levels, res0.levels)
self.assertEqual(targ.names, res0.names)
self.assertEqual(targ.labels, res0.labels)
def _convert_levels(levels):
"""Convert a list of levels to the format pandas returns for a MultiIndex.
Parameters
----------
levels : list
The list of levels to convert.
Returns
-------
list
The the level in `list` converted to values like what pandas will give.
"""
levels = list(levels)
for i, level in enumerate(levels):
if hasattr(level, 'lower'):
try:
level = unicode(level)
except NameError:
pass
elif hasattr(level, 'date'):
levels[i] = pd.DatetimeIndex(data=[level])
continue
elif level is None:
levels[i] = pd.Index([])
continue
levels[i] = pd.Index([level])
return levels
@unittest.skipUnless(HAVE_PANDAS, 'requires pandas')
class ConvertValueSafeTestCase(unittest.TestCase):
def test__convert_value_safe__float(self):
targ = 5.5
value = targ
res = ep._convert_value_safe(value)
self.assertIs(res, targ)
def test__convert_value_safe__str(self):
targ = 'test'
value = targ
res = ep._convert_value_safe(value)
self.assertIs(res, targ)
def test__convert_value_safe__bytes(self):
targ = 'test'
value = b'test'
res = ep._convert_value_safe(value)
self.assertEqual(res, targ)
def test__convert_value_safe__numpy_int_scalar(self):
targ = 5
value = np.array(5)
res = ep._convert_value_safe(value)
self.assertEqual(res, targ)
self.assertFalse(hasattr(res, 'dtype'))
def test__convert_value_safe__numpy_float_scalar(self):
targ = 5.
value = np.array(5.)
res = ep._convert_value_safe(value)
self.assertEqual(res, targ)
self.assertFalse(hasattr(res, 'dtype'))
def test__convert_value_safe__numpy_unicode_scalar(self):
targ = u'test'
value = np.array('test', dtype='U')
res = ep._convert_value_safe(value)
self.assertEqual(res, targ)
self.assertFalse(hasattr(res, 'dtype'))
def test__convert_value_safe__numpy_str_scalar(self):
targ = u'test'
value = np.array('test', dtype='S')
res = ep._convert_value_safe(value)
self.assertEqual(res, targ)
self.assertFalse(hasattr(res, 'dtype'))
def test__convert_value_safe__quantity_scalar(self):
targ = (10., 'ms')
value = 10. * pq.ms
res = ep._convert_value_safe(value)
self.assertEqual(res, targ)
self.assertFalse(hasattr(res[0], 'dtype'))
self.assertFalse(hasattr(res[0], 'units'))
@unittest.skipUnless(HAVE_PANDAS, 'requires pandas')
class SpiketrainToDataframeTestCase(unittest.TestCase):
def test__spiketrain_to_dataframe__parents_empty(self):
obj = fake_neo('SpikeTrain', seed=0)
res0 = ep.spiketrain_to_dataframe(obj)
res1 = ep.spiketrain_to_dataframe(obj, child_first=True)
res2 = ep.spiketrain_to_dataframe(obj, child_first=False)
res3 = ep.spiketrain_to_dataframe(obj, parents=True)
res4 = ep.spiketrain_to_dataframe(obj, parents=True,
child_first=True)
res5 = ep.spiketrain_to_dataframe(obj, parents=True,
child_first=False)
res6 = ep.spiketrain_to_dataframe(obj, parents=False)
res7 = ep.spiketrain_to_dataframe(obj, parents=False, child_first=True)
res8 = ep.spiketrain_to_dataframe(obj, parents=False,
child_first=False)
targvalues = pq.Quantity(obj.magnitude, units=obj.units)
targvalues = targvalues.rescale('s').magnitude[np.newaxis].T
targindex = np.arange(len(targvalues))
attrs = ep._extract_neo_attrs_safe(obj, parents=True, child_first=True)
keys, values = zip(*sorted(attrs.items()))
values = _convert_levels(values)
self.assertEqual(1, len(res0.columns))
self.assertEqual(1, len(res1.columns))
self.assertEqual(1, len(res2.columns))
self.assertEqual(1, len(res3.columns))
self.assertEqual(1, len(res4.columns))
self.assertEqual(1, len(res5.columns))
self.assertEqual(1, len(res6.columns))
self.assertEqual(1, len(res7.columns))
self.assertEqual(1, len(res8.columns))
self.assertEqual(len(obj), len(res0.index))
self.assertEqual(len(obj), len(res1.index))
self.assertEqual(len(obj), len(res2.index))
self.assertEqual(len(obj), len(res3.index))
self.assertEqual(len(obj), len(res4.index))
self.assertEqual(len(obj), len(res5.index))
self.assertEqual(len(obj), len(res6.index))
self.assertEqual(len(obj), len(res7.index))
self.assertEqual(len(obj), len(res8.index))
assert_array_equal(targvalues, res0.values)
assert_array_equal(targvalues, res1.values)
assert_array_equal(targvalues, res2.values)
assert_array_equal(targvalues, res3.values)
assert_array_equal(targvalues, res4.values)
assert_array_equal(targvalues, res5.values)
assert_array_equal(targvalues, res6.values)
assert_array_equal(targvalues, res7.values)
assert_array_equal(targvalues, res8.values)
assert_array_equal(targindex, res0.index)
assert_array_equal(targindex, res1.index)
assert_array_equal(targindex, res2.index)
assert_array_equal(targindex, res3.index)
assert_array_equal(targindex, res4.index)
assert_array_equal(targindex, res5.index)
assert_array_equal(targindex, res6.index)
assert_array_equal(targindex, res7.index)
assert_array_equal(targindex, res8.index)
self.assertEqual(['spike_number'], res0.index.names)
self.assertEqual(['spike_number'], res1.index.names)
self.assertEqual(['spike_number'], res2.index.names)
self.assertEqual(['spike_number'], res3.index.names)
self.assertEqual(['spike_number'], res4.index.names)
self.assertEqual(['spike_number'], res5.index.names)
self.assertEqual(['spike_number'], res6.index.names)
self.assertEqual(['spike_number'], res7.index.names)
self.assertEqual(['spike_number'], res8.index.names)
self.assertEqual(keys, res0.columns.names)
self.assertEqual(keys, res1.columns.names)
self.assertEqual(keys, res2.columns.names)
self.assertEqual(keys, res3.columns.names)
self.assertEqual(keys, res4.columns.names)
self.assertEqual(keys, res5.columns.names)
self.assertEqual(keys, res6.columns.names)
self.assertEqual(keys, res7.columns.names)
self.assertEqual(keys, res8.columns.names)
for value, level in zip(values, res0.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res1.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res2.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res3.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res4.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res5.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res6.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res7.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res8.columns.levels):
assert_index_equal(value, level)
def test__spiketrain_to_dataframe__noparents(self):
blk = fake_neo('Block', seed=0)
obj = blk.list_children_by_class('SpikeTrain')[0]
res0 = ep.spiketrain_to_dataframe(obj, parents=False)
res1 = ep.spiketrain_to_dataframe(obj, parents=False,
child_first=True)
res2 = ep.spiketrain_to_dataframe(obj, parents=False,
child_first=False)
targvalues = pq.Quantity(obj.magnitude, units=obj.units)
targvalues = targvalues.rescale('s').magnitude[np.newaxis].T
targindex = np.arange(len(targvalues))
attrs = ep._extract_neo_attrs_safe(obj, parents=False,
child_first=True)
keys, values = zip(*sorted(attrs.items()))
values = _convert_levels(values)
self.assertEqual(1, len(res0.columns))
self.assertEqual(1, len(res1.columns))
self.assertEqual(1, len(res2.columns))
self.assertEqual(len(obj), len(res0.index))
self.assertEqual(len(obj), len(res1.index))
self.assertEqual(len(obj), len(res2.index))
assert_array_equal(targvalues, res0.values)
assert_array_equal(targvalues, res1.values)
assert_array_equal(targvalues, res2.values)
assert_array_equal(targindex, res0.index)
assert_array_equal(targindex, res1.index)
assert_array_equal(targindex, res2.index)
self.assertEqual(['spike_number'], res0.index.names)
self.assertEqual(['spike_number'], res1.index.names)
self.assertEqual(['spike_number'], res2.index.names)
self.assertEqual(keys, res0.columns.names)
self.assertEqual(keys, res1.columns.names)
self.assertEqual(keys, res2.columns.names)
for value, level in zip(values, res0.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res1.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res2.columns.levels):
assert_index_equal(value, level)
def test__spiketrain_to_dataframe__parents_childfirst(self):
blk = fake_neo('Block', seed=0)
obj = blk.list_children_by_class('SpikeTrain')[0]
res0 = ep.spiketrain_to_dataframe(obj)
res1 = ep.spiketrain_to_dataframe(obj, child_first=True)
res2 = ep.spiketrain_to_dataframe(obj, parents=True)
res3 = ep.spiketrain_to_dataframe(obj, parents=True, child_first=True)
targvalues = pq.Quantity(obj.magnitude, units=obj.units)
targvalues = targvalues.rescale('s').magnitude[np.newaxis].T
targindex = np.arange(len(targvalues))
attrs = ep._extract_neo_attrs_safe(obj, parents=True, child_first=True)
keys, values = zip(*sorted(attrs.items()))
values = _convert_levels(values)
self.assertEqual(1, len(res0.columns))
self.assertEqual(1, len(res1.columns))
self.assertEqual(1, len(res2.columns))
self.assertEqual(1, len(res3.columns))
self.assertEqual(len(obj), len(res0.index))
self.assertEqual(len(obj), len(res1.index))
self.assertEqual(len(obj), len(res2.index))
self.assertEqual(len(obj), len(res3.index))
assert_array_equal(targvalues, res0.values)
assert_array_equal(targvalues, res1.values)
assert_array_equal(targvalues, res2.values)
assert_array_equal(targvalues, res3.values)
assert_array_equal(targindex, res0.index)
assert_array_equal(targindex, res1.index)
assert_array_equal(targindex, res2.index)
assert_array_equal(targindex, res3.index)
self.assertEqual(['spike_number'], res0.index.names)
self.assertEqual(['spike_number'], res1.index.names)
self.assertEqual(['spike_number'], res2.index.names)
self.assertEqual(['spike_number'], res3.index.names)
self.assertEqual(keys, res0.columns.names)
self.assertEqual(keys, res1.columns.names)
self.assertEqual(keys, res2.columns.names)
self.assertEqual(keys, res3.columns.names)
for value, level in zip(values, res0.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res1.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res2.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res3.columns.levels):
assert_index_equal(value, level)
def test__spiketrain_to_dataframe__parents_parentfirst(self):
blk = fake_neo('Block', seed=0)
obj = blk.list_children_by_class('SpikeTrain')[0]
res0 = ep.spiketrain_to_dataframe(obj, child_first=False)
res1 = ep.spiketrain_to_dataframe(obj, parents=True, child_first=False)
targvalues = pq.Quantity(obj.magnitude, units=obj.units)
targvalues = targvalues.rescale('s').magnitude[np.newaxis].T
targindex = np.arange(len(targvalues))
attrs = ep._extract_neo_attrs_safe(obj, parents=True,
child_first=False)
keys, values = zip(*sorted(attrs.items()))
values = _convert_levels(values)
self.assertEqual(1, len(res0.columns))
self.assertEqual(1, len(res1.columns))
self.assertEqual(len(obj), len(res0.index))
self.assertEqual(len(obj), len(res1.index))
assert_array_equal(targvalues, res0.values)
assert_array_equal(targvalues, res1.values)
assert_array_equal(targindex, res0.index)
assert_array_equal(targindex, res1.index)
self.assertEqual(['spike_number'], res0.index.names)
self.assertEqual(['spike_number'], res1.index.names)
self.assertEqual(keys, res0.columns.names)
self.assertEqual(keys, res1.columns.names)
for value, level in zip(values, res0.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res1.columns.levels):
assert_index_equal(value, level)
@unittest.skipUnless(HAVE_PANDAS, 'requires pandas')
class EventToDataframeTestCase(unittest.TestCase):
def test__event_to_dataframe__parents_empty(self):
obj = fake_neo('Event', seed=42)
res0 = ep.event_to_dataframe(obj)
res1 = ep.event_to_dataframe(obj, child_first=True)
res2 = ep.event_to_dataframe(obj, child_first=False)
res3 = ep.event_to_dataframe(obj, parents=True)
res4 = ep.event_to_dataframe(obj, parents=True, child_first=True)
res5 = ep.event_to_dataframe(obj, parents=True, child_first=False)
res6 = ep.event_to_dataframe(obj, parents=False)
res7 = ep.event_to_dataframe(obj, parents=False, child_first=True)
res8 = ep.event_to_dataframe(obj, parents=False, child_first=False)
targvalues = obj.labels[:len(obj.times)][np.newaxis].T.astype('U')
targindex = obj.times[:len(obj.labels)].rescale('s').magnitude
attrs = ep._extract_neo_attrs_safe(obj, parents=True, child_first=True)
keys, values = zip(*sorted(attrs.items()))
values = _convert_levels(values)
self.assertEqual(1, len(res0.columns))
self.assertEqual(1, len(res1.columns))
self.assertEqual(1, len(res2.columns))
self.assertEqual(1, len(res3.columns))
self.assertEqual(1, len(res4.columns))
self.assertEqual(1, len(res5.columns))
self.assertEqual(1, len(res6.columns))
self.assertEqual(1, len(res7.columns))
self.assertEqual(1, len(res8.columns))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res0.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res1.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res2.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res3.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res4.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res5.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res6.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res7.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res8.index))
assert_array_equal(targvalues, res0.values)
assert_array_equal(targvalues, res1.values)
assert_array_equal(targvalues, res2.values)
assert_array_equal(targvalues, res3.values)
assert_array_equal(targvalues, res4.values)
assert_array_equal(targvalues, res5.values)
assert_array_equal(targvalues, res6.values)
assert_array_equal(targvalues, res7.values)
assert_array_equal(targvalues, res8.values)
assert_array_equal(targindex, res0.index)
assert_array_equal(targindex, res1.index)
assert_array_equal(targindex, res2.index)
assert_array_equal(targindex, res3.index)
assert_array_equal(targindex, res4.index)
assert_array_equal(targindex, res5.index)
assert_array_equal(targindex, res6.index)
assert_array_equal(targindex, res7.index)
assert_array_equal(targindex, res8.index)
self.assertEqual(['times'], res0.index.names)
self.assertEqual(['times'], res1.index.names)
self.assertEqual(['times'], res2.index.names)
self.assertEqual(['times'], res3.index.names)
self.assertEqual(['times'], res4.index.names)
self.assertEqual(['times'], res5.index.names)
self.assertEqual(['times'], res6.index.names)
self.assertEqual(['times'], res7.index.names)
self.assertEqual(['times'], res8.index.names)
self.assertEqual(keys, res0.columns.names)
self.assertEqual(keys, res1.columns.names)
self.assertEqual(keys, res2.columns.names)
self.assertEqual(keys, res3.columns.names)
self.assertEqual(keys, res4.columns.names)
self.assertEqual(keys, res5.columns.names)
self.assertEqual(keys, res6.columns.names)
self.assertEqual(keys, res7.columns.names)
self.assertEqual(keys, res8.columns.names)
for value, level in zip(values, res0.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res1.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res2.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res3.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res4.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res5.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res6.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res7.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res8.columns.levels):
assert_index_equal(value, level)
def test__event_to_dataframe__noparents(self):
blk = fake_neo('Block', seed=42)
obj = blk.list_children_by_class('Event')[0]
res0 = ep.event_to_dataframe(obj, parents=False)
res1 = ep.event_to_dataframe(obj, parents=False, child_first=False)
res2 = ep.event_to_dataframe(obj, parents=False, child_first=True)
targvalues = obj.labels[:len(obj.times)][np.newaxis].T.astype('U')
targindex = obj.times[:len(obj.labels)].rescale('s').magnitude
attrs = ep._extract_neo_attrs_safe(obj, parents=False,
child_first=True)
keys, values = zip(*sorted(attrs.items()))
values = _convert_levels(values)
self.assertEqual(1, len(res0.columns))
self.assertEqual(1, len(res1.columns))
self.assertEqual(1, len(res2.columns))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res0.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res1.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res2.index))
assert_array_equal(targvalues, res0.values)
assert_array_equal(targvalues, res1.values)
assert_array_equal(targvalues, res2.values)
assert_array_equal(targindex, res0.index)
assert_array_equal(targindex, res1.index)
assert_array_equal(targindex, res2.index)
self.assertEqual(['times'], res0.index.names)
self.assertEqual(['times'], res1.index.names)
self.assertEqual(['times'], res2.index.names)
self.assertEqual(keys, res0.columns.names)
self.assertEqual(keys, res1.columns.names)
self.assertEqual(keys, res2.columns.names)
for value, level in zip(values, res0.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res1.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res2.columns.levels):
assert_index_equal(value, level)
def test__event_to_dataframe__parents_childfirst(self):
blk = fake_neo('Block', seed=42)
obj = blk.list_children_by_class('Event')[0]
res0 = ep.event_to_dataframe(obj)
res1 = ep.event_to_dataframe(obj, child_first=True)
res2 = ep.event_to_dataframe(obj, parents=True)
res3 = ep.event_to_dataframe(obj, parents=True, child_first=True)
targvalues = obj.labels[:len(obj.times)][np.newaxis].T.astype('U')
targindex = obj.times[:len(obj.labels)].rescale('s').magnitude
attrs = ep._extract_neo_attrs_safe(obj, parents=True, child_first=True)
keys, values = zip(*sorted(attrs.items()))
values = _convert_levels(values)
self.assertEqual(1, len(res0.columns))
self.assertEqual(1, len(res1.columns))
self.assertEqual(1, len(res2.columns))
self.assertEqual(1, len(res3.columns))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res0.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res1.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res2.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res3.index))
assert_array_equal(targvalues, res0.values)
assert_array_equal(targvalues, res1.values)
assert_array_equal(targvalues, res2.values)
assert_array_equal(targvalues, res3.values)
assert_array_equal(targindex, res0.index)
assert_array_equal(targindex, res1.index)
assert_array_equal(targindex, res2.index)
assert_array_equal(targindex, res3.index)
self.assertEqual(['times'], res0.index.names)
self.assertEqual(['times'], res1.index.names)
self.assertEqual(['times'], res2.index.names)
self.assertEqual(['times'], res3.index.names)
self.assertEqual(keys, res0.columns.names)
self.assertEqual(keys, res1.columns.names)
self.assertEqual(keys, res2.columns.names)
self.assertEqual(keys, res3.columns.names)
for value, level in zip(values, res0.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res1.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res2.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res3.columns.levels):
assert_index_equal(value, level)
def test__event_to_dataframe__parents_parentfirst(self):
blk = fake_neo('Block', seed=42)
obj = blk.list_children_by_class('Event')[0]
res0 = ep.event_to_dataframe(obj, child_first=False)
res1 = ep.event_to_dataframe(obj, parents=True, child_first=False)
targvalues = obj.labels[:len(obj.times)][np.newaxis].T.astype('U')
targindex = obj.times[:len(obj.labels)].rescale('s').magnitude
attrs = ep._extract_neo_attrs_safe(obj, parents=True,
child_first=False)
keys, values = zip(*sorted(attrs.items()))
values = _convert_levels(values)
self.assertEqual(1, len(res0.columns))
self.assertEqual(1, len(res1.columns))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res0.index))
self.assertEqual(min(len(obj.times), len(obj.labels)),
len(res1.index))
assert_array_equal(targvalues, res0.values)
assert_array_equal(targvalues, res1.values)
assert_array_equal(targindex, res0.index)
assert_array_equal(targindex, res1.index)
self.assertEqual(['times'], res0.index.names)
self.assertEqual(['times'], res1.index.names)
self.assertEqual(keys, res0.columns.names)
self.assertEqual(keys, res1.columns.names)
for value, level in zip(values, res0.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res1.columns.levels):
assert_index_equal(value, level)
@unittest.skipUnless(HAVE_PANDAS, 'requires pandas')
class EpochToDataframeTestCase(unittest.TestCase):
def test__epoch_to_dataframe__parents_empty(self):
obj = fake_neo('Epoch', seed=42)
res0 = ep.epoch_to_dataframe(obj)
res1 = ep.epoch_to_dataframe(obj, child_first=True)
res2 = ep.epoch_to_dataframe(obj, child_first=False)
res3 = ep.epoch_to_dataframe(obj, parents=True)
res4 = ep.epoch_to_dataframe(obj, parents=True, child_first=True)
res5 = ep.epoch_to_dataframe(obj, parents=True, child_first=False)
res6 = ep.epoch_to_dataframe(obj, parents=False)
res7 = ep.epoch_to_dataframe(obj, parents=False, child_first=True)
res8 = ep.epoch_to_dataframe(obj, parents=False, child_first=False)
minlen = min([len(obj.times), len(obj.durations), len(obj.labels)])
targvalues = obj.labels[:minlen][np.newaxis].T.astype('U')
targindex = np.vstack([obj.durations[:minlen].rescale('s').magnitude,
obj.times[:minlen].rescale('s').magnitude])
targvalues = targvalues[targindex.argsort()[0], :]
targindex.sort()
attrs = ep._extract_neo_attrs_safe(obj, parents=True,
child_first=True)
keys, values = zip(*sorted(attrs.items()))
values = _convert_levels(values)
self.assertEqual(1, len(res0.columns))
self.assertEqual(1, len(res1.columns))
self.assertEqual(1, len(res2.columns))
self.assertEqual(1, len(res3.columns))
self.assertEqual(1, len(res4.columns))
self.assertEqual(1, len(res5.columns))
self.assertEqual(1, len(res6.columns))
self.assertEqual(1, len(res7.columns))
self.assertEqual(1, len(res8.columns))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res0.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res1.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res2.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res3.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res4.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res5.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res6.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res7.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res8.index))
assert_array_equal(targvalues, res0.values)
assert_array_equal(targvalues, res1.values)
assert_array_equal(targvalues, res2.values)
assert_array_equal(targvalues, res3.values)
assert_array_equal(targvalues, res4.values)
assert_array_equal(targvalues, res5.values)
assert_array_equal(targvalues, res6.values)
assert_array_equal(targvalues, res7.values)
assert_array_equal(targvalues, res8.values)
self.assertEqual(keys, res0.columns.names)
self.assertEqual(keys, res1.columns.names)
self.assertEqual(keys, res2.columns.names)
self.assertEqual(keys, res3.columns.names)
self.assertEqual(keys, res4.columns.names)
self.assertEqual(keys, res5.columns.names)
self.assertEqual(keys, res6.columns.names)
self.assertEqual(keys, res7.columns.names)
self.assertEqual(keys, res8.columns.names)
self.assertEqual([u'durations', u'times'], res0.index.names)
self.assertEqual([u'durations', u'times'], res1.index.names)
self.assertEqual([u'durations', u'times'], res2.index.names)
self.assertEqual([u'durations', u'times'], res3.index.names)
self.assertEqual([u'durations', u'times'], res4.index.names)
self.assertEqual([u'durations', u'times'], res5.index.names)
self.assertEqual([u'durations', u'times'], res6.index.names)
self.assertEqual([u'durations', u'times'], res7.index.names)
self.assertEqual([u'durations', u'times'], res8.index.names)
self.assertEqual(2, len(res0.index.levels))
self.assertEqual(2, len(res1.index.levels))
self.assertEqual(2, len(res2.index.levels))
self.assertEqual(2, len(res3.index.levels))
self.assertEqual(2, len(res4.index.levels))
self.assertEqual(2, len(res5.index.levels))
self.assertEqual(2, len(res6.index.levels))
self.assertEqual(2, len(res7.index.levels))
self.assertEqual(2, len(res8.index.levels))
assert_array_equal(targindex, res0.index.levels)
assert_array_equal(targindex, res1.index.levels)
assert_array_equal(targindex, res2.index.levels)
assert_array_equal(targindex, res3.index.levels)
assert_array_equal(targindex, res4.index.levels)
assert_array_equal(targindex, res5.index.levels)
assert_array_equal(targindex, res6.index.levels)
assert_array_equal(targindex, res7.index.levels)
assert_array_equal(targindex, res8.index.levels)
for value, level in zip(values, res0.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res1.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res2.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res3.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res4.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res5.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res6.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res7.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res8.columns.levels):
assert_index_equal(value, level)
def test__epoch_to_dataframe__noparents(self):
blk = fake_neo('Block', seed=42)
obj = blk.list_children_by_class('Epoch')[0]
res0 = ep.epoch_to_dataframe(obj, parents=False)
res1 = ep.epoch_to_dataframe(obj, parents=False, child_first=True)
res2 = ep.epoch_to_dataframe(obj, parents=False, child_first=False)
minlen = min([len(obj.times), len(obj.durations), len(obj.labels)])
targvalues = obj.labels[:minlen][np.newaxis].T.astype('U')
targindex = np.vstack([obj.durations[:minlen].rescale('s').magnitude,
obj.times[:minlen].rescale('s').magnitude])
targvalues = targvalues[targindex.argsort()[0], :]
targindex.sort()
attrs = ep._extract_neo_attrs_safe(obj, parents=False,
child_first=True)
keys, values = zip(*sorted(attrs.items()))
values = _convert_levels(values)
self.assertEqual(1, len(res0.columns))
self.assertEqual(1, len(res1.columns))
self.assertEqual(1, len(res2.columns))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res0.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res1.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res2.index))
assert_array_equal(targvalues, res0.values)
assert_array_equal(targvalues, res1.values)
assert_array_equal(targvalues, res2.values)
self.assertEqual(keys, res0.columns.names)
self.assertEqual(keys, res1.columns.names)
self.assertEqual(keys, res2.columns.names)
self.assertEqual([u'durations', u'times'], res0.index.names)
self.assertEqual([u'durations', u'times'], res1.index.names)
self.assertEqual([u'durations', u'times'], res2.index.names)
self.assertEqual(2, len(res0.index.levels))
self.assertEqual(2, len(res1.index.levels))
self.assertEqual(2, len(res2.index.levels))
assert_array_equal(targindex, res0.index.levels)
assert_array_equal(targindex, res1.index.levels)
assert_array_equal(targindex, res2.index.levels)
for value, level in zip(values, res0.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res1.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res2.columns.levels):
assert_index_equal(value, level)
def test__epoch_to_dataframe__parents_childfirst(self):
blk = fake_neo('Block', seed=42)
obj = blk.list_children_by_class('Epoch')[0]
res0 = ep.epoch_to_dataframe(obj)
res1 = ep.epoch_to_dataframe(obj, child_first=True)
res2 = ep.epoch_to_dataframe(obj, parents=True)
res3 = ep.epoch_to_dataframe(obj, parents=True, child_first=True)
minlen = min([len(obj.times), len(obj.durations), len(obj.labels)])
targvalues = obj.labels[:minlen][np.newaxis].T.astype('U')
targindex = np.vstack([obj.durations[:minlen].rescale('s').magnitude,
obj.times[:minlen].rescale('s').magnitude])
targvalues = targvalues[targindex.argsort()[0], :]
targindex.sort()
attrs = ep._extract_neo_attrs_safe(obj, parents=True, child_first=True)
keys, values = zip(*sorted(attrs.items()))
values = _convert_levels(values)
self.assertEqual(1, len(res0.columns))
self.assertEqual(1, len(res1.columns))
self.assertEqual(1, len(res2.columns))
self.assertEqual(1, len(res3.columns))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res0.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res1.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res2.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res3.index))
assert_array_equal(targvalues, res0.values)
assert_array_equal(targvalues, res1.values)
assert_array_equal(targvalues, res2.values)
assert_array_equal(targvalues, res3.values)
self.assertEqual(keys, res0.columns.names)
self.assertEqual(keys, res1.columns.names)
self.assertEqual(keys, res2.columns.names)
self.assertEqual(keys, res3.columns.names)
self.assertEqual([u'durations', u'times'], res0.index.names)
self.assertEqual([u'durations', u'times'], res1.index.names)
self.assertEqual([u'durations', u'times'], res2.index.names)
self.assertEqual([u'durations', u'times'], res3.index.names)
self.assertEqual(2, len(res0.index.levels))
self.assertEqual(2, len(res1.index.levels))
self.assertEqual(2, len(res2.index.levels))
self.assertEqual(2, len(res3.index.levels))
assert_array_equal(targindex, res0.index.levels)
assert_array_equal(targindex, res1.index.levels)
assert_array_equal(targindex, res2.index.levels)
assert_array_equal(targindex, res3.index.levels)
for value, level in zip(values, res0.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res1.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res2.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res3.columns.levels):
assert_index_equal(value, level)
def test__epoch_to_dataframe__parents_parentfirst(self):
blk = fake_neo('Block', seed=42)
obj = blk.list_children_by_class('Epoch')[0]
res0 = ep.epoch_to_dataframe(obj, child_first=False)
res1 = ep.epoch_to_dataframe(obj, parents=True, child_first=False)
minlen = min([len(obj.times), len(obj.durations), len(obj.labels)])
targvalues = obj.labels[:minlen][np.newaxis].T.astype('U')
targindex = np.vstack([obj.durations[:minlen].rescale('s').magnitude,
obj.times[:minlen].rescale('s').magnitude])
targvalues = targvalues[targindex.argsort()[0], :]
targindex.sort()
attrs = ep._extract_neo_attrs_safe(obj, parents=True,
child_first=False)
keys, values = zip(*sorted(attrs.items()))
values = _convert_levels(values)
self.assertEqual(1, len(res0.columns))
self.assertEqual(1, len(res1.columns))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res0.index))
self.assertEqual(min(len(obj.times), len(obj.durations),
len(obj.labels)),
len(res1.index))
assert_array_equal(targvalues, res0.values)
assert_array_equal(targvalues, res1.values)
self.assertEqual(keys, res0.columns.names)
self.assertEqual(keys, res1.columns.names)
self.assertEqual([u'durations', u'times'], res0.index.names)
self.assertEqual([u'durations', u'times'], res1.index.names)
self.assertEqual(2, len(res0.index.levels))
self.assertEqual(2, len(res1.index.levels))
assert_array_equal(targindex, res0.index.levels)
assert_array_equal(targindex, res1.index.levels)
for value, level in zip(values, res0.columns.levels):
assert_index_equal(value, level)
for value, level in zip(values, res1.columns.levels):
assert_index_equal(value, level)
@unittest.skipUnless(HAVE_PANDAS, 'requires pandas')
class MultiSpiketrainsToDataframeTestCase(unittest.TestCase):
def setUp(self):
if hasattr(self, 'assertItemsEqual'):
self.assertCountEqual = self.assertItemsEqual
def test__multi_spiketrains_to_dataframe__single(self):
obj = fake_neo('SpikeTrain', seed=0, n=5)
res0 = ep.multi_spiketrains_to_dataframe(obj)
res1 = ep.multi_spiketrains_to_dataframe(obj, parents=False)
res2 = ep.multi_spiketrains_to_dataframe(obj, parents=True)
res3 = ep.multi_spiketrains_to_dataframe(obj, child_first=True)
res4 = ep.multi_spiketrains_to_dataframe(obj, parents=False,
child_first=True)
res5 = ep.multi_spiketrains_to_dataframe(obj, parents=True,
child_first=True)
res6 = ep.multi_spiketrains_to_dataframe(obj, child_first=False)
res7 = ep.multi_spiketrains_to_dataframe(obj, parents=False,
child_first=False)
res8 = ep.multi_spiketrains_to_dataframe(obj, parents=True,
child_first=False)
targ = ep.spiketrain_to_dataframe(obj)
keys = ep._extract_neo_attrs_safe(obj, parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = 1
targlen = len(obj)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targwidth, len(res3.columns))
self.assertEqual(targwidth, len(res4.columns))
self.assertEqual(targwidth, len(res5.columns))
self.assertEqual(targwidth, len(res6.columns))
self.assertEqual(targwidth, len(res7.columns))
self.assertEqual(targwidth, len(res8.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertEqual(targlen, len(res3.index))
self.assertEqual(targlen, len(res4.index))
self.assertEqual(targlen, len(res5.index))
self.assertEqual(targlen, len(res6.index))
self.assertEqual(targlen, len(res7.index))
self.assertEqual(targlen, len(res8.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
self.assertCountEqual(keys, res3.columns.names)
self.assertCountEqual(keys, res4.columns.names)
self.assertCountEqual(keys, res5.columns.names)
self.assertCountEqual(keys, res6.columns.names)
self.assertCountEqual(keys, res7.columns.names)
self.assertCountEqual(keys, res8.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_array_equal(targ.values, res3.values)
assert_array_equal(targ.values, res4.values)
assert_array_equal(targ.values, res5.values)
assert_array_equal(targ.values, res6.values)
assert_array_equal(targ.values, res7.values)
assert_array_equal(targ.values, res8.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
assert_frame_equal(targ, res3)
assert_frame_equal(targ, res4)
assert_frame_equal(targ, res5)
assert_frame_equal(targ, res6)
assert_frame_equal(targ, res7)
assert_frame_equal(targ, res8)
def test__multi_spiketrains_to_dataframe__unit_default(self):
obj = fake_neo('Unit', seed=0, n=5)
res0 = ep.multi_spiketrains_to_dataframe(obj)
objs = obj.spiketrains
targ = [ep.spiketrain_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = max(len(iobj) for iobj in objs)
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
def test__multi_spiketrains_to_dataframe__segment_default(self):
obj = fake_neo('Segment', seed=0, n=5)
res0 = ep.multi_spiketrains_to_dataframe(obj)
objs = obj.spiketrains
targ = [ep.spiketrain_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = max(len(iobj) for iobj in objs)
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
def test__multi_spiketrains_to_dataframe__block_noparents(self):
obj = fake_neo('Block', seed=0, n=3)
res0 = ep.multi_spiketrains_to_dataframe(obj, parents=False)
res1 = ep.multi_spiketrains_to_dataframe(obj, parents=False,
child_first=True)
res2 = ep.multi_spiketrains_to_dataframe(obj, parents=False,
child_first=False)
objs = obj.list_children_by_class('SpikeTrain')
targ = [ep.spiketrain_to_dataframe(iobj,
parents=False, child_first=True)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=False,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = max(len(iobj) for iobj in objs)
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
def test__multi_spiketrains_to_dataframe__block_parents_childfirst(self):
obj = fake_neo('Block', seed=0, n=3)
res0 = ep.multi_spiketrains_to_dataframe(obj)
res1 = ep.multi_spiketrains_to_dataframe(obj, parents=True)
res2 = ep.multi_spiketrains_to_dataframe(obj, child_first=True)
res3 = ep.multi_spiketrains_to_dataframe(obj, parents=True,
child_first=True)
objs = obj.list_children_by_class('SpikeTrain')
targ = [ep.spiketrain_to_dataframe(iobj,
parents=True, child_first=True)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = max(len(iobj) for iobj in objs)
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targwidth, len(res3.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertEqual(targlen, len(res3.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
self.assertCountEqual(keys, res3.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_array_equal(targ.values, res3.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
assert_frame_equal(targ, res3)
def test__multi_spiketrains_to_dataframe__block_parents_parentfirst(self):
obj = fake_neo('Block', seed=0, n=3)
res0 = ep.multi_spiketrains_to_dataframe(obj, child_first=False)
res1 = ep.multi_spiketrains_to_dataframe(obj, parents=True,
child_first=False)
objs = obj.list_children_by_class('SpikeTrain')
targ = [ep.spiketrain_to_dataframe(iobj,
parents=True, child_first=False)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=False).keys()
keys = list(keys)
targwidth = len(objs)
targlen = max(len(iobj) for iobj in objs)
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
def test__multi_spiketrains_to_dataframe__list_noparents(self):
obj = [fake_neo('Block', seed=i, n=3) for i in range(3)]
res0 = ep.multi_spiketrains_to_dataframe(obj, parents=False)
res1 = ep.multi_spiketrains_to_dataframe(obj, parents=False,
child_first=True)
res2 = ep.multi_spiketrains_to_dataframe(obj, parents=False,
child_first=False)
objs = (iobj.list_children_by_class('SpikeTrain') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.spiketrain_to_dataframe(iobj,
parents=False, child_first=True)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=False,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = max(len(iobj) for iobj in objs)
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
def test__multi_spiketrains_to_dataframe__list_parents_childfirst(self):
obj = [fake_neo('Block', seed=i, n=3) for i in range(3)]
res0 = ep.multi_spiketrains_to_dataframe(obj)
res1 = ep.multi_spiketrains_to_dataframe(obj, parents=True)
res2 = ep.multi_spiketrains_to_dataframe(obj, child_first=True)
res3 = ep.multi_spiketrains_to_dataframe(obj, parents=True,
child_first=True)
objs = (iobj.list_children_by_class('SpikeTrain') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.spiketrain_to_dataframe(iobj,
parents=True, child_first=True)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = max(len(iobj) for iobj in objs)
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targwidth, len(res3.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertEqual(targlen, len(res3.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
self.assertCountEqual(keys, res3.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_array_equal(targ.values, res3.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
assert_frame_equal(targ, res3)
def test__multi_spiketrains_to_dataframe__list_parents_parentfirst(self):
obj = [fake_neo('Block', seed=i, n=3) for i in range(3)]
res0 = ep.multi_spiketrains_to_dataframe(obj, child_first=False)
res1 = ep.multi_spiketrains_to_dataframe(obj, parents=True,
child_first=False)
objs = (iobj.list_children_by_class('SpikeTrain') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.spiketrain_to_dataframe(iobj,
parents=True, child_first=False)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=False).keys()
keys = list(keys)
targwidth = len(objs)
targlen = max(len(iobj) for iobj in objs)
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
def test__multi_spiketrains_to_dataframe__tuple_default(self):
obj = tuple(fake_neo('Block', seed=i, n=3) for i in range(3))
res0 = ep.multi_spiketrains_to_dataframe(obj)
objs = (iobj.list_children_by_class('SpikeTrain') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.spiketrain_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = max(len(iobj) for iobj in objs)
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
def test__multi_spiketrains_to_dataframe__iter_default(self):
obj = [fake_neo('Block', seed=i, n=3) for i in range(3)]
res0 = ep.multi_spiketrains_to_dataframe(iter(obj))
objs = (iobj.list_children_by_class('SpikeTrain') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.spiketrain_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = max(len(iobj) for iobj in objs)
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
def test__multi_spiketrains_to_dataframe__dict_default(self):
obj = dict((i, fake_neo('Block', seed=i, n=3)) for i in range(3))
res0 = ep.multi_spiketrains_to_dataframe(obj)
objs = (iobj.list_children_by_class('SpikeTrain') for iobj in
obj.values())
objs = list(chain.from_iterable(objs))
targ = [ep.spiketrain_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = max(len(iobj) for iobj in objs)
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
@unittest.skipUnless(HAVE_PANDAS, 'requires pandas')
class MultiEventsToDataframeTestCase(unittest.TestCase):
def setUp(self):
if hasattr(self, 'assertItemsEqual'):
self.assertCountEqual = self.assertItemsEqual
def test__multi_events_to_dataframe__single(self):
obj = fake_neo('Event', seed=0, n=5)
res0 = ep.multi_events_to_dataframe(obj)
res1 = ep.multi_events_to_dataframe(obj, parents=False)
res2 = ep.multi_events_to_dataframe(obj, parents=True)
res3 = ep.multi_events_to_dataframe(obj, child_first=True)
res4 = ep.multi_events_to_dataframe(obj, parents=False,
child_first=True)
res5 = ep.multi_events_to_dataframe(obj, parents=True,
child_first=True)
res6 = ep.multi_events_to_dataframe(obj, child_first=False)
res7 = ep.multi_events_to_dataframe(obj, parents=False,
child_first=False)
res8 = ep.multi_events_to_dataframe(obj, parents=True,
child_first=False)
targ = ep.event_to_dataframe(obj)
keys = ep._extract_neo_attrs_safe(obj, parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = 1
targlen = min(len(obj.times), len(obj.labels))
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targwidth, len(res3.columns))
self.assertEqual(targwidth, len(res4.columns))
self.assertEqual(targwidth, len(res5.columns))
self.assertEqual(targwidth, len(res6.columns))
self.assertEqual(targwidth, len(res7.columns))
self.assertEqual(targwidth, len(res8.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertEqual(targlen, len(res3.index))
self.assertEqual(targlen, len(res4.index))
self.assertEqual(targlen, len(res5.index))
self.assertEqual(targlen, len(res6.index))
self.assertEqual(targlen, len(res7.index))
self.assertEqual(targlen, len(res8.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
self.assertCountEqual(keys, res3.columns.names)
self.assertCountEqual(keys, res4.columns.names)
self.assertCountEqual(keys, res5.columns.names)
self.assertCountEqual(keys, res6.columns.names)
self.assertCountEqual(keys, res7.columns.names)
self.assertCountEqual(keys, res8.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_array_equal(targ.values, res3.values)
assert_array_equal(targ.values, res4.values)
assert_array_equal(targ.values, res5.values)
assert_array_equal(targ.values, res6.values)
assert_array_equal(targ.values, res7.values)
assert_array_equal(targ.values, res8.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
assert_frame_equal(targ, res3)
assert_frame_equal(targ, res4)
assert_frame_equal(targ, res5)
assert_frame_equal(targ, res6)
assert_frame_equal(targ, res7)
assert_frame_equal(targ, res8)
def test__multi_events_to_dataframe__segment_default(self):
obj = fake_neo('Segment', seed=0, n=5)
res0 = ep.multi_events_to_dataframe(obj)
objs = obj.events
targ = [ep.event_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.labels))]
for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
def test__multi_events_to_dataframe__block_noparents(self):
obj = fake_neo('Block', seed=0, n=3)
res0 = ep.multi_events_to_dataframe(obj, parents=False)
res1 = ep.multi_events_to_dataframe(obj, parents=False,
child_first=True)
res2 = ep.multi_events_to_dataframe(obj, parents=False,
child_first=False)
objs = obj.list_children_by_class('Event')
targ = [ep.event_to_dataframe(iobj, parents=False, child_first=True)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=False,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.labels))]
for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
def test__multi_events_to_dataframe__block_parents_childfirst(self):
obj = fake_neo('Block', seed=0, n=3)
res0 = ep.multi_events_to_dataframe(obj)
res1 = ep.multi_events_to_dataframe(obj, parents=True)
res2 = ep.multi_events_to_dataframe(obj, child_first=True)
res3 = ep.multi_events_to_dataframe(obj, parents=True,
child_first=True)
objs = obj.list_children_by_class('Event')
targ = [ep.event_to_dataframe(iobj, parents=True, child_first=True)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.labels))]
for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targwidth, len(res3.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertEqual(targlen, len(res3.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
self.assertCountEqual(keys, res3.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_array_equal(targ.values, res3.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
assert_frame_equal(targ, res3)
def test__multi_events_to_dataframe__block_parents_parentfirst(self):
obj = fake_neo('Block', seed=0, n=3)
res0 = ep.multi_events_to_dataframe(obj, child_first=False)
res1 = ep.multi_events_to_dataframe(obj, parents=True,
child_first=False)
objs = obj.list_children_by_class('Event')
targ = [ep.event_to_dataframe(iobj, parents=True, child_first=False)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=False).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.labels))]
for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
def test__multi_events_to_dataframe__list_noparents(self):
obj = [fake_neo('Block', seed=i, n=3) for i in range(3)]
res0 = ep.multi_events_to_dataframe(obj, parents=False)
res1 = ep.multi_events_to_dataframe(obj, parents=False,
child_first=True)
res2 = ep.multi_events_to_dataframe(obj, parents=False,
child_first=False)
objs = (iobj.list_children_by_class('Event') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.event_to_dataframe(iobj, parents=False, child_first=True)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=False,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.labels))]
for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
def test__multi_events_to_dataframe__list_parents_childfirst(self):
obj = [fake_neo('Block', seed=i, n=3) for i in range(3)]
res0 = ep.multi_events_to_dataframe(obj)
res1 = ep.multi_events_to_dataframe(obj, parents=True)
res2 = ep.multi_events_to_dataframe(obj, child_first=True)
res3 = ep.multi_events_to_dataframe(obj, parents=True,
child_first=True)
objs = (iobj.list_children_by_class('Event') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.event_to_dataframe(iobj, parents=True, child_first=True)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.labels))]
for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targwidth, len(res3.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertEqual(targlen, len(res3.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
self.assertCountEqual(keys, res3.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_array_equal(targ.values, res3.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
assert_frame_equal(targ, res3)
def test__multi_events_to_dataframe__list_parents_parentfirst(self):
obj = [fake_neo('Block', seed=i, n=3) for i in range(3)]
res0 = ep.multi_events_to_dataframe(obj, child_first=False)
res1 = ep.multi_events_to_dataframe(obj, parents=True,
child_first=False)
objs = (iobj.list_children_by_class('Event') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.event_to_dataframe(iobj, parents=True, child_first=False)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=False).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.labels))]
for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
def test__multi_events_to_dataframe__tuple_default(self):
obj = tuple(fake_neo('Block', seed=i, n=3) for i in range(3))
res0 = ep.multi_events_to_dataframe(obj)
objs = (iobj.list_children_by_class('Event') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.event_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.labels))]
for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
def test__multi_events_to_dataframe__iter_default(self):
obj = [fake_neo('Block', seed=i, n=3) for i in range(3)]
res0 = ep.multi_events_to_dataframe(iter(obj))
objs = (iobj.list_children_by_class('Event') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.event_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.labels))]
for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
def test__multi_events_to_dataframe__dict_default(self):
obj = dict((i, fake_neo('Block', seed=i, n=3)) for i in range(3))
res0 = ep.multi_events_to_dataframe(obj)
objs = (iobj.list_children_by_class('Event') for iobj in
obj.values())
objs = list(chain.from_iterable(objs))
targ = [ep.event_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.labels))]
for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
@unittest.skipUnless(HAVE_PANDAS, 'requires pandas')
class MultiEpochsToDataframeTestCase(unittest.TestCase):
def setUp(self):
if hasattr(self, 'assertItemsEqual'):
self.assertCountEqual = self.assertItemsEqual
def test__multi_epochs_to_dataframe__single(self):
obj = fake_neo('Epoch', seed=0, n=5)
res0 = ep.multi_epochs_to_dataframe(obj)
res1 = ep.multi_epochs_to_dataframe(obj, parents=False)
res2 = ep.multi_epochs_to_dataframe(obj, parents=True)
res3 = ep.multi_epochs_to_dataframe(obj, child_first=True)
res4 = ep.multi_epochs_to_dataframe(obj, parents=False,
child_first=True)
res5 = ep.multi_epochs_to_dataframe(obj, parents=True,
child_first=True)
res6 = ep.multi_epochs_to_dataframe(obj, child_first=False)
res7 = ep.multi_epochs_to_dataframe(obj, parents=False,
child_first=False)
res8 = ep.multi_epochs_to_dataframe(obj, parents=True,
child_first=False)
targ = ep.epoch_to_dataframe(obj)
keys = ep._extract_neo_attrs_safe(obj, parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = 1
targlen = min(len(obj.times), len(obj.durations), len(obj.labels))
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targwidth, len(res3.columns))
self.assertEqual(targwidth, len(res4.columns))
self.assertEqual(targwidth, len(res5.columns))
self.assertEqual(targwidth, len(res6.columns))
self.assertEqual(targwidth, len(res7.columns))
self.assertEqual(targwidth, len(res8.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertEqual(targlen, len(res3.index))
self.assertEqual(targlen, len(res4.index))
self.assertEqual(targlen, len(res5.index))
self.assertEqual(targlen, len(res6.index))
self.assertEqual(targlen, len(res7.index))
self.assertEqual(targlen, len(res8.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
self.assertCountEqual(keys, res3.columns.names)
self.assertCountEqual(keys, res4.columns.names)
self.assertCountEqual(keys, res5.columns.names)
self.assertCountEqual(keys, res6.columns.names)
self.assertCountEqual(keys, res7.columns.names)
self.assertCountEqual(keys, res8.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_array_equal(targ.values, res3.values)
assert_array_equal(targ.values, res4.values)
assert_array_equal(targ.values, res5.values)
assert_array_equal(targ.values, res6.values)
assert_array_equal(targ.values, res7.values)
assert_array_equal(targ.values, res8.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
assert_frame_equal(targ, res3)
assert_frame_equal(targ, res4)
assert_frame_equal(targ, res5)
assert_frame_equal(targ, res6)
assert_frame_equal(targ, res7)
assert_frame_equal(targ, res8)
def test__multi_epochs_to_dataframe__segment_default(self):
obj = fake_neo('Segment', seed=0, n=5)
res0 = ep.multi_epochs_to_dataframe(obj)
objs = obj.epochs
targ = [ep.epoch_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.durations),
len(iobj.labels))] for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
def test__multi_epochs_to_dataframe__block_noparents(self):
obj = fake_neo('Block', seed=0, n=3)
res0 = ep.multi_epochs_to_dataframe(obj, parents=False)
res1 = ep.multi_epochs_to_dataframe(obj, parents=False,
child_first=True)
res2 = ep.multi_epochs_to_dataframe(obj, parents=False,
child_first=False)
objs = obj.list_children_by_class('Epoch')
targ = [ep.epoch_to_dataframe(iobj, parents=False, child_first=True)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=False,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.durations),
len(iobj.labels))] for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
def test__multi_epochs_to_dataframe__block_parents_childfirst(self):
obj = fake_neo('Block', seed=0, n=3)
res0 = ep.multi_epochs_to_dataframe(obj)
res1 = ep.multi_epochs_to_dataframe(obj, parents=True)
res2 = ep.multi_epochs_to_dataframe(obj, child_first=True)
res3 = ep.multi_epochs_to_dataframe(obj, parents=True,
child_first=True)
objs = obj.list_children_by_class('Epoch')
targ = [ep.epoch_to_dataframe(iobj, parents=True, child_first=True)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.durations),
len(iobj.labels))] for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targwidth, len(res3.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertEqual(targlen, len(res3.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
self.assertCountEqual(keys, res3.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_array_equal(targ.values, res3.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
assert_frame_equal(targ, res3)
def test__multi_epochs_to_dataframe__block_parents_parentfirst(self):
obj = fake_neo('Block', seed=0, n=3)
res0 = ep.multi_epochs_to_dataframe(obj, child_first=False)
res1 = ep.multi_epochs_to_dataframe(obj, parents=True,
child_first=False)
objs = obj.list_children_by_class('Epoch')
targ = [ep.epoch_to_dataframe(iobj, parents=True, child_first=False)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=False).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.durations),
len(iobj.labels))] for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
def test__multi_epochs_to_dataframe__list_noparents(self):
obj = [fake_neo('Block', seed=i, n=3) for i in range(3)]
res0 = ep.multi_epochs_to_dataframe(obj, parents=False)
res1 = ep.multi_epochs_to_dataframe(obj, parents=False,
child_first=True)
res2 = ep.multi_epochs_to_dataframe(obj, parents=False,
child_first=False)
objs = (iobj.list_children_by_class('Epoch') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.epoch_to_dataframe(iobj, parents=False, child_first=True)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=False,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.durations),
len(iobj.labels))] for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
def test__multi_epochs_to_dataframe__list_parents_childfirst(self):
obj = [fake_neo('Block', seed=i, n=3) for i in range(3)]
res0 = ep.multi_epochs_to_dataframe(obj)
res1 = ep.multi_epochs_to_dataframe(obj, parents=True)
res2 = ep.multi_epochs_to_dataframe(obj, child_first=True)
res3 = ep.multi_epochs_to_dataframe(obj, parents=True,
child_first=True)
objs = (iobj.list_children_by_class('Epoch') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.epoch_to_dataframe(iobj, parents=True, child_first=True)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.durations),
len(iobj.labels))] for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targwidth, len(res2.columns))
self.assertEqual(targwidth, len(res3.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertEqual(targlen, len(res2.index))
self.assertEqual(targlen, len(res3.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
self.assertCountEqual(keys, res2.columns.names)
self.assertCountEqual(keys, res3.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_array_equal(targ.values, res2.values)
assert_array_equal(targ.values, res3.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
assert_frame_equal(targ, res3)
def test__multi_epochs_to_dataframe__list_parents_parentfirst(self):
obj = [fake_neo('Block', seed=i, n=3) for i in range(3)]
res0 = ep.multi_epochs_to_dataframe(obj, child_first=False)
res1 = ep.multi_epochs_to_dataframe(obj, parents=True,
child_first=False)
objs = (iobj.list_children_by_class('Epoch') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.epoch_to_dataframe(iobj, parents=True, child_first=False)
for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=False).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.durations),
len(iobj.labels))] for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targwidth, len(res1.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertEqual(targlen, len(res1.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
self.assertCountEqual(keys, res1.columns.names)
assert_array_equal(targ.values, res0.values)
assert_array_equal(targ.values, res1.values)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
def test__multi_epochs_to_dataframe__tuple_default(self):
obj = tuple(fake_neo('Block', seed=i, n=3) for i in range(3))
res0 = ep.multi_epochs_to_dataframe(obj)
objs = (iobj.list_children_by_class('Epoch') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.epoch_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.durations),
len(iobj.labels))] for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
def test__multi_epochs_to_dataframe__iter_default(self):
obj = [fake_neo('Block', seed=i, n=3) for i in range(3)]
res0 = ep.multi_epochs_to_dataframe(iter(obj))
objs = (iobj.list_children_by_class('Epoch') for iobj in obj)
objs = list(chain.from_iterable(objs))
targ = [ep.epoch_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.durations),
len(iobj.labels))] for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
def test__multi_epochs_to_dataframe__dict_default(self):
obj = dict((i, fake_neo('Block', seed=i, n=3)) for i in range(3))
res0 = ep.multi_epochs_to_dataframe(obj)
objs = (iobj.list_children_by_class('Epoch') for iobj in
obj.values())
objs = list(chain.from_iterable(objs))
targ = [ep.epoch_to_dataframe(iobj) for iobj in objs]
targ = ep._sort_inds(pd.concat(targ, axis=1), axis=1)
keys = ep._extract_neo_attrs_safe(objs[0], parents=True,
child_first=True).keys()
keys = list(keys)
targwidth = len(objs)
targlen = [iobj.times[:min(len(iobj.times), len(iobj.durations),
len(iobj.labels))] for iobj in objs]
targlen = len(np.unique(np.hstack(targlen)))
self.assertGreater(len(objs), 0)
self.assertEqual(targwidth, len(targ.columns))
self.assertEqual(targwidth, len(res0.columns))
self.assertEqual(targlen, len(targ.index))
self.assertEqual(targlen, len(res0.index))
self.assertCountEqual(keys, targ.columns.names)
self.assertCountEqual(keys, res0.columns.names)
assert_array_equal(targ.values, res0.values)
assert_frame_equal(targ, res0)
@unittest.skipUnless(HAVE_PANDAS, 'requires pandas')
class SliceSpiketrainTestCase(unittest.TestCase):
def setUp(self):
obj = [fake_neo('SpikeTrain', seed=i, n=3) for i in range(10)]
self.obj = ep.multi_spiketrains_to_dataframe(obj)
def test_single_none(self):
targ_start = self.obj.columns.get_level_values('t_start').values
targ_stop = self.obj.columns.get_level_values('t_stop').values
res0 = ep.slice_spiketrain(self.obj)
res1 = ep.slice_spiketrain(self.obj, t_start=None)
res2 = ep.slice_spiketrain(self.obj, t_stop=None)
res3 = ep.slice_spiketrain(self.obj, t_start=None, t_stop=None)
res0_start = res0.columns.get_level_values('t_start').values
res1_start = res1.columns.get_level_values('t_start').values
res2_start = res2.columns.get_level_values('t_start').values
res3_start = res3.columns.get_level_values('t_start').values
res0_stop = res0.columns.get_level_values('t_stop').values
res1_stop = res1.columns.get_level_values('t_stop').values
res2_stop = res2.columns.get_level_values('t_stop').values
res3_stop = res3.columns.get_level_values('t_stop').values
targ = self.obj
self.assertFalse(res0 is targ)
self.assertFalse(res1 is targ)
self.assertFalse(res2 is targ)
self.assertFalse(res3 is targ)
assert_frame_equal(targ, res0)
assert_frame_equal(targ, res1)
assert_frame_equal(targ, res2)
assert_frame_equal(targ, res3)
assert_array_equal(targ_start, res0_start)
assert_array_equal(targ_start, res1_start)
assert_array_equal(targ_start, res2_start)
assert_array_equal(targ_start, res3_start)
assert_array_equal(targ_stop, res0_stop)
assert_array_equal(targ_stop, res1_stop)
assert_array_equal(targ_stop, res2_stop)
assert_array_equal(targ_stop, res3_stop)
def test_single_t_start(self):
targ_start = .0001
targ_stop = self.obj.columns.get_level_values('t_stop').values
res0 = ep.slice_spiketrain(self.obj, t_start=targ_start)
res1 = ep.slice_spiketrain(self.obj, t_start=targ_start, t_stop=None)
res0_start = res0.columns.get_level_values('t_start').unique().tolist()
res1_start = res1.columns.get_level_values('t_start').unique().tolist()
res0_stop = res0.columns.get_level_values('t_stop').values
res1_stop = res1.columns.get_level_values('t_stop').values
targ = self.obj.values
targ[targ < targ_start] = np.nan
self.assertFalse(res0 is targ)
self.assertFalse(res1 is targ)
assert_array_equal(targ, res0.values)
assert_array_equal(targ, res1.values)
self.assertEqual([targ_start], res0_start)
self.assertEqual([targ_start], res1_start)
| assert_array_equal(targ_stop, res0_stop) | numpy.testing.utils.assert_array_equal |
# Authors: <NAME> <<EMAIL>>
# License: TBC
import numpy as np
class EventOrder(object):
def __init__(self, ordering=None, n_biomarkers=None, score=None):
super(EventOrder, self).__init__()
if ordering is None and n_biomarkers is None:
raise ValueError('EventOrder __init__ takes one arguement,'
' zero given')
if ordering is None:
self.ordering = np.arange(n_biomarkers)
np.random.shuffle(self.ordering)
self.n_biomarkers = n_biomarkers
else:
self.ordering = ordering
self.n_biomarkers = ordering.shape[0]
self.score = score
def score_ordering(self, prob_mat):
k = prob_mat.shape[1]+1
p_perm = self.calc_perm_matrix(prob_mat)
likelihood = np.sum(np.log(np.sum((1./k)*p_perm, 1)+1e-250))
self.score = likelihood
return likelihood
def calc_indiv_likelihoods(self, prob_mat):
k = prob_mat.shape[1]+1
p_perm = self.calc_perm_matrix(prob_mat)
likelihoods = np.log(np.sum((1./k)*p_perm, 1)+1e-250)
return likelihoods
def calc_perm_matrix(self, prob_mat):
event_order = self.ordering
p_yes = np.array(prob_mat[:, event_order, 1])
p_no = np.array(prob_mat[:, event_order, 0])
k = prob_mat.shape[1]+1
p_perm = np.zeros((prob_mat.shape[0], k))
for i in range(k):
p_perm[:, i] = np.prod(p_yes[:, :i], 1)*np.prod(p_no[:, i:k-1], 1)
return p_perm
def stage_data(self, prob_mat):
event_order = self.ordering
p_yes = np.array(prob_mat[:, event_order, 1])
p_no = np.array(prob_mat[:, event_order, 0])
n_particp, n_biomarkers = p_yes.shape
k = n_biomarkers+1
stage_likelihoods = np.empty((n_particp, n_biomarkers+1))
for i in range(k):
stage_likelihoods[:, i] = np.prod(p_yes[:, :i], 1)* | np.prod(p_no[:, i:n_biomarkers], 1) | numpy.prod |
"""62-make-diffusionmaps-and-geometricharmonicsinterpolator-compatible-with-scikit-learn-api
Unit test for the Geometric Harmonics module.
"""
import unittest
import diffusion_maps as legacy_dmap
import matplotlib.pyplot as plt
import numpy as np
from sklearn.datasets import make_swiss_roll
from sklearn.model_selection import ParameterGrid
from sklearn.utils.estimator_checks import check_estimator
from datafold.dynfold.outofsample import (
GeometricHarmonicsInterpolator,
LaplacianPyramidsInterpolator,
MultiScaleGeometricHarmonicsInterpolator,
)
from datafold.dynfold.tests.helper import *
from datafold.pcfold.distance import IS_IMPORTED_RDIST
from datafold.pcfold.kernels import DmapKernelFixed, GaussianKernel
def plot_scatter(points: np.ndarray, values: np.ndarray, **kwargs) -> None:
title = kwargs.pop("title", None)
if title:
plt.title(title)
plt.scatter(
points[:, 0],
points[:, 1],
c=values,
marker="o",
rasterized=True,
s=2.5,
**kwargs,
)
cb = plt.colorbar()
cb.set_clim([np.min(values), np.max(values)])
cb.set_ticks(np.linspace(np.min(values), np.max(values), 5))
plt.xlim([-4, 4])
plt.ylim([-4, 4])
plt.xlabel("$x$")
plt.ylabel("$y$")
plt.gca().set_aspect("equal")
def f(points: np.ndarray) -> np.ndarray:
"""Function to interpolate."""
# return np.ones(points.shape[0])
# return np.arange(points.shape[0])
return np.sin( | np.linalg.norm(points, axis=-1) | numpy.linalg.norm |
"""Use GTR to model distribution of future viral sequences
"""
import numpy as np
from scipy.linalg import expm
class GTRSubstitutionModel:
"""GTR Substitution model to model distribution of future viral sequences
"""
def __init__(self, piA, piC, piG, piT, rAC, rAG, rAT, rCG, rCT, rGT, mu, t):
self.piA = piA
self.piC = piC
self.piG = piG
self.piT = piT
self.rAC = rAC
self.rAG = rAG
self.rAT = rAT
self.rCG = rCG
self.rCT = rCT
self.rGT = rGT
self.mu = mu
self.t = t
self.Q = self._construct_rateQ()
self.P = self._construct_P()
def _construct_rateQ(self):
"""Computes transition rate matrix Q, given base frequencies and transition rates under GTR model (Tavaré 1986).
"""
beta = 1 / (2*(self.piA * (self.rAC*self.piC + self.rAG*self.piG + self.rAT*self.piT) + self.piC * (self.rCG*self.piG + self.rCT*self.piT) + self.piG*self.piT))
Q = | np.array(
[
[-(self.rAC*self.piC + self.rAG*self.piG + self.rAT*self.piT), self.rAC*self.piC, self.rAG*self.piG, self.rAT*self.piT],
[self.rAC*self.piA, -(self.rAC*self.piA + self.rCG*self.piG + self.rCT*self.piT), self.rCG*self.piG, self.rCT*self.piT],
[self.rAG*self.piA, self.rCG*self.piC, -(self.rAG*self.piA + self.rCG*self.piC + self.rGT*self.piT), self.rGT*self.piT],
[self.rAT*self.piA, self.rCT*self.piC, self.rGT*self.piG, -(self.rAT*self.piA + self.rCT*self.piC + self.rGT*self.piG)]
]) | numpy.array |
import sys
import warnings
import numpy as np
from tempfile import mkdtemp
from astropy.stats import sigma_clipped_stats
from sfft.utils.pyAstroMatic.PYSEx import PY_SEx
from sfft.utils.HoughDetection import Hough_Detection
__author__ = "<NAME> <<EMAIL>>"
__version__ = "v1.0"
"""
# MeLOn Notes
# @ Point-Source Extractor
# A) A PSFEx suggested Morphological Classifier, based on a 2D distribution diagram
# FLUX_RADIUS [X-axis] - MAG_AUTO [Y-axis], A universal but naive approach.
# We first draw all isolated sources on the plane, and the typical distribution will form a 'Y' shape.
# A nearly vertical branch, A nearly horizontal branch and their cross with a tail at faint side.
#
# Here I give rough conclusions with comments, note I have compared with Legacy Survety Tractor Catalog.
# a. The point sources would be distributed around the nearly vertical stright line. {vertical branch}
# NOTE At the faint end, point sources no longer cling to the line, being diffuse in the cross and tail.
# b. Close to the bright end of the stright-line are saturated or slight-nonlinear sources, with a deviated direction.
# c. The right side of the line are typically extended structure, mainly including various galaxies. {horizontal branch}
# NOTE At the faint end, likewise, extended sources also exist, being diffuse in the cross and tail.
# d. Scattering points are located at very left side of the line, they are generally hotpix, cosmic-ray or
# some small-scale artifacts. Keep in mind, they are typically outlier-like and away from the cross and tail.
#
# METHOD: For simplicity, we only crudely divide the diagram into 3 regions, w.r.t. the vetical line.
# they are, Radius-Mid (FR-M), Radius-Large (FR-L) and Radius-Small (FR-S).
#
# B) 3 hierarchic groups
# > Good Sources:
# + NOT in FR-S region (union of FR-M & FR-L)
# NOTE Good Sources is consist of the vertical & horizontal branches with their cross (not the tail),
# which is roughly equivalent to the set of REAL Point-Sources & Extended Sources
# with rejection the samples in the tail (at faint & small-radius end).
# NOTE Good Sources are commonly used as FITTING Candidates in Image Subtraction.
# It is acceptable to lose the samples in the tail.
#
# >> {subgroup} Point Sources:
# + Restricted into FR-M Region ||| Should be located around the Hough-Line
# + Basically Circular-Shape ||| PsfEx-ELLIPTICITY = (A-B) / (A+B) < PS_ELLIPThresh
# NOTE At cross region, this identification criteria mis-include some extended source
# On the flip side, some REAL PointSource samples are missing in the tail.
# NOTE Point Sources are usually employed as FWHM Estimator.
# NOTE We may lossen PS_ELLIPThresh if psf itself is significantly asymmetric (e.g. tracking problem).
#
# >>> {sub-subgroup} High-SNR Point Sources
# + SNR_WIN > HPS_SNRThresh, then reject the bright end [typically, 15% (HPS_Reject)] point-sources.
# ++ If remaining sources are less than 30 (HPS_NumLowerLimit),
# Simply Use the point-sources with highest SNR_WIN.
# NOTE In Common, this subset is for Flux-Calibration & Building PSF Model.
# NOTE The defult HPS_SNRThresh = 100 might be too high, you may loosen it to
# ~ 15 to make sure you have enough samples, especially for psf modeling.
#
# @ Remarks on the HPS BrightEnd-Cutoff
# Assume SExtractor received precise SATURATE, saturated sources should be fully rejected via FLAG constrain.
# However, in practice, it's hard to fullfill this condition strictly, that is why we design a simple BrightEnd-Cutoff
# to prevent the set from such contaminations. Compared with mentioned usage of GS & PS, that of HPS is more
# vulnerable to such situation. FLUX-Calibtation and Building PSF-Model do not require sample completeness, but
# likely to be sensitive to the sources with appreiable non-linear response.
#
# C) Additional WARNINGS
# a. This extracor is ONLY designed for sparse field (isolated sources dominated case).
# We just take these isloated & non-saturated sources (FLAGS=0) into account in this function.
#
# b. We employ Hough Transformation to detect the Stright-Line feature in the image,
# naturally sampled from the raw scatter diagram. But note such diagram makes sense
# only if we could detect enough sources (typically > 200) in the given image.
# NOTE Reversed axes employed --- MAG_AUTO [X-axis] - FLUX_RADIUS [Y-axis].
"""
class Hough_MorphClassifier:
def MakeCatalog(FITS_obj, GAIN_KEY='GAIN', SATUR_KEY='SATURATE', \
BACK_TYPE='AUTO', BACK_VALUE='0.0', BACK_SIZE=64, BACK_FILTERSIZE=3, \
DETECT_THRESH=2.0, DETECT_MINAREA=5, DETECT_MAXAREA=0, \
BACKPHOTO_TYPE='LOCAL', CHECKIMAGE_TYPE='NONE', \
AddRD=False, BoundarySIZE=30, AddSNR=True):
# * Trigger SExtractor
# NOTE: it is a compromise to adopt XY rather than XYWIN for both point and extended sources.
# NOTE: only takes Isolated & Non-Saturated sources (FLAGS = 0) into account.
# FIXME: one may need to tune DETECT_THRESH & DETECT_MINAREA for specific program.
PL = ['X_IMAGE', 'Y_IMAGE', 'FLUX_AUTO', 'FLUXERR_AUTO', 'MAG_AUTO', 'MAGERR_AUTO', \
'FLAGS', 'FLUX_RADIUS', 'FWHM_IMAGE', 'A_IMAGE', 'B_IMAGE']
if AddSNR: PL.append('SNR_WIN')
PYSEX_OP = PY_SEx.PS(FITS_obj=FITS_obj, PL=PL, GAIN_KEY=GAIN_KEY, SATUR_KEY=SATUR_KEY, \
BACK_TYPE=BACK_TYPE, BACK_VALUE=BACK_VALUE, BACK_SIZE=BACK_SIZE, BACK_FILTERSIZE=BACK_FILTERSIZE, \
DETECT_THRESH=DETECT_THRESH, DETECT_MINAREA=DETECT_MINAREA, DETECT_MAXAREA=DETECT_MAXAREA, \
BACKPHOTO_TYPE=BACKPHOTO_TYPE, CHECKIMAGE_TYPE=CHECKIMAGE_TYPE, AddRD=AddRD, ONLY_FLAG0=True, \
XBoundary=BoundarySIZE, YBoundary=BoundarySIZE, MDIR=None)
return PYSEX_OP
def Classifier(AstSEx, Hough_FRLowerLimit=0.1, Hough_res=0.05, Hough_count_thresh=1, Hough_peakclip=0.7, \
LineTheta_thresh=0.2, BeltHW=0.2, PS_ELLIPThresh=0.3, Return_HPS=False, \
HPS_SNRThresh=100.0, HPS_Reject=0.15, HPS_NumLowerLimit=30):
A_IMAGE = np.array(AstSEx['A_IMAGE'])
B_IMAGE = np.array(AstSEx['B_IMAGE'])
MA_FR = np.array([AstSEx['MAG_AUTO'], AstSEx['FLUX_RADIUS']]).T
ELLIP = (A_IMAGE - B_IMAGE)/(A_IMAGE + B_IMAGE)
MASK_ELLIP = ELLIP < PS_ELLIPThresh
# * Trigger Hough Dectection
# Use Hough-Transformation detect the Point-Source-Line from the scatter points in
# diagram X [MAG_AUTO] - Y [FLUX_RADIUS], which is a nearly-horizon stright line.
# ** Remarks on the Mask for Hough Transformation
# It is s useful to make restriction on FLUX_RADIUS (R) of the scatter points for hough detection.
# I. Exclude the sources with unusally large R > 20.0 can speed up the process.
# II. The sources with small R (typically ~ 0.5) are likely hot pixels or cosmic rays.
# The parameter Hough_FRLowerLimit is the lower bound of FLUX_RATIO for Hough transformation.
# Setting a proper lower bound can avoid to detect some line features by chance,
# which are not contributed from point sources but resides in the small-FLUX_RATIO region.
# NOTE: One need to choose a proper Hough_FRLowerLimit according to the fact if the image is
# under/well/over-sampling (depending on the instrumental configuration and typical seeing conditions)
# recommended values of Hough_FRLowerLimit range from 0.1 to 1.0
MA, FR = MA_FR[:, 0], MA_FR[:, 1]
MA_MID = np.nanmedian(MA)
Hmask = np.logical_and.reduce((FR > Hough_FRLowerLimit, FR < 10.0, MA > MA_MID-7.0, MA < MA_MID+7.0))
HDOP = Hough_Detection.HD(XY_obj=MA_FR, Hmask=Hmask, res=Hough_res, \
count_thresh=Hough_count_thresh, peakclip=Hough_peakclip)
ThetaPeaks, RhoPeaks, ScaLineDIS = HDOP[1], HDOP[2], HDOP[4]
# NOTE: consider the strongest nearly-horizon peak as the one associated with the point source feature.
Avmask = np.abs(ThetaPeaks) < LineTheta_thresh
AvIDX = np.where(Avmask)[0]
if len(AvIDX) == 0:
Horindex = None
warnings.warn('MeLOn WARNING: NO nearly-horizon peak as Point-Source-Line!')
if len(AvIDX) == 1:
Horindex = AvIDX[0]
print('MeLOn CheckPoint: the UNIQUE nearly-horizon peak as Point-Source-Line!')
if len(AvIDX) > 1:
Horindex = np.min(AvIDX)
warnings.warn('MeLOn WARNING: there are MULTIPLE nearly-horizon peaks and use the STRONGEST as Point-Source-Line!')
if Horindex is not None:
HorThetaPeak = ThetaPeaks[Horindex]
HorRhoPeak = RhoPeaks[Horindex]
HorScaLineDIS = ScaLineDIS[:, Horindex]
print('MeLOn CheckPoint: the Hough-Detected Point-Source-Line is characterized by (%s, %s)' \
%(HorThetaPeak, HorRhoPeak))
# NOTE: Note that HorThetaPeak is around 0, thus cos(HorThetaPeak) around 1 then >> 0,
# thus above-line/FRL region is x_above * sin(HorThetaPeak) + y_above * cos(HorRhoPeak) > rho.
MASK_FRM = HorScaLineDIS < BeltHW
MASK_FRL = MA_FR[:, 0] * np.sin(HorThetaPeak) + MA_FR[:, 1] * np.cos(HorThetaPeak) > HorRhoPeak
MASK_FRL = np.logical_and(MASK_FRL, ~MASK_FRM)
else:
# NOTE: If we have enough samples, using the bright & small-FR subgroup might be
# more appropriate for the estimate. However, it is quite tricky to find a generic
# reliable way to find the point sources when the Hough Transformation doesn't work.
# Here we only simply reject the samples with low significance.
BPmask = AstSEx['MAGERR_AUTO'] < 0.2
Rmid = sigma_clipped_stats(MA_FR[BPmask, 1], sigma=3.0, maxiters=5)[1]
MASK_FRM = np.abs(MA_FR[:, 1] - Rmid) < BeltHW
MASK_FRL = MA_FR[:, 1] - Rmid > BeltHW
warnings.warn('MeLOn WARNING: the STANDBY approach is actived to determine the FRM region!')
MASK_FRS = ~np.logical_or(MASK_FRM, MASK_FRL)
LABEL_FR = np.array(['FR-S'] * len(AstSEx))
LABEL_FR[MASK_FRM] = 'FR-M'
LABEL_FR[MASK_FRL] = 'FR-L'
print('MeLOn CheckPoint: count Lables from Hough Transformation [FR-S (%s) / FR-M (%s) / FR-L (%s)] !' \
%(np.sum(MASK_FRS), np.sum(MASK_FRM), np.sum(MASK_FRL)))
# * Produce the 3 hierarchic groups
# ** Good Sources
MASK_GS = ~MASK_FRS
# *** Point Sources
MASK_PS = | np.logical_and(MASK_FRM, MASK_ELLIP) | numpy.logical_and |
import sys
import numpy
import scipy.ndimage.measurements
from skimage.morphology import watershed
from clarity.Analysis.Voxelization import voxelizePixel
from clarity.ImageProcessing.StackProcessing import writeSubStack
from clarity.Utils.Timer import Timer
from clarity.Utils.ParameterTools import getParameter, writeParameter
from clarity.Visualization.Plot import plotOverlayLabel
import clarity.IO as io
def detectCellShape(img, peaks, detectCellShapeParameter = None, compactWatershedParameter=0,threshold = None, save = None, verbose = False,
subStack = None, out = sys.stdout, **parameter):
"""Find cell shapes as labeled image
Arguments:
img (array): image data
peaks (array): point data of cell centers / seeds
detectCellShape (dict):
============ =================== ===========================================================
Name Type Descritption
============ =================== ===========================================================
*threshold* (float or None) threshold to determine mask, pixel below this are background
if None no mask is generated
*save* (tuple) size of the box on which to perform the *method*
*verbose* (bool or int) print / plot information about this step
============ =================== ===========================================================
verbose (bool): print progress info
out (object): object to write progress info to
Returns:
array: labeled image where each label indicates a cell
"""
threshold = getParameter(detectCellShapeParameter, "threshold", threshold)
save = getParameter(detectCellShapeParameter, "save", save)
verbose = getParameter(detectCellShapeParameter, "verbose", verbose)
if verbose:
writeParameter(out = out, head = 'Cell shape detection:', threshold = threshold, save = save)
# extended maxima
timer = Timer()
if threshold is None:
imgmask = None
else:
imgmask = img > threshold
imgpeaks = voxelizePixel(peaks, dataSize = img.shape, weights = numpy.arange(1, peaks.shape[0]+1))
#imgpeaks = voxelizePixel(peaks, dataSize = img.shape, weights = numpy.arange(2, peaks.shape[0]+2))
#imgws = cv2.watershed(img, imgpeaks)
imgws = watershed(-img, imgpeaks, mask = imgmask)
#imgws = watershed_ift(-img.astype('uint16'), imgpeaks)
#imgws[numpy.logical_not(imgmask)] = 0
if not save is None:
'''
Edit: WG, 8/4/17: writeSubStack won't work because we can't specify a start slice.
'''
writeSubStack(save, imgws.astype('int32'), subStack = subStack)
# io.writeData(save, imgws.astype('int32'))
if verbose > 1:
#plotTiling(img)
plotOverlayLabel(img * 0.01, imgws, alpha = False)
#plotOverlayLabel(img, imgmax.astype('int64'), alpha = True)
if verbose:
out.write(timer.elapsedTime(head = 'Cell Shape:') + '\n')
return imgws
def findCellSize(imglabel, findCelSizeParameter = None, maxLabel = None, verbose = False,
out = sys.stdout, **parameter):
"""Find cell size given cell shapes as labled image
Arguments:
imglabel (array or str): labeled image, where each cell has its own label
findCelSizeParameter (dict):
=========== =================== ===========================================================
Name Type Descritption
=========== =================== ===========================================================
*maxLabel* (int or None) maximal label to include, if None determine automatically
*verbose* (bool or int) print / plot information about this step
=========== =================== ===========================================================
verbose (bool): print progress info
out (object): object to write progress info to
Returns:
array: measured intensities
"""
maxLabel = getParameter(findCelSizeParameter, "maxLabel", maxLabel)
verbose = getParameter(findCelSizeParameter, "verbose", verbose)
if verbose:
writeParameter(out = out, head = 'Cell size detection:', maxLabel = maxLabel)
timer = Timer()
if maxLabel is None:
maxLabel = int(imglabel.max())
size = scipy.ndimage.measurements.sum(numpy.ones(imglabel.shape, dtype = bool), labels = imglabel, index = numpy.arange(1, maxLabel + 1))
if verbose:
out.write(timer.elapsedTime(head = 'Cell size detection:') + '\n')
return size
def findCellIntensity(img, imglabel, findCellIntensityParameter = None, maxLabel = None, method = 'sum', verbose = False,
out = sys.stdout, **parameter):
"""Find integrated cell intensity given cell shapes as labled image
Arguments:
img (array or str): image data
imglabel (array or str): labeled image, where each cell has its own label
findCellIntensityParameter (dict):
=========== =================== ===========================================================
Name Type Descritption
=========== =================== ===========================================================
*maxLabel* (int or None) maximal label to include, if None determine automatically
*method* (str) method to use for measurment: 'Sum', 'Mean', 'Max', 'Min'
*verbose* (bool or int) print / plot information about this step
=========== =================== ===========================================================
verbose (bool): print progress info
out (object): object to write progress info to
Returns:
array: measured intensities
"""
maxLabel = getParameter(findCellIntensityParameter, "maxLabel", maxLabel)
method = getParameter(findCellIntensityParameter, "method", method)
verbose = getParameter(findCellIntensityParameter, "verbose", verbose)
if verbose:
writeParameter(out = out, head = 'Cell intensity detection:', method = method, maxLabel = maxLabel)
timer = Timer()
if maxLabel is None:
maxLabel = imglabel.max()
if method.lower() == 'sum':
i = scipy.ndimage.measurements.sum(img, labels = imglabel, index = | numpy.arange(1, maxLabel + 1) | numpy.arange |
# -*- coding: utf-8 -*-
"""
Created on Thu Dec 21 14:23:13 2017
@author: mat.mathews
"""
import numpy as np
import matplotlib.pyplot as plt
filename1 = './init_field_hit.dat'
filename2 = './init_field_hit_2.dat'
dataIn1 = np.loadtxt(filename1,dtype=np.double)
dataIn2 = np.loadtxt(filename2,dtype=np.double)
N = 129
U1 = np.empty((N-1,N-1,N-1),dtype=np.double)
V1 = np.empty((N-1,N-1,N-1),dtype=np.double)
W1 = np.empty((N-1,N-1,N-1),dtype=np.double)
U2 = np.empty((N-1,N-1,N-1),dtype=np.double)
V2 = np.empty((N-1,N-1,N-1),dtype=np.double)
W2 = np.empty((N-1,N-1,N-1),dtype=np.double)
dx = 2*np.pi/N
dy = 2*np.pi/N
dz = 2*np.pi/N
for k in range(0,N-1):
for j in range(0,N-1):
for i in range(0,N-1):
ii = k*N*N + j*N + i
U1[i,j,k] = dataIn1[ii,3]
V1[i,j,k] = dataIn1[ii,4]
W1[i,j,k] = dataIn1[ii,5]
U2[i,j,k] = dataIn2[ii,3]
V2[i,j,k] = dataIn2[ii,4]
W2[i,j,k] = dataIn2[ii,5]
#%%
uprime1 = 0
uprime2 = 0
q1 = 0
q2 = 0
for k in range(0,N-1):
for j in range(0,N-1):
for i in range(0,N-1):
uprime1 += (U1[i,j,k]**2 + V1[i,j,k]**2 + W1[i,j,k]**2)/3
q1 += (U1[i,j,k]**2 + V1[i,j,k]**2 + W1[i,j,k]**2)
uprime2 += (U2[i,j,k]**2 + V2[i,j,k]**2 + W2[i,j,k]**2)/3
q2 += (U2[i,j,k]**2 + V2[i,j,k]**2 + W2[i,j,k]**2)
uprime1 = uprime1/(N-1)/(N-1)/(N-1)
q1 = q1/(N-1)/(N-1)/(N-1)
uprime1 = np.sqrt(uprime1)
q1 = np.sqrt(q1)
uprime2 = uprime2/(N-1)/(N-1)/(N-1)
q2 = q2/(N-1)/(N-1)/(N-1)
uprime2 = np.sqrt(uprime2)
q2 = np.sqrt(q2)
#%%
uprimeGoal = 1
U1 = U1*uprimeGoal/uprime1
V1 = V1*uprimeGoal/uprime1
W1 = W1*uprimeGoal/uprime1
U2 = U2*uprimeGoal/uprime2
V2 = V2*uprimeGoal/uprime2
W2 = W2*uprimeGoal/uprime2
#%%
#Need to get the source field for the poisson eqn.
#these are rough perturbations for the field, 2nd order central should be enough
S = np.empty((N-1,N-1,N-1),dtype=np.double)
Ux = np.empty((N-1,N-1,N-1),dtype=np.double)
Uy = np.empty((N-1,N-1,N-1),dtype=np.double)
Uz = np.empty((N-1,N-1,N-1),dtype=np.double)
Vx = np.empty((N-1,N-1,N-1),dtype=np.double)
Vy = np.empty((N-1,N-1,N-1),dtype=np.double)
Vz = np.empty((N-1,N-1,N-1),dtype=np.double)
Wx = np.empty((N-1,N-1,N-1),dtype=np.double)
Wy = np.empty((N-1,N-1,N-1),dtype=np.double)
Wz = np.empty((N-1,N-1,N-1),dtype=np.double)
for k in range(0,N-1):
for j in range(0, N-1):
for i in range(0, N-1):
if i==0:
Ux[0,j,k] = (U1[1,j,k] - U1[-1,j,k])/(2*dx)
Vx[0,j,k] = (V1[1,j,k] - V1[-1,j,k])/(2*dx)
Wx[0,j,k] = (W1[1,j,k] - W1[-1,j,k])/(2*dx)
elif i==(N-2):
Ux[-1,j,k] = (U1[0,j,k] - U1[-2,j,k])/(2*dx)
Vx[-1,j,k] = (V1[0,j,k] - V1[-2,j,k])/(2*dx)
Wx[-1,j,k] = (W1[0,j,k] - W1[-2,j,k])/(2*dx)
else:
Ux[i,j,k] = (U1[i+1,j,k] - U1[i-1,j,k])/(2*dx)
Vx[i,j,k] = (V1[i+1,j,k] - V1[i-1,j,k])/(2*dx)
Wx[i,j,k] = (W1[i+1,j,k] - W1[i-1,j,k])/(2*dx)
if j==0:
Uy[i,0,k] = (U1[i,1,k] - U1[i,-1,k])/(2*dx)
Vy[i,0,k] = (V1[i,1,k] - V1[i,-1,k])/(2*dx)
Wy[i,0,k] = (W1[i,1,k] - W1[i,-1,k])/(2*dx)
elif j==(N-2):
Uy[i,-1,k] = (U1[i,0,k] - U1[i,-2,k])/(2*dx)
Vy[i,-1,k] = (V1[i,0,k] - V1[i,-2,k])/(2*dx)
Wy[i,-1,k] = (W1[i,0,k] - W1[i,-2,k])/(2*dx)
else:
Uy[i,j,k] = (U1[i,j+1,k] - U1[i,j-1,k])/(2*dx)
Vy[i,j,k] = (V1[i,j+1,k] - V1[i,j-1,k])/(2*dx)
Wy[i,j,k] = (W1[i,j+1,k] - W1[i,j-1,k])/(2*dx)
if k==0:
Uz[i,j,0] = (U1[i,j,1] - U1[i,j,-1])/(2*dx)
Vz[i,j,0] = (V1[i,j,1] - V1[i,j,-1])/(2*dx)
Wz[i,j,0] = (W1[i,j,1] - W1[i,j,-1])/(2*dx)
elif k==(N-2):
Uz[i,j,-1] = (U1[i,j,0] - U1[i,j,-2])/(2*dx)
Vz[i,j,-1] = (V1[i,j,0] - V1[i,j,-2])/(2*dx)
Wz[i,j,-1] = (W1[i,j,0] - W1[i,j,-2])/(2*dx)
else:
Uz[i,j,k] = (U1[i,j,k+1] - U1[i,j,k-1])/(2*dx)
Vz[i,j,k] = (V1[i,j,k+1] - V1[i,j,k-1])/(2*dx)
Wz[i,j,k] = (W1[i,j,k+1] - W1[i,j,k-1])/(2*dx)
S = -(Ux*Ux + Vy*Vy + Wz*Wz + 2*Uy*Vx + 2*Vz*Wy + 2*Uz*Wx)
#%%
ptilde1 = np.empty((N-1,N-1,N-1),dtype=np.double)
ptilde2 = np.empty((N-1,N-1,N-1),dtype=np.double)
ppadtemp = np.empty((N+1,N+1,N+1),dtype=np.double)
r = np.empty((N-1,N-1,N-1),dtype=np.double)
ptilde1[:,:,:] = 0.0
ptilde2[:,:,:] = 0.0
r[:,:,:] = 0.0
omega = 2 / ( 1 + np.sin(np.pi/(N)) )
for kk in range(0,2000):
ppadtemp[:,:,:] = 0.0
ppadtemp[1:-1,1:-1, 1:-1] = ptilde1
ppadtemp[0 ,1:-1, 1:-1] = ptilde1[-1,:,:]
ppadtemp[-1 ,1:-1, 1:-1] = ptilde1[ 0,:,:]
ppadtemp[1:-1,0 , 1:-1] = ptilde1[:,-1,:]
ppadtemp[1:-1,-1 , 1:-1] = ptilde1[:, 0,:]
ppadtemp[1:-1,1:-1, 0] = ptilde1[:,:,-1]
ppadtemp[1:-1,1:-1, -1] = ptilde1[:,:, 0]
r[:,:,:] = 0.0
r -= S*dx*dx
#r[i,j,k] -= 0 #6*ptilde1[i,j,k]
r[:,:,:] += ppadtemp[0:-2,1:-1,1:-1]
r[:,:,:] += ppadtemp[2: ,1:-1,1:-1]
r[:,:,:] += ppadtemp[1:-1,0:-2,1:-1]
r[:,:,:] += ppadtemp[1:-1,2: ,1:-1]
r[:,:,:] += ppadtemp[1:-1,1:-1,0:-2]
r[:,:,:] += ppadtemp[1:-1,1:-1,2:]
ptilde2 = (1/6)*r
res_norm = np.sum((ptilde2-ptilde1)**2)
ptilde1 = ptilde2
print(kk)
print(res_norm)
if res_norm < 0.001:
break
p1 = ptilde1
#%%
for k in range(0,N-1):
for j in range(0, N-1):
for i in range(0, N-1):
if i==0:
Ux[0,j,k] = (U2[1,j,k] - U2[-1,j,k])/(2*dx)
Vx[0,j,k] = (V2[1,j,k] - V2[-1,j,k])/(2*dx)
Wx[0,j,k] = (W2[1,j,k] - W2[-1,j,k])/(2*dx)
elif i==(N-2):
Ux[-1,j,k] = (U2[0,j,k] - U2[-2,j,k])/(2*dx)
Vx[-1,j,k] = (V2[0,j,k] - V2[-2,j,k])/(2*dx)
Wx[-1,j,k] = (W2[0,j,k] - W2[-2,j,k])/(2*dx)
else:
Ux[i,j,k] = (U2[i+1,j,k] - U2[i-1,j,k])/(2*dx)
Vx[i,j,k] = (V2[i+1,j,k] - V2[i-1,j,k])/(2*dx)
Wx[i,j,k] = (W2[i+1,j,k] - W2[i-1,j,k])/(2*dx)
if j==0:
Uy[i,0,k] = (U2[i,1,k] - U2[i,-1,k])/(2*dx)
Vy[i,0,k] = (V2[i,1,k] - V2[i,-1,k])/(2*dx)
Wy[i,0,k] = (W2[i,1,k] - W2[i,-1,k])/(2*dx)
elif j==(N-2):
Uy[i,-1,k] = (U2[i,0,k] - U2[i,-2,k])/(2*dx)
Vy[i,-1,k] = (V2[i,0,k] - V2[i,-2,k])/(2*dx)
Wy[i,-1,k] = (W2[i,0,k] - W2[i,-2,k])/(2*dx)
else:
Uy[i,j,k] = (U2[i,j+1,k] - U2[i,j-1,k])/(2*dx)
Vy[i,j,k] = (V2[i,j+1,k] - V2[i,j-1,k])/(2*dx)
Wy[i,j,k] = (W2[i,j+1,k] - W2[i,j-1,k])/(2*dx)
if k==0:
Uz[i,j,0] = (U2[i,j,1] - U2[i,j,-1])/(2*dx)
Vz[i,j,0] = (V2[i,j,1] - V2[i,j,-1])/(2*dx)
Wz[i,j,0] = (W2[i,j,1] - W2[i,j,-1])/(2*dx)
elif k==(N-2):
Uz[i,j,-1] = (U2[i,j,0] - U2[i,j,-2])/(2*dx)
Vz[i,j,-1] = (V2[i,j,0] - V2[i,j,-2])/(2*dx)
Wz[i,j,-1] = (W2[i,j,0] - W2[i,j,-2])/(2*dx)
else:
Uz[i,j,k] = (U2[i,j,k+1] - U2[i,j,k-1])/(2*dx)
Vz[i,j,k] = (V2[i,j,k+1] - V2[i,j,k-1])/(2*dx)
Wz[i,j,k] = (W2[i,j,k+1] - W2[i,j,k-1])/(2*dx)
S = -(Ux*Ux + Vy*Vy + Wz*Wz + 2*Uy*Vx + 2*Vz*Wy + 2*Uz*Wx)
#%%
ptilde1 = np.empty((N-1,N-1,N-1),dtype=np.double)
ptilde2 = np.empty((N-1,N-1,N-1),dtype=np.double)
ppadtemp = np.empty((N+1,N+1,N+1),dtype=np.double)
r = np.empty((N-1,N-1,N-1),dtype=np.double)
ptilde1[:,:,:] = 0.0
ptilde2[:,:,:] = 0.0
r[:,:,:] = 0.0
omega = 2 / ( 1 + np.sin(np.pi/(N)) )
for kk in range(0,2000):
ppadtemp[:,:,:] = 0.0
ppadtemp[1:-1,1:-1, 1:-1] = ptilde1
ppadtemp[0 ,1:-1, 1:-1] = ptilde1[-1,:,:]
ppadtemp[-1 ,1:-1, 1:-1] = ptilde1[ 0,:,:]
ppadtemp[1:-1,0 , 1:-1] = ptilde1[:,-1,:]
ppadtemp[1:-1,-1 , 1:-1] = ptilde1[:, 0,:]
ppadtemp[1:-1,1:-1, 0] = ptilde1[:,:,-1]
ppadtemp[1:-1,1:-1, -1] = ptilde1[:,:, 0]
r[:,:,:] = 0.0
r -= S*dx*dx
#r[i,j,k] -= 0 #6*ptilde1[i,j,k]
r[:,:,:] += ppadtemp[0:-2,1:-1,1:-1]
r[:,:,:] += ppadtemp[2: ,1:-1,1:-1]
r[:,:,:] += ppadtemp[1:-1,0:-2,1:-1]
r[:,:,:] += ppadtemp[1:-1,2: ,1:-1]
r[:,:,:] += ppadtemp[1:-1,1:-1,0:-2]
r[:,:,:] += ppadtemp[1:-1,1:-1,2:]
ptilde2 = (1/6)*r
res_norm = np.sum((ptilde2-ptilde1)**2)
ptilde1 = ptilde2
print(kk)
print(res_norm)
if res_norm < 0.001:
break
p2 = ptilde1
#%%
Pxx = np.empty((N-1,N-1,N-1),dtype=np.double)
Pyy = np.empty((N-1,N-1,N-1),dtype=np.double)
Pzz = np.empty((N-1,N-1,N-1),dtype=np.double)
PS = np.empty((N-1,N-1,N-1),dtype=np.double)
for k in range(0,N-1):
for j in range(0, N-1):
for i in range(0, N-1):
if i==0:
Pxx[0,j,k] = (ptilde1[1,j,k] -2*ptilde1[0,j,k] + ptilde1[-1,j,k])/(dx*dx)
elif i==(N-2):
Pxx[-1,j,k] = (ptilde1[0,j,k] -2*ptilde1[-1,j,k] + ptilde1[-2,j,k])/(dx*dx)
else:
Pxx[i,j,k] = (ptilde1[i+1,j,k] -2*ptilde1[i,j,k] + ptilde1[i-1,j,k])/(dx*dx)
if j==0:
Pyy[i,0,k] = (ptilde1[i,1,k] -2*ptilde1[i,0,k] + ptilde1[i,-1,k])/(dx*dx)
elif j==(N-2):
Pyy[i,-1,k] = (ptilde1[i,0,k] -2*ptilde1[i,-1,k] + ptilde1[i,-2,k])/(dx*dx)
else:
Pyy[i,j,k] = (ptilde1[i,j+1,k] -2*ptilde1[i,j,k] + ptilde1[i,j-1,k])/(dx*dx)
if k==0:
Pzz[i,j,0] = (ptilde1[i,j,1] -2*ptilde1[i,j,0] + ptilde1[i,j,-1])/(dx*dx)
elif k==(N-2):
Pzz[i,j,-1] = (ptilde1[i,j,0] -2*ptilde1[i,j,-1] + ptilde1[i,j,-2])/(dx*dx)
else:
Pzz[i,j,k] = (ptilde1[i,j,k+1] -2*ptilde1[i,j,k] + ptilde1[i,j,k-1])/(dx*dx)
PS = Pxx + Pyy + Pzz
#%%
#Chop the domain into three chunks
#Chunk1
U1a = U1[:,:,0:42]
V1a = V1[:,:,0:42]
W1a = W1[:,:,0:42]
P1a = p1[:,:,0:42]
#Chunk2
U2a = U1[:,:,42:84]
V2a = V1[:,:,42:84]
W2a = W1[:,:,42:84]
P2a = p1[:,:,42:84]
#Chunk3
U3a = U1[:,:,84:126]
V3a = V1[:,:,84:126]
W3a = W1[:,:,84:126]
P3a = p1[:,:,84:126]
#Chunk4
U4a = U2[:,:,0:42]
V4a = V2[:,:,0:42]
W4a = W2[:,:,0:42]
P4a = p2[:,:,0:42]
#Chunk5
U5a = U2[:,:,42:84]
V5a = V2[:,:,42:84]
W5a = W2[:,:,42:84]
P5a = p2[:,:,42:84]
#Chunk6
U6a = U2[:,:,84:126]
V6a = V2[:,:,84:126]
W6a = W2[:,:,84:126]
P6a = p2[:,:,84:126]
totalX = 512
currentX = 128*6
totalOverlap = currentX - totalX
#%%
Ufinal = np.empty((totalX,N-1,42),dtype=np.double)
Vfinal = np.empty((totalX,N-1,42),dtype=np.double)
Wfinal = np.empty((totalX,N-1,42),dtype=np.double)
Pfinal = np.empty((totalX,N-1,42),dtype=np.double)
#%%
Ufinal[42:86,:,:] = U1a[42:86,:,:]
Vfinal[42:86,:,:] = V1a[42:86,:,:]
Wfinal[42:86,:,:] = W1a[42:86,:,:]
Pfinal[42:86,:,:] = P1a[42:86,:,:]
Ufinal[128:172,:,:] = U2a[42:86,:,:]
Vfinal[128:172,:,:] = V2a[42:86,:,:]
Wfinal[128:172,:,:] = W2a[42:86,:,:]
Pfinal[128:172,:,:] = P2a[42:86,:,:]
Ufinal[214:258,:,:] = U3a[42:86,:,:]
Vfinal[214:258,:,:] = V3a[42:86,:,:]
Wfinal[214:258,:,:] = W3a[42:86,:,:]
Pfinal[214:258,:,:] = P3a[42:86,:,:]
Ufinal[300:344,:,:] = U4a[42:86,:,:]
Vfinal[300:344,:,:] = V4a[42:86,:,:]
Wfinal[300:344,:,:] = W4a[42:86,:,:]
Pfinal[300:344,:,:] = P4a[42:86,:,:]
Ufinal[386:430,:,:] = U5a[42:86,:,:]
Vfinal[386:430,:,:] = V5a[42:86,:,:]
Wfinal[386:430,:,:] = W5a[42:86,:,:]
Pfinal[386:430,:,:] = P5a[42:86,:,:]
Ufinal[472:512,:,:] = U6a[42:82,:,:]
Vfinal[472:512,:,:] = V6a[42:82,:,:]
Wfinal[472:512,:,:] = W6a[42:82,:,:]
Pfinal[472:512,:,:] = P6a[42:82,:,:]
for i in range(0,42):
#beta = 1 - np.cos((np.pi/2.0)*float(i)/41.0)
beta = float(i)/41.0
theta = (np.pi/2.0)*beta
Ufinal[i,:,:] = np.cos(theta)*U6a[82+i,:,:] + np.sin(theta)*U1a[i,:,:]
Vfinal[i,:,:] = np.cos(theta)*V6a[82+i,:,:] + np.sin(theta)*V1a[i,:,:]
Wfinal[i,:,:] = np.cos(theta)*W6a[82+i,:,:] + np.sin(theta)*W1a[i,:,:]
Pfinal[i,:,:] = np.cos(theta)*P6a[82+i,:,:] + np.sin(theta)*P1a[i,:,:]
Ufinal[86+i,:,:] = np.cos(theta)*U1a[86+i,:,:] + np.sin(theta)*U2a[i,:,:]
Vfinal[86+i,:,:] = np.cos(theta)*V1a[86+i,:,:] + np.sin(theta)*V2a[i,:,:]
Wfinal[86+i,:,:] = np.cos(theta)*W1a[86+i,:,:] + np.sin(theta)*W2a[i,:,:]
Pfinal[86+i,:,:] = np.cos(theta)*P1a[86+i,:,:] + np.sin(theta)*P2a[i,:,:]
Ufinal[172+i,:,:] = np.cos(theta)*U2a[86+i,:,:] + np.sin(theta)*U3a[i,:,:]
Vfinal[172+i,:,:] = np.cos(theta)*V2a[86+i,:,:] + np.sin(theta)*V3a[i,:,:]
Wfinal[172+i,:,:] = np.cos(theta)*W2a[86+i,:,:] + np.sin(theta)*W3a[i,:,:]
Pfinal[172+i,:,:] = np.cos(theta)*P2a[86+i,:,:] + np.sin(theta)*P3a[i,:,:]
Ufinal[258+i,:,:] = np.cos(theta)*U3a[86+i,:,:] + np.sin(theta)*U4a[i,:,:]
Vfinal[258+i,:,:] = np.cos(theta)*V3a[86+i,:,:] + np.sin(theta)*V4a[i,:,:]
Wfinal[258+i,:,:] = np.cos(theta)*W3a[86+i,:,:] + np.sin(theta)*W4a[i,:,:]
Pfinal[258+i,:,:] = np.cos(theta)*P3a[86+i,:,:] + np.sin(theta)*P4a[i,:,:]
Ufinal[344+i,:,:] = np.cos(theta)*U4a[86+i,:,:] + np.sin(theta)*U5a[i,:,:]
Vfinal[344+i,:,:] = np.cos(theta)*V4a[86+i,:,:] + np.sin(theta)*V5a[i,:,:]
Wfinal[344+i,:,:] = np.cos(theta)*W4a[86+i,:,:] + np.sin(theta)*W5a[i,:,:]
Pfinal[344+i,:,:] = np.cos(theta)*P4a[86+i,:,:] + np.sin(theta)*P5a[i,:,:]
Ufinal[430+i,:,:] = np.cos(theta)*U5a[86+i,:,:] + np.sin(theta)*U6a[i,:,:]
Vfinal[430+i,:,:] = np.cos(theta)*V5a[86+i,:,:] + np.sin(theta)*V6a[i,:,:]
Wfinal[430+i,:,:] = np.cos(theta)*W5a[86+i,:,:] + np.sin(theta)*W6a[i,:,:]
Pfinal[430+i,:,:] = | np.cos(theta) | numpy.cos |
import numpy as np
from scipy import linalg
import pathlib, sys
file_path = pathlib.Path(__file__).parent.absolute()
from pressio4py import logger, solvers, ode, rom
from pressio4py.apps.burgers1d import Burgers1d
np.set_printoptions(linewidth=140)
goldBdf1 = np.array([
1.23924618529016e+00,
1.00513224142691e+00,
1.00258744050401e+00,
1.00283530274169e+00,
1.00313333759789e+00,
1.00346287207285e+00,
1.00382706443916e+00,
1.00422955914887e+00,
1.00467438433032e+00,
1.00516599192553e+00,
1.00570930192065e+00,
1.00630975185226e+00,
1.00697335112295e+00,
1.00770674109302e+00,
1.00851726134268e+00,
1.00941302387047e+00,
1.01040299320197e+00,
1.01149707707594e+00,
1.01270622473792e+00,
1.01404253728095e+00])
goldBdf2 = np.array([
1.23947296257898,
1.004911840673181,
1.002583292436882,
1.002835486018458,
1.003133591274698,
1.003463152789714,
1.003827374922797,
1.004229902417551,
1.004674763912067,
1.005166411588689,
1.005709766002342,
1.006310265072025,
1.006973918660976,
1.0077073687177,
1.008517955621836,
1.009413791794709,
1.01040384277086,
1.011498016939365,
1.012707264750251,
1.014043688232101])
#----------------------------
class MyQRSolver:
def __init__(self, meshSize, romSize):
self.Q_ = np.zeros((meshSize, romSize))
self.R_ = np.zeros((romSize, romSize))
def computeThin(self, A):
self.Q_, self.R_ = np.linalg.qr(A, mode='reduced')
def applyQTranspose(self, operand, result):
result[:] = self.Q_.T.dot(operand)
def applyRTranspose(self, operand, result):
result[:] = self.R_.T.dot(operand)
def solveRxb(self, b, x):
x[:] = linalg.solve(self.R_, b)
#----------------------------------------
class OdeObserver:
def __call__(self, timeStep, time, state):
print(state)
assert(state.shape[0]==11)
#----------------------------
def test_euler():
meshSize = 20
romSize = 11
Nsteps = 10
dt = 0.01
t0 = 0.
# create app
appObj = Burgers1d(meshSize)
# set reference state
yRef = np.ones(meshSize)
# I have to make phi a column-major array to ensure
# pressio does not make a copy of this
basisFile = str(file_path) + "/basis_bdf1.txt"
phi = np.copy(np.loadtxt(basisFile), order='F')
# decoder
decoder = rom.Decoder(phi)
# LSPG state
yRom = np.zeros(romSize)
# lspg problem
scheme = ode.stepscheme.BDF1
problem = rom.lspg.unsteady.DefaultProblem(scheme, appObj, decoder, yRom, yRef)
# qr and non linear solver
qrS = MyQRSolver(meshSize, romSize)
nlsO = solvers.create_gauss_newton_qr(problem, yRom, qrS)
nlsO.setUpdatingCriterion(solvers.update.Standard)
nlsO.setMaxIterations(2)
nlsO.setStoppingCriterion(solvers.stop.AfterMaxIters)
# solve
myObs = OdeObserver()
ode.advance_n_steps_and_observe(problem, yRom, t0,dt, Nsteps, myObs, nlsO)
fomRecon = problem.fomStateReconstructor()
yFomFinal = fomRecon(yRom)
np.set_printoptions(precision=15)
print(yFomFinal)
for y1,y2 in zip(goldBdf1, yFomFinal):
assert( np.abs(y1-y2) < 1e-10)
#----------------------------
def test_bdf2():
meshSize = 20
romSize = 11
Nsteps = 10
dt = 0.01
t0 = 0.
logger.initialize(logger.logto.terminal, "null")
logger.setVerbosity([logger.loglevel.info])
# create app
appObj = Burgers1d(meshSize)
# set reference state
yRef = | np.ones(meshSize) | numpy.ones |
import unittest
import numpy as np
from feastruct.pre.material import Steel
from feastruct.pre.section import Section
import feastruct.fea.cases as cases
from feastruct.fea.frame_analysis import FrameAnalysis2D
from feastruct.solvers.linstatic import LinearStatic
class TestUDL(unittest.TestCase):
"""Tests problems related to 1D beam bending from the American Wood Council:
https://www.awc.org/pdf/codes-standards/publications/design-aids/AWC-DA6-BeamFormulas-0710.pdf
"""
def setUp(self):
self.steel = Steel()
self.elastic_modulus = self.steel.elastic_modulus
self.ixx = np.random.uniform(10e6, 200e6)
self.length = np.random.uniform(2e3, 10e3)
self.q = -np.random.uniform(1, 10)
self.pl = -np.random.uniform(5e3, 50e3)
def test_fig1(self):
"""Simple Beam – Uniformly Distributed Load"""
# create 2d frame analysis object
analysis = FrameAnalysis2D()
# create section
section = Section(ixx=self.ixx)
# create nodes
node_a = analysis.create_node(coords=[0])
node_b = analysis.create_node(coords=[self.length])
# create beam elements
element = analysis.create_element(
el_type='EB2-2D', nodes=[node_a, node_b], material=self.steel, section=section
)
# add supports
freedom_case = cases.FreedomCase()
freedom_case.add_nodal_support(node=node_a, val=0, dof=0)
freedom_case.add_nodal_support(node=node_a, val=0, dof=1)
freedom_case.add_nodal_support(node=node_b, val=0, dof=1)
# add loads
load_case = cases.LoadCase()
load_case.add_element_load(element.generate_udl(q=self.q))
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case, load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check displacements
def analytical_disp(x):
factor = self.q * x / 24 / self.elastic_modulus / self.ixx
l0 = self.length
return factor * (l0 * l0 * l0 - 2 * l0 * x * x + x * x * x)
# get displacements
displacements = element.get_displacements(11, analysis_case)
# loop through each station
for disp in displacements:
xi = disp[0]
x = self.length * xi
v = disp[2]
# check displacements
self.assertTrue(np.isclose(v, analytical_disp(x), atol=1e-06))
# check max displacement
l0 = self.length
v_max = 5 * self.q * l0 * l0 * l0 * l0 / 384 / self.elastic_modulus / self.ixx
# check value
self.assertTrue(np.isclose(abs(v_max), max(np.abs(displacements[:, 2]))))
# check position
self.assertTrue(np.isclose(0.5, displacements[np.abs(displacements[:, 2]).argmax(), 0],
atol=1e-06))
# check bending moments
def analytical_bmd(x):
return self.q * x / 2 * (self.length - x)
# get bmd
(xis, bmd) = element.get_bmd(11, analysis_case)
# loop through each station
for (i, m) in enumerate(bmd):
xi = xis[i]
x = self.length * xi
# check bending moment
self.assertTrue(np.isclose(m, analytical_bmd(x), atol=1e-06))
# check max bending moment
l0 = self.length
m_max = self.q * l0 * l0 / 8
# check value
self.assertTrue(np.isclose(abs(m_max), max(np.abs(bmd)), atol=1e-06))
# check position
self.assertTrue(np.isclose(0.5, xis[np.abs(bmd).argmax()], atol=1e-06))
# check shear force
def analytical_sfd(x):
return self.q * (x - self.length / 2)
# get sfd
(xis, sfd) = element.get_sfd(11, analysis_case)
# loop through each station
for (i, sf) in enumerate(sfd):
xi = xis[i]
x = self.length * xi
# check shear force
self.assertTrue(np.isclose(sf, analytical_sfd(x), atol=1e-06))
def test_fig2(self):
"""Simple Beam – Uniform Load Partially Distributed"""
a = self.length * np.random.uniform(0.1, 0.4)
c = self.length * np.random.uniform(0.1, 0.4)
b = self.length - a - c
# create 2d frame analysis object
analysis = FrameAnalysis2D()
# create section
section = Section(ixx=self.ixx)
# create nodes
node_a = analysis.create_node(coords=[0])
node_b = analysis.create_node(coords=[a])
node_c = analysis.create_node(coords=[a+b])
node_d = analysis.create_node(coords=[self.length])
# create beam elements
element_ab = analysis.create_element(
el_type='EB2-2D', nodes=[node_a, node_b], material=self.steel, section=section
)
element_bc = analysis.create_element(
el_type='EB2-2D', nodes=[node_b, node_c], material=self.steel, section=section
)
element_cd = analysis.create_element(
el_type='EB2-2D', nodes=[node_c, node_d], material=self.steel, section=section
)
# add supports
freedom_case = cases.FreedomCase()
freedom_case.add_nodal_support(node=node_a, val=0, dof=0)
sup1 = freedom_case.add_nodal_support(node=node_a, val=0, dof=1)
sup2 = freedom_case.add_nodal_support(node=node_d, val=0, dof=1)
# add loads
load_case = cases.LoadCase()
load_case.add_element_load(element_bc.generate_udl(q=self.q))
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case, load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check reactions
r1 = -sup1.get_reaction(analysis_case)
r2 = -sup2.get_reaction(analysis_case)
self.assertTrue(np.isclose(r1, self.q * b / 2 / self.length * (2 * c + b), atol=1e-06))
self.assertTrue(np.isclose(r2, self.q * b / 2 / self.length * (2 * a + b), atol=1e-06))
# check bending moments
def analytical_bmd_ab(x):
return r1 * x
def analytical_bmd_bc(x):
return r1 * x - self.q / 2 * (x - a) * (x - a)
def analytical_bmd_cd(x):
return r2 * (self.length - x)
# get bmds
(xis_ab, bmd_ab) = element_ab.get_bmd(11, analysis_case)
(xis_bc, bmd_bc) = element_bc.get_bmd(11, analysis_case)
(xis_cd, bmd_cd) = element_cd.get_bmd(11, analysis_case)
# element_ab - loop through each station
for (i, m) in enumerate(bmd_ab):
xi = xis_ab[i]
x = a * xi
# check bending moments
self.assertTrue(np.isclose(m, analytical_bmd_ab(x), atol=1e-06))
# element_bc - loop through each station
for (i, m) in enumerate(bmd_bc):
xi = xis_bc[i]
x = b * xi + a
# check bending moments
self.assertTrue(np.isclose(m, analytical_bmd_bc(x), atol=1e-06))
# element_cd - loop through each station
for (i, m) in enumerate(bmd_cd):
xi = xis_cd[i]
x = c * xi + a + b
# check bending moments
self.assertTrue(np.isclose(m, analytical_bmd_cd(x), atol=1e-06))
# check max bending moment
m_max = r1 * (a + r1 / 2 / self.q)
pos = a + r1 / self.q
x = 1 / b * (pos - a)
# check value
self.assertTrue(np.isclose(abs(m_max), max(np.abs(bmd_bc)), atol=1e-06))
# check position
self.assertTrue(np.isclose(x, xis_bc[np.abs(bmd_bc).argmax()], atol=1e-06))
# check shear force
def analytical_sfd_ab(x):
return -r1
def analytical_sfd_bc(x):
return -r1 + self.q * (x - a)
def analytical_sfd_cd(x):
return r2
# get sfds
(xis_ab, sfd_ab) = element_ab.get_sfd(11, analysis_case)
(xis_bc, sfd_bc) = element_bc.get_sfd(11, analysis_case)
(xis_cd, sfd_cd) = element_cd.get_sfd(11, analysis_case)
# element_ab - loop through each station
for (i, sf) in enumerate(sfd_ab):
xi = xis_ab[i]
x = a * xi
# check shear forces
self.assertTrue(np.isclose(sf, analytical_sfd_ab(x), atol=1e-06))
# element_bc - loop through each station
for (i, sf) in enumerate(sfd_bc):
xi = xis_bc[i]
x = b * xi + a
# check shear forces
self.assertTrue(np.isclose(sf, analytical_sfd_bc(x), atol=1e-06))
# element_cd - loop through each station
for (i, sf) in enumerate(sfd_cd):
xi = xis_cd[i]
x = c * xi + a + b
# check shear forces
self.assertTrue(np.isclose(sf, analytical_sfd_cd(x), atol=1e-06))
def test_fig3(self):
"""Simple Beam – Uniform Load Partially Distributed at One End"""
a = self.length * np.random.uniform(0.1, 0.9)
# create 2d frame analysis object
analysis = FrameAnalysis2D()
# create section
section = Section(ixx=self.ixx)
# create nodes
node_a = analysis.create_node(coords=[0])
node_b = analysis.create_node(coords=[a])
node_c = analysis.create_node(coords=[self.length])
# create beam elements
element_ab = analysis.create_element(
el_type='EB2-2D', nodes=[node_a, node_b], material=self.steel, section=section
)
element_bc = analysis.create_element(
el_type='EB2-2D', nodes=[node_b, node_c], material=self.steel, section=section
)
# add supports
freedom_case = cases.FreedomCase()
freedom_case.add_nodal_support(node=node_a, val=0, dof=0)
sup1 = freedom_case.add_nodal_support(node=node_a, val=0, dof=1)
sup2 = freedom_case.add_nodal_support(node=node_c, val=0, dof=1)
# add loads
load_case = cases.LoadCase()
load_case.add_element_load(element_ab.generate_udl(q=self.q))
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case, load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check reactions
r1 = -sup1.get_reaction(analysis_case)
r2 = -sup2.get_reaction(analysis_case)
self.assertTrue(np.isclose(r1, self.q * a / 2 / self.length * (2 * self.length - a),
atol=1e-06))
self.assertTrue(np.isclose(r2, self.q * a * a / 2 / self.length, atol=1e-06))
# check displacements
def analytical_disp_ab(x):
l0 = self.length
factor = self.q * x / 24 / self.elastic_modulus / self.ixx / l0
return factor * (a * a * (2 * l0 - a) * (2 * l0 - a) - 2 * a * x * x * (
2 * l0 - a) + l0 * x * x * x)
def analytical_disp_bc(x):
l0 = self.length
factor = self.q * a * a * (l0 - x) / 24 / self.elastic_modulus / self.ixx / l0
return factor * (4 * x * l0 - 2 * x * x - a * a)
# get displacements
displacements_ab = element_ab.get_displacements(11, analysis_case)
displacements_bc = element_bc.get_displacements(11, analysis_case)
# loop through each station
for disp in displacements_ab:
xi = disp[0]
x = a * xi
v = disp[2]
# check displacements
self.assertTrue(np.isclose(v, analytical_disp_ab(x), atol=1e-06))
# loop through each station
for disp in displacements_bc:
xi = disp[0]
x = (self.length - a) * xi + a
v = disp[2]
# check displacements
self.assertTrue(np.isclose(v, analytical_disp_bc(x), atol=1e-06))
# check bending moments
def analytical_bmd_ab(x):
return r1 * x - self.q * x * x / 2
def analytical_bmd_bc(x):
return r2 * (self.length - x)
# get bmds
(xis_ab, bmd_ab) = element_ab.get_bmd(11, analysis_case)
(xis_bc, bmd_bc) = element_bc.get_bmd(11, analysis_case)
# element_ab - loop through each station
for (i, m) in enumerate(bmd_ab):
xi = xis_ab[i]
x = a * xi
# check bending moments
self.assertTrue(np.isclose(m, analytical_bmd_ab(x), atol=1e-06))
# element_bc - loop through each station
for (i, m) in enumerate(bmd_bc):
xi = xis_bc[i]
x = (self.length - a) * xi + a
# check bending moments
self.assertTrue(np.isclose(m, analytical_bmd_bc(x), atol=1e-06))
# check max bending moment
m_max = r1 * r1 / 2 / self.q
pos = r1 / self.q
x = pos / a
# check value
self.assertTrue(np.isclose(abs(m_max), max(np.abs(bmd_ab)), atol=1e-06))
# check position
self.assertTrue(np.isclose(x, xis_ab[np.abs(bmd_ab).argmax()], atol=1e-06))
# check shear force
def analytical_sfd_ab(x):
return -r1 + self.q * x
def analytical_sfd_bc(x):
return r2
# get sfds
(xis_ab, sfd_ab) = element_ab.get_sfd(11, analysis_case)
(xis_bc, sfd_bc) = element_bc.get_sfd(11, analysis_case)
# element_ab - loop through each station
for (i, sf) in enumerate(sfd_ab):
xi = xis_ab[i]
x = a * xi
# check shear forces
self.assertTrue(np.isclose(sf, analytical_sfd_ab(x), atol=1e-06))
# element_bc - loop through each station
for (i, sf) in enumerate(sfd_bc):
xi = xis_bc[i]
x = (self.length - a) * xi + a
# check shear forces
self.assertTrue(np.isclose(sf, analytical_sfd_bc(x), atol=1e-06))
def test_fig4(self):
"""Simple Beam – Uniform Load Partially Distributed at Each End"""
a = self.length * np.random.uniform(0.1, 0.4)
c = self.length * np.random.uniform(0.1, 0.4)
b = self.length - a - c
q2 = -np.random.uniform(1, 10)
# create 2d frame analysis object
analysis = FrameAnalysis2D()
# create section
section = Section(ixx=self.ixx)
# create nodes
node_a = analysis.create_node(coords=[0])
node_b = analysis.create_node(coords=[a])
node_c = analysis.create_node(coords=[a+b])
node_d = analysis.create_node(coords=[self.length])
# create beam elements
element_ab = analysis.create_element(
el_type='EB2-2D', nodes=[node_a, node_b], material=self.steel, section=section
)
element_bc = analysis.create_element(
el_type='EB2-2D', nodes=[node_b, node_c], material=self.steel, section=section
)
element_cd = analysis.create_element(
el_type='EB2-2D', nodes=[node_c, node_d], material=self.steel, section=section
)
# add supports
freedom_case = cases.FreedomCase()
freedom_case.add_nodal_support(node=node_a, val=0, dof=0)
sup1 = freedom_case.add_nodal_support(node=node_a, val=0, dof=1)
sup2 = freedom_case.add_nodal_support(node=node_d, val=0, dof=1)
# add loads
load_case = cases.LoadCase()
load_case.add_element_load(element_ab.generate_udl(q=self.q))
load_case.add_element_load(element_cd.generate_udl(q=q2))
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case, load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check reactions
r1 = -sup1.get_reaction(analysis_case)
r1_ana = (self.q * a * (2 * self.length - a) + q2 * c * c) / (2 * self.length)
r2 = -sup2.get_reaction(analysis_case)
r2_ana = (q2 * c * (2 * self.length - c) + self.q * a * a) / (2 * self.length)
self.assertTrue(np.isclose(r1, r1_ana, atol=1e-06))
self.assertTrue(np.isclose(r2, r2_ana, atol=1e-06))
# check bending moments
def analytical_bmd_ab(x):
return r1 * x - self.q * 0.5 * x * x
def analytical_bmd_bc(x):
return r1 * x - self.q * a * 0.5 * (2 * x - a)
def analytical_bmd_cd(x):
return r2 * (self.length - x) - q2 * (self.length - x) * (self.length - x) * 0.5
# get bmds
(xis_ab, bmd_ab) = element_ab.get_bmd(11, analysis_case)
(xis_bc, bmd_bc) = element_bc.get_bmd(11, analysis_case)
(xis_cd, bmd_cd) = element_cd.get_bmd(11, analysis_case)
# element_ab - loop through each station
for (i, m) in enumerate(bmd_ab):
xi = xis_ab[i]
x = a * xi
# check bending moments
self.assertTrue(np.isclose(m, analytical_bmd_ab(x), atol=1e-06))
# element_bc - loop through each station
for (i, m) in enumerate(bmd_bc):
xi = xis_bc[i]
x = b * xi + a
# check bending moments
self.assertTrue(np.isclose(m, analytical_bmd_bc(x), atol=1e-06))
# element_cd - loop through each station
for (i, m) in enumerate(bmd_cd):
xi = xis_cd[i]
x = c * xi + a + b
# check bending moments
self.assertTrue(np.isclose(m, analytical_bmd_cd(x), atol=1e-06))
# check max bending moment
if abs(r1) < abs(self.q * a):
m_max = r1 * r1 / 2 / self.q
pos = r1 / self.q
x = pos / a
# check value
self.assertTrue(np.isclose(abs(m_max), max(np.abs(bmd_ab)), atol=1e-06))
# check position
self.assertTrue(np.isclose(x, xis_ab[np.abs(bmd_ab).argmax()], atol=1e-06))
if abs(r2) < abs(q2 * c):
m_max = r2 * r2 / 2 / q2
pos = self.length - r2 / q2
x = 1 / c * (pos - a - b)
# check value
self.assertTrue(np.isclose(abs(m_max), max(np.abs(bmd_cd)), atol=1e-06))
# check position
self.assertTrue(np.isclose(x, xis_cd[np.abs(bmd_cd).argmax()], atol=1e-06))
# check shear force
def analytical_sfd_ab(x):
return -r1 + self.q * x
def analytical_sfd_bc(x):
return -r1 + self.q * a
def analytical_sfd_cd(x):
return r2 - q2 * (self.length - x)
# get sfds
(xis_ab, sfd_ab) = element_ab.get_sfd(11, analysis_case)
(xis_bc, sfd_bc) = element_bc.get_sfd(11, analysis_case)
(xis_cd, sfd_cd) = element_cd.get_sfd(11, analysis_case)
# element_ab - loop through each station
for (i, sf) in enumerate(sfd_ab):
xi = xis_ab[i]
x = a * xi
# check shear forces
self.assertTrue(np.isclose(sf, analytical_sfd_ab(x), atol=1e-06))
# element_bc - loop through each station
for (i, sf) in enumerate(sfd_bc):
xi = xis_bc[i]
x = b * xi + a
# check shear forces
self.assertTrue(np.isclose(sf, analytical_sfd_bc(x), atol=1e-06))
# element_cd - loop through each station
for (i, sf) in enumerate(sfd_cd):
xi = xis_cd[i]
x = c * xi + a + b
# check shear forces
self.assertTrue(np.isclose(sf, analytical_sfd_cd(x), atol=1e-06))
def test_fig5(self):
"""Simple Beam – Load Increasing Uniformly to One End"""
# not yet implemented
pass
def test_fig6(self):
"""Simple Beam – Load Increasing Uniformly to Center"""
# not yet implemented
pass
def test_fig7(self):
"""Simple Beam – Concentrated Load at Center"""
# create 2d frame analysis object
analysis = FrameAnalysis2D()
# create section
section = Section(ixx=self.ixx)
# create nodes
node_a = analysis.create_node(coords=[0])
node_b = analysis.create_node(coords=[self.length * 0.5])
node_c = analysis.create_node(coords=[self.length])
# create beam elements
element_ab = analysis.create_element(
el_type='EB2-2D', nodes=[node_a, node_b], material=self.steel, section=section
)
element_bc = analysis.create_element(
el_type='EB2-2D', nodes=[node_b, node_c], material=self.steel, section=section
)
# add supports
freedom_case = cases.FreedomCase()
freedom_case.add_nodal_support(node=node_a, val=0, dof=0)
freedom_case.add_nodal_support(node=node_a, val=0, dof=1)
freedom_case.add_nodal_support(node=node_c, val=0, dof=1)
# add loads
load_case = cases.LoadCase()
load_case.add_nodal_load(node=node_b, val=self.pl, dof=1)
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case, load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check displacements
def analytical_disp_ab(x):
factor = self.pl * x / 48 / self.elastic_modulus / self.ixx
l0 = self.length
return factor * (3 * l0 * l0 - 4 * x * x)
def analytical_disp_bc(x):
x = self.length - x
factor = self.pl * x / 48 / self.elastic_modulus / self.ixx
l0 = self.length
return factor * (3 * l0 * l0 - 4 * x * x)
# get displacements
displacements_ab = element_ab.get_displacements(11, analysis_case)
displacements_bc = element_bc.get_displacements(11, analysis_case)
# loop through each station
for disp in displacements_ab:
xi = disp[0]
x = self.length * 0.5 * xi
v = disp[2]
# check displacements
self.assertTrue(np.isclose(v, analytical_disp_ab(x), atol=1e-06))
# loop through each station
for disp in displacements_bc:
xi = disp[0]
x = self.length * 0.5 + self.length * 0.5 * xi
v = disp[2]
# check displacements
self.assertTrue(np.isclose(v, analytical_disp_bc(x), atol=1e-06))
# check max displacement
l0 = self.length
v_max = self.pl * l0 * l0 * l0 / 48 / self.elastic_modulus / self.ixx
# check value
self.assertTrue(np.isclose(abs(v_max), max(np.abs(displacements_ab[:, 2])), atol=1e-06))
# check position
self.assertTrue(
np.isclose(1, displacements_ab[np.abs(displacements_ab[:, 2]).argmax(), 0],
atol=1e-06))
# check bending moments
def analytical_bmd_ab(x):
return self.pl * x / 2
def analytical_bmd_bc(x):
x = self.length - x
return self.pl * x / 2
# get bmd
(xis_ab, bmd_ab) = element_ab.get_bmd(11, analysis_case)
(xis_bc, bmd_bc) = element_bc.get_bmd(11, analysis_case)
# loop through each station
for (i, m) in enumerate(bmd_ab):
xi = xis_ab[i]
x = self.length * 0.5 * xi
# check bending moment
self.assertTrue(np.isclose(m, analytical_bmd_ab(x), atol=1e-06))
# loop through each station
for (i, m) in enumerate(bmd_bc):
xi = xis_bc[i]
x = self.length * 0.5 + self.length * 0.5 * xi
# check bending moment
self.assertTrue(np.isclose(m, analytical_bmd_bc(x), atol=1e-06))
# check max bending moment
l0 = self.length
m_max = self.pl * l0 / 4
# check value
self.assertTrue(np.isclose(abs(m_max), max( | np.abs(bmd_ab) | numpy.abs |
"""
Calculation of Earth layers and electron densities.
"""
from __future__ import division
import numpy as np
try:
import numba
except ImportError:
numba = None
from pisa import FTYPE
from pisa.utils.fileio import from_file
from pisa.utils.log import logging, set_verbosity
__all__ = ['extCalcLayers', 'Layers']
__author__ = '<NAME>'
__license__ = '''Copyright (c) 2014-2017, The IceCube Collaboration
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.'''
if numba is None:
class jit(object):
"""Decorator class to mimic Numba's `jit` when Numba is missing"""
def __init__(self, *args, **kwargs):
pass
def __call__(self, *args):
return args[0]
else:
jit = numba.jit
ftype = numba.typeof(FTYPE(1))
@jit(nopython=True, nogil=True, cache=True)
def extCalcLayers(
cz,
r_detector,
prop_height,
detector_depth,
max_layers,
min_detector_depth,
rhos,
YeFrac,
YeOuterRadius,
default_elec_frac,
coszen_limit,
radii):
"""Layer density/distance calculator for each coszen specified.
Accelerated with Numba if present.
Parameters
----------
cz
r_detector
prop_height
detector_depth
max_layers
min_detector_depth
rhos
YeFrac
YeOuterRadius
default_elec_frac
coszen_limit
Returns
-------
n_layers : int number of layers
density : array of densities, flattened from (cz, max_layers)
distance : array of distances per layer, flattened from (cz, max_layers)
"""
# Something to store the final results in
shape = (np.int64(len(cz)), np.int64(max_layers))
n_layers = np.zeros(shape[0], dtype=np.int32)
distance = np.zeros(shape=shape, dtype=FTYPE)
density = np.zeros(shape=shape, dtype=FTYPE)
# Loop over all CZ values
for k, coszen in enumerate(cz):
tot_earth_len = -2 * coszen * r_detector
# To store results
traverse_rhos = np.zeros(max_layers, dtype=FTYPE)
traverse_dist = np.zeros(max_layers, dtype=FTYPE)
traverse_electron_frac = np.zeros(max_layers, dtype=FTYPE)
# Above horizon
if coszen >= 0:
kappa = (detector_depth + prop_height)/r_detector
path_len = (
r_detector * np.sqrt(coszen**2 - 1 + (1 + kappa)**2)
- r_detector * coszen
)
# Path through the air:
kappa = detector_depth / r_detector
lam = (
coszen + np.sqrt(coszen**2 - 1 + (1 + kappa) * (1 + kappa))
)
lam *= r_detector
path_thru_atm = (
prop_height * (prop_height + 2*detector_depth + 2*r_detector)
/ (path_len + lam)
)
path_thru_outerlayer = path_len - path_thru_atm
traverse_rhos[0] = 0.0
traverse_dist[0] = path_thru_atm
traverse_electron_frac[0] = default_elec_frac
# In that case the neutrino passes through some earth (?)
layers = 1
if detector_depth > min_detector_depth:
traverse_rhos[1] = rhos[0]
traverse_dist[1] = path_thru_outerlayer
traverse_electron_frac[1] = YeFrac[-1]
layers += 1
# Below horizon
else:
path_len = (
np.sqrt((r_detector + prop_height + detector_depth)**2
- r_detector**2 * (1 - coszen**2))
- r_detector * coszen
)
# Path through air (that's down from production height in the
# atmosphere?)
traverse_rhos[0] = 0
traverse_dist[0] = (
prop_height * (prop_height + detector_depth + 2*r_detector)
/ path_len
)
# TODO: Why default here?
traverse_electron_frac[0] = default_elec_frac
i_trav = 1
# Path through the final layer above the detector (if necessary)
# NOTE: outer top layer is assumed to be the same as the next layer
# inward.
if detector_depth > min_detector_depth:
traverse_rhos[1] = rhos[0]
traverse_dist[1] = path_len - tot_earth_len - traverse_dist[0]
traverse_electron_frac[1] = YeFrac[-1]
i_trav += 1
# See how many layers we will pass
layers = 0
for val in coszen_limit:
if coszen < val:
layers += 1
# The zeroth layer is the air!
# ... and the first layer is the top layer (if detector is not on
# surface)
for i in range(layers):
# this is the density
traverse_rhos[i+i_trav] = rhos[i]
# TODO: Why default? is this air with density 0 and electron
# fraction just doesn't matter?
traverse_electron_frac[i+i_trav] = default_elec_frac
for rad_i in range(len(YeOuterRadius)):
# TODO: why 1.001 here?
if radii[i] < (YeOuterRadius[rad_i] * 1.001):
traverse_electron_frac[i+i_trav] = YeFrac[rad_i]
break
# Now calculate the distance travele in layer
c2 = coszen**2
R2 = r_detector**2
s1 = radii[i]**2 - R2*(1 -c2)
s2 = radii[i+1]**2 - R2*(1 -c2)
cross_this = 2. * np.sqrt(s1)
if i < layers - 1:
cross_next = 2. * np.sqrt(s2)
traverse_dist[i+i_trav] = 0.5 * (cross_this - cross_next)
else:
traverse_dist[i+i_trav] = cross_this
# Assumes azimuthal symmetry
if i > 0 and i < layers:
index = 2 * layers - i + i_trav - 1
traverse_rhos[index] = traverse_rhos[i+i_trav-1]
traverse_dist[index] = traverse_dist[i+i_trav-1]
traverse_electron_frac[index] = (
traverse_electron_frac[i+i_trav-1]
)
# That is now the total
layers = 2 * layers + i_trav - 1
n_layers[k] = np.int32(layers)
density[k] = traverse_rhos * traverse_electron_frac
distance[k] = traverse_dist
return n_layers, density.ravel(), distance.ravel()
class Layers(object):
"""
Calculate the path through earth for a given layer model with densities
(PREM), the electron fractions (Ye) and an array of coszen values
Parameters
----------
prem_file : str
path to PREM file containing layer radii and densities as white space
separated txt
detector_depth : float
depth of detector underground in km
prop_height : float
the production height of the neutrinos in the atmosphere in km (?)
Attributes:
----------
max_layers : int
maximum number of layers (this is important for the shape of the
output! if less than maximumm number of layers are crossed, it's
filled up with 0s
n_layers : 1d int array of length len(cz)
number of layers crossed for every CZ value
density : 1d float array of length (max_layers * len(cz))
containing density values and filled up with 0s otherwise
distance : 1d float array of length (max_layers * len(cz))
containing distance values and filled up with 0s otherwise
"""
def __init__(self, prem_file, detector_depth=1., prop_height=2.):
# Load earth model
if prem_file is not None :
self.using_earth_model = True
prem = from_file(prem_file, as_array=True)
self.rhos = prem[...,1][::-1].astype(FTYPE)
self.radii = prem[...,0][::-1].astype(FTYPE)
r_earth = prem[-1][0]
self.default_elec_frac = 0.5
n_prem = len(self.radii) - 1
self.max_layers = 2 * n_prem + 1
else :
self.using_earth_model = False
r_earth = 6371.0 #If no Earth model provided, use a standard Earth radius value
# Set some other
self.r_detector = r_earth - detector_depth
self.prop_height = prop_height
self.detector_depth = detector_depth
self.min_detector_depth = 1.0e-3 # <-- Why? // [km] so min is ~ 1 m
# Some additional handling of the Earth model
if self.using_earth_model:
# Change outermost radius to a bit underground, where the detector
if self.detector_depth >= self.min_detector_depth:
self.radii[0] -= detector_depth
self.max_layers += 1
# Compute coszen limit
self.computeMinLengthToLayers()
def setElecFrac(self, YeI, YeO, YeM):
"""
Parameters
----------
YeI, YeO, YeM : scalars
Three electron fractions (Ye), where I=inner core, O=outer core,
and M=mantle
"""
if not self.using_earth_model :
raise ValueError("Cannot set electron fraction when not using an Earth model")
self.YeFrac = np.array([YeI, YeO, YeM], dtype=FTYPE)
# TODO: these numbers are just hard coded for some reason...?
self.YeOuterRadius = np.array([1121.5, 3480.0, self.r_detector],
dtype=FTYPE)
def computeMinLengthToLayers(self):
# Compute which layer is tangeted at which angle
coszen_limit = []
# First element of self.radii is largest radius!
for i, rad in enumerate(self.radii):
# Using a cosine threshold instead!
if i == 0:
x = 0
else:
x = - np.sqrt(1 - (rad**2 / self.r_detector**2))
coszen_limit.append(x)
self.coszen_limit = | np.array(coszen_limit, dtype=FTYPE) | numpy.array |
import scipy.ndimage as nd
from scipy.optimize import curve_fit
import numpy as np
import matplotlib.pyplot as p
import astropy.units as u
from astropy.table import QTable
from .profile import profile_line
eight_conn = np.ones((3, 3))
end_structs = [np.array([[1, 0, 0],
[0, 1, 0],
[0, 0, 0]]),
np.array([[0, 1, 0],
[0, 1, 0],
[0, 0, 0]]),
np.array([[0, 0, 1],
[0, 1, 0],
[0, 0, 0]]),
np.array([[0, 0, 0],
[1, 1, 0],
[0, 0, 0]]),
np.array([[0, 0, 0],
[0, 1, 1],
[0, 0, 0]]),
np.array([[0, 0, 0],
[0, 1, 0],
[1, 0, 0]]),
np.array([[0, 0, 0],
[0, 1, 0],
[0, 1, 0]]),
np.array([[0, 0, 0],
[0, 1, 0],
[0, 0, 1]])]
four_conn_posns = [1, 3, 5, 7]
eight_conn_posns = [0, 2, 6, 8]
def filament_profile(skeleton, image, pixscale, max_dist=0.025 * u.pc,
distance=250. * u.pc, num_avg=3, verbose=False,
bright_unit="Jy km/s", noise=None, fit_profiles=True):
'''
Calculate radial profiles along the main extent of a skeleton (ie. the
longest path). The skeleton must contain a single branch with no
intersections.
Parameters
----------
skeleton : np.ndarray
Boolean array containing the skeleton
image : np.ndarray
Image to compute the profiles from. Must match the spatial extent
of the skeleton array.
pixscale : `~astropy.units.Quantity`
Angular size of a pixel in the image. Must have units equivalent to
degrees.
max_dist : astropy Quantity, optional
The angular or physical (when distance is given) extent to create the
profile away from the centre skeleton pixel. The entire profile will
be twice this value (for each side of the profile).
distance : astropy Quantity, optional
Physical distance to the region in the image. If None is given,
results will be in angular units based on the header.
num_avg : int, optional
Number of points before and after a pixel that is used when computing
the normal vector. Using at least three points is recommended due to
small pixel instabilities in the skeletons.
verbose : bool, optional
Enable plotting of the profile and the accompanying for each pixel in
the skeleton.
bright_unit : string or astropy Unit
Brightness unit of the image.
noise : np.ndarray, optional
RMS array for the accompanying image. When provided, the errors
are calculated along each of the profiles and used as weights in the
fitting.
fit_profiles : bool, optional
When enabled, fits a Gaussian model to the profiles. Otherwise only
the profiles are returned.
Returns
-------
line_distances : list
Distances along the profiles.
line_profiles : list
Radial profiles.
profile_extents : list
Contains the pixel position of the start of the profile,
the skeleton pixel, and the end of the profile.
tab : astropy QTable
Table of the fit results and errors with appropriate units.
'''
deg_per_pix = pixscale.to(u.deg) / u.pixel
if distance is not None:
phys_per_pix = distance * (np.pi / 180.) * deg_per_pix / u.deg
max_pixel = (max_dist / phys_per_pix).value
else:
# max_dist should then be in pixel or angular units
if not isinstance(max_dist, u.Quantity):
# Assume pixels
max_pixel = max_dist
else:
try:
max_pixel = max_dist.to(u.pix).value
except u.UnitConversionError:
# In angular units
equiv = [(u.pixel, u.deg, lambda x: x / (pixscale * u.pix),
lambda x: x * pixscale * u.pix)]
max_pixel = max_dist.to(u.pix, equivalencies=equiv).value
if bright_unit is None:
bright_unit = u.dimensionless_unscaled
elif isinstance(bright_unit, str):
bright_unit = u.Unit(bright_unit)
elif isinstance(bright_unit, u.UnitBase):
pass
else:
raise TypeError("bright_unit must be compatible with astropy.units.")
# Make sure the noise array is the same shape
if noise is not None:
assert noise.shape == image.shape
# Get the points in the skeleton (in order)
skel_pts = walk_through_skeleton(skeleton)
line_profiles = []
line_distances = []
profile_extents = []
profile_fits = []
red_chisqs = []
for j, i in enumerate(range(num_avg, len(skel_pts) - num_avg)):
# Calculate the normal direction from the surrounding pixels
pt1 = avg_pts([skel_pts[i + j] for j in range(-num_avg, 0)])
pt2 = avg_pts([skel_pts[i + j] for j in range(1, num_avg + 1)])
vec = np.array([float(x2 - x1) for x2, x1 in
zip(pt1, pt2)])
vec /= np.linalg.norm(vec)
per_vec = perpendicular(vec)
line_pts = find_path_ends(skel_pts[i], max_pixel, per_vec)
left_profile, left_dists = \
profile_line(image, skel_pts[i], line_pts[0])
right_profile, right_dists = \
profile_line(image, skel_pts[i], line_pts[1])
total_profile = np.append(left_profile[::-1], right_profile) * \
bright_unit
if noise is not None:
left_profile, _ = \
profile_line(noise, skel_pts[i], line_pts[0])
right_profile, _ = \
profile_line(noise, skel_pts[i], line_pts[1])
noise_profile = np.append(left_profile[::-1], right_profile) * \
bright_unit
else:
noise_profile = None
if distance is not None:
total_dists = np.append(-left_dists[::-1], right_dists) \
* u.pix * phys_per_pix
else:
total_dists = np.append(-left_dists[::-1], right_dists) \
* u.pix * deg_per_pix
if noise is not None:
if len(total_profile) != len(noise_profile):
raise ValueError("Intensity and noise profile lengths do not"
" match. Have you applied the same mask to"
" both?")
line_profiles.append(total_profile)
line_distances.append(total_dists)
profile_extents.append([line_pts[0], skel_pts[i], line_pts[1]])
if fit_profiles:
# Now fit!
profile_fit, profile_fit_err, red_chisq = \
gauss_fit(total_dists.value, total_profile.value,
sigma=noise_profile)
profile_fits.append(np.hstack([profile_fit, profile_fit_err]))
red_chisqs.append(red_chisq)
if verbose:
p.subplot(121)
p.imshow(image, origin='lower')
p.contour(skeleton, colors='r')
p.plot(skel_pts[i][1], skel_pts[i][0], 'bD')
p.plot(line_pts[0][1], line_pts[0][0], 'bD')
p.plot(line_pts[1][1], line_pts[1][0], 'bD')
p.subplot(122)
p.plot(total_dists, total_profile, 'bD')
pts = np.linspace(total_dists.min().value,
total_dists.max().value, 100)
if fit_profiles:
p.plot(pts, gaussian(pts, *profile_fit), 'r')
if distance is not None:
unit = (u.pix * phys_per_pix).unit.to_string()
else:
unit = (u.pix * deg_per_pix).unit.to_string()
p.xlabel("Distance from skeleton (" + unit + ")")
p.ylabel("Surface Brightness (" + bright_unit.to_string() + ")")
p.tight_layout()
p.show()
if fit_profiles:
profile_fits = np.asarray(profile_fits)
red_chisqs = np.asarray(red_chisqs)
# Create an astropy table of the fit results
param_names = ["Amplitude", "Std Dev", "Background"]
param_errs = [par + " Error" for par in param_names]
colnames = param_names + param_errs
in_bright_units = [True, False, True] * 2
tab = QTable()
tab["Number"] = np.arange(profile_fits.shape[0])
tab.add_index("Number")
tab["Red Chisq"] = red_chisqs
for i, (name, is_bright) in enumerate(zip(colnames, in_bright_units)):
if is_bright:
col_unit = bright_unit
else:
if distance is not None:
col_unit = (u.pix * phys_per_pix).unit
else:
col_unit = (u.pix * deg_per_pix).unit
tab[name] = profile_fits[:, i] * col_unit
return line_distances, line_profiles, profile_extents, tab
else:
return line_distances, line_profiles
def perpendicular(a):
'''
Return the perpendicular vector to a given 2D vector.
'''
b = np.empty_like(a)
b[0] = -a[1]
b[1] = a[0]
return b
def walk_through_skeleton(skeleton):
'''
Starting from one end, walk through a skeleton in order. Intended for use
with skeletons that contain no branches.
'''
# Calculate the end points
end_pts = return_ends(skeleton)
if len(end_pts) != 2:
raise ValueError("Skeleton must contain no intersections.")
# Force the first end point to be closest to the image origin.
if two_point_dist(end_pts[1], [0, 0]) < two_point_dist(end_pts[0], [0, 0]):
end_pts = end_pts[::-1]
all_pts = int(np.sum(skeleton))
yy, xx = np.mgrid[-1:2, -1:2]
yy = yy.ravel()
xx = xx.ravel()
for i in range(all_pts):
if i == 0:
ordered_pts = [end_pts[0]]
prev_pt = end_pts[0]
else:
# Check for neighbors
y, x = prev_pt
# Extract the connected region
neighbors = skeleton[y - 1:y + 2, x - 1:x + 2].ravel()
# Define the corresponding array indices.
yy_inds = yy + y
xx_inds = xx + x
hits = [int(elem) for elem in np.argwhere(neighbors)]
# Remove the centre point and any points already in the list
for pos, (y_ind, x_ind) in enumerate(zip(yy_inds, xx_inds)):
if (y_ind, x_ind) in ordered_pts:
hits.remove(pos)
num_hits = len(hits)
if num_hits == 0:
# You've reached the end. It better be the other end point
if prev_pt[0] != end_pts[1][0] or prev_pt[1] != end_pts[1][1]:
raise ValueError("Final point does not match expected"
" end point. Check input skeleton for"
" intersections.")
break
elif num_hits == 1:
# You have found the next point
posn = hits[0]
next_pt = (y + yy[posn], x + xx[posn])
ordered_pts.append(next_pt)
else:
# There's at least a couple neighbours (for some reason)
# Pick the 4-connected component since it is the closest
for fours in four_conn_posns:
if fours in hits:
posn = hits[hits.index(fours)]
break
else:
raise ValueError("Disconnected eight-connected pixels?")
next_pt = (y + yy[posn], x + xx[posn])
ordered_pts.append(next_pt)
prev_pt = next_pt
return ordered_pts
def return_ends(skeleton):
'''
Find the endpoints of the skeleton.
'''
end_points = []
for i, struct in enumerate(end_structs):
hits = nd.binary_hit_or_miss(skeleton, structure1=struct)
if not np.any(hits):
continue
for y, x in zip(*np.where(hits)):
end_points.append((y, x))
return end_points
def find_path_ends(posn, max_dist, vector):
'''
Find ends of a path for line_profile given
a vector direction.
'''
vector = vector.astype(float) / np.linalg.norm(vector)
max_size = np.ceil(max_dist).astype(int)
yy, xx = np.mgrid[-max_size:max_size + 1, -max_size:max_size + 1]
max_circle = yy**2 + xx**2 <= max_dist**2
ring = \
np.logical_xor(max_circle,
nd.binary_erosion(max_circle, eight_conn))
radius_pts = [(y + posn[0], x + posn[1]) for y, x in zip(*np.where(ring))]
x_step = vector[1]
y_step = vector[0]
y_diff = max_size * y_step
x_diff = max_size * x_step
neg_line_posn = (posn[0] - y_diff, posn[1] - x_diff)
pos_line_posn = (posn[0] + y_diff, posn[1] + x_diff)
# pos_dists = np.array([two_point_dist(pos_line_posn, pt)
# for pt in radius_pts])
# neg_dists = np.array([two_point_dist(neg_line_posn, pt)
# for pt in radius_pts])
# These should be the ones used to ensure
# proper distance from the skeleton point.
# pos_posn give weird results though...
# pos_posn = radius_pts[np.argmin(pos_dists)]
# neg_posn = radius_pts[np.argmin(neg_dists)]
return [neg_line_posn, pos_line_posn]
def two_point_dist(pt1, pt2):
return np.linalg.norm([x2 - x1 for x2, x1 in zip(pt1, pt2)])
def avg_pts(pts):
dims = len(pts[0])
avg_pt = []
for dim in range(dims):
avg_pt.append(np.mean([pt[dim] for pt in pts]).astype(int))
return avg_pt
def gaussian(x, *p):
'''
Parameters
----------
x : list or numpy.ndarray
1D array of values where the model is evaluated
p : tuple
Components are:
* p[0] Amplitude
* p[1] Mean
* p[2] Width
* p[3] Background
'''
return (p[0] - p[2]) * np.exp(-1 * np.power(x, 2) /
(2 * | np.power(p[1], 2) | numpy.power |
from ..initial_param.kinect_para import Kinect_para
import numpy as np
from math import acos
from scipy.signal import argrelextrema
from scipy.ndimage.filters import gaussian_filter1d as gf
import inflect,pdb
class Swing(object):
""" Dectect if body bend to left or right.
Also if arm is straight or not.
"""
def __init__(self):
self.angle_mean = []
self.angel_le = []
self.angel_re = []
self.angle_ini = 90.0
self.bend_max = []
self.bend_min = []
self.cnvt = inflect.engine() # converting numerals into ordinals
self.max_ary = np.array([[0, 0]])
self.min_ary = np.array([[0, np.inf]])
self.max_len = 1
self.min_len = 1
self.bend_th = 20
self.kpm = Kinect_para()
self.bend_left = True
# default parameters
self.cnt = 0
self.do = False
self.err = []
self.errsum = []
self.evalstr = ''
self.eval = ''
def vec_angle(self, vec1, vec2= | np.array([1, 0, 0]) | numpy.array |
from deepNets import layers
from deepNets import layer_utils
import numpy as np
# from layers import *
# from layer_utils import *
class Net(object):
def __init__(self):
self.params = {}
self.reg = 0.0
self.dtype = np.float64
self.seed = None
self.layer_defs = []
self.layers_length = 0
self.layerDims = []
self.bn_params = []
def check_syntax(self,layer,inp=False,loss=False):
layer_check = layer.get("layer_type",None)
if inp:
assert layer_check != None and layer_check == "input", "Input layer required"
elif loss:
assert layer_check != None and layer_check == "loss", "loss layer required"
layer_check = layer.get("num_classes",None)
assert layer_check != None and layer_check > 0 , "Number of classes required"
else:
assert layer_check != None and (layer_check == "relu" or layer_check == "batchnorm" or layer_check == "layernorm" or layer_check == "conv" or layer_check == "pool") , "Incorrect layer found"
if layer_check == "relu":
hidden = layer.get("hidden_layers",0)
assert hidden > 0 ,"Hidden layers not specified"
elif layer_check == "conv":
filters = layer.get("filters",0)
filter_size = layer.get("filter_size",0)
padding = layer.get("padding",0)
stride = layer.get("stride",1)
assert filters > 0 and filter_size > 0 and padding >= 0 and stride >= 1 , "Wrong parameters for conv layer"
elif layer_check == "pool":
filter_size = layer.get("filter_size",0)
stride = layer.get("stride",1)
assert filter_size > 0 and stride >= 1 , "Wrong parameters for conv layer"
else:
self.layers_length -= 1
def makeLayerDims(self,layer_defs):
inp_dim = layer_defs[0].get("inp",None)
if(len(inp_dim[0].shape)==3):
c,h,w = inp_dim[0].shape
conv_flag = False
for i in range(len(layer_defs)-1):
if i == 0:
checkConv = layer_defs[i+1].get("layer_type",None)
if checkConv == "conv":
conv_flag = True
continue
get_inp = layer_defs[i].get("inp",None)
xdim = get_inp[0].shape
self.layerDims.append(np.prod(xdim))
continue
self.check_syntax(layer_defs[i],False,False)
get_layer = layer_defs[i].get("layer_type",None)
if get_layer == "relu":
if conv_flag:
conv_flag = False
self.layerDims.append(c*h*w)
get_hidden = layer_defs[i].get("hidden_layers",None)
self.layerDims.append(get_hidden)
elif get_layer == "conv":
dims = [layer_defs[i].get("filters",0),layer_defs[i].get("filter_size",0)]
assert conv_flag , "Cannot unpack " + str(self.layerDims[-1]) + " into " + str(dims[0]) + " x " + str(dims[1]) + " x " + str(dims[1])
padding = layer_defs[i].get("padding",0)
stride = layer_defs[i].get("stride",1)
#updating the parameters channel,height and width for flattening
c = dims[0]
assert (h - dims[1] + 2*padding)%stride == 0, "Conv filter height not proper"
assert (w - dims[1] + 2*padding)%stride == 0, "Conv filter width not proper"
h = (h - dims[1] + 2*padding)//stride + 1
w = (w - dims[1] + 2*padding)//stride + 1
self.layerDims.append(dims)
elif get_layer == "pool":
assert conv_flag , "Input layer cannot be pooled without conv layer on top"
filter_size = layer_defs[i].get("filter_size",0)
stride = layer_defs[i].get("stride",1) #Default 1
assert (h - filter_size)%stride == 0, "Pool filter height not proper"
assert (w - filter_size)%stride == 0, "Pool filter width not proper"
h = (h - filter_size)//stride + 1
w = (w - filter_size)//stride + 1
self.layers_length -= 1
#For loss layer
if conv_flag:
conv_flag = False
self.layerDims.append(c*h*w)
self.layerDims.append(layer_defs[-1].get("num_classes",None))
return
def makeLayers(self,layer_defs,initialization="None",weight_scale=1e-3):
self.layer_defs = layer_defs
self.layers_length = len(layer_defs) - 1
input_layer = layer_defs[0]
self.check_syntax(input_layer,True,False)
loss_layer = layer_defs[-1]
self.check_syntax(loss_layer,False,True)
self.makeLayerDims(layer_defs)
channel = 0
for i in range(self.layers_length):
if type(self.layerDims[i]) is list:
if channel == 0:
channel = input_layer.get("inp").shape[1] # 3 channel image is preferred
self.params["W"+str(i+1)] = weight_scale * np.random.randn(self.layerDims[i][0],channel,self.layerDims[i][1],self.layerDims[i][1])
self.params["b"+str(i+1)] = np.zeros(self.layerDims[i][0])
self.params["gamma"+str(i+1)] = np.ones(self.layerDims[i][0])
self.params["beta"+str(i+1)] = | np.zeros(self.layerDims[i][0]) | numpy.zeros |
from itertools import product
import numpy as np
from aif360.metrics import BinaryLabelDatasetMetric, utils
from aif360.datasets import BinaryLabelDataset
class ClassificationMetric(BinaryLabelDatasetMetric):
"""Class for computing metrics based on two BinaryLabelDatasets.
The first dataset is the original one and the second is the output of the
classification transformer (or similar).
"""
def __init__(self, dataset, classified_dataset,
unprivileged_groups=None, privileged_groups=None):
"""
Args:
dataset (BinaryLabelDataset): Dataset containing ground-truth
labels.
classified_dataset (BinaryLabelDataset): Dataset containing
predictions.
privileged_groups (list(dict)): Privileged groups. Format is a list
of `dicts` where the keys are `protected_attribute_names` and
the values are values in `protected_attributes`. Each `dict`
element describes a single group. See examples for more details.
unprivileged_groups (list(dict)): Unprivileged groups in the same
format as `privileged_groups`.
Raises:
TypeError: `dataset` and `classified_dataset` must be
:obj:`~aif360.datasets.BinaryLabelDataset` types.
"""
if not isinstance(dataset, BinaryLabelDataset):
raise TypeError("'dataset' should be a BinaryLabelDataset")
# sets self.dataset, self.unprivileged_groups, self.privileged_groups
super(ClassificationMetric, self).__init__(dataset,
unprivileged_groups=unprivileged_groups,
privileged_groups=privileged_groups)
if isinstance(classified_dataset, BinaryLabelDataset):
self.classified_dataset = classified_dataset
else:
raise TypeError("'classified_dataset' should be a "
"BinaryLabelDataset.")
# Verify if everything except the predictions and metadata are the same
# for the two datasets
with self.dataset.temporarily_ignore('labels', 'scores'):
if self.dataset != self.classified_dataset:
raise ValueError("The two datasets are expected to differ only "
"in 'labels' or 'scores'.")
def binary_confusion_matrix(self, privileged=None):
"""Compute the number of true/false positives/negatives, optionally
conditioned on protected attributes.
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Returns:
dict: Number of true positives, false positives, true negatives,
false negatives (optionally conditioned).
"""
condition = self._to_condition(privileged)
return utils.compute_num_TF_PN(self.dataset.protected_attributes,
self.dataset.labels, self.classified_dataset.labels,
self.dataset.instance_weights,
self.dataset.protected_attribute_names,
self.dataset.favorable_label, self.dataset.unfavorable_label,
condition=condition)
def generalized_binary_confusion_matrix(self, privileged=None):
"""Compute the number of generalized true/false positives/negatives,
optionally conditioned on protected attributes. Generalized counts are
based on scores and not on the hard predictions.
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Returns:
dict: Number of generalized true positives, generalized false
positives, generalized true negatives, generalized false negatives
(optionally conditioned).
"""
condition = self._to_condition(privileged)
return utils.compute_num_gen_TF_PN(self.dataset.protected_attributes,
self.dataset.labels, self.classified_dataset.scores,
self.dataset.instance_weights,
self.dataset.protected_attribute_names,
self.dataset.favorable_label, self.dataset.unfavorable_label,
condition=condition)
def num_true_positives(self, privileged=None):
r"""Return the number of instances in the dataset where both the
predicted and true labels are 'favorable',
:math:`TP = \sum_{i=1}^n \mathbb{1}[y_i = \text{favorable}]\mathbb{1}[\hat{y}_i = \text{favorable}]`,
optionally conditioned on protected attributes.
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.binary_confusion_matrix(privileged=privileged)['TP']
def num_false_positives(self, privileged=None):
r""":math:`FP = \sum_{i=1}^n \mathbb{1}[y_i = \text{unfavorable}]\mathbb{1}[\hat{y}_i = \text{favorable}]`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.binary_confusion_matrix(privileged=privileged)['FP']
def num_false_negatives(self, privileged=None):
r""":math:`FN = \sum_{i=1}^n \mathbb{1}[y_i = \text{favorable}]\mathbb{1}[\hat{y}_i = \text{unfavorable}]`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.binary_confusion_matrix(privileged=privileged)['FN']
def num_true_negatives(self, privileged=None):
r""":math:`TN = \sum_{i=1}^n \mathbb{1}[y_i = \text{unfavorable}]\mathbb{1}[\hat{y}_i = \text{unfavorable}]`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.binary_confusion_matrix(privileged=privileged)['TN']
def num_generalized_true_positives(self, privileged=None):
"""Return the generalized number of true positives, :math:`GTP`, the
weighted sum of predicted scores where true labels are 'favorable',
optionally conditioned on protected attributes.
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.generalized_binary_confusion_matrix(
privileged=privileged)['GTP']
def num_generalized_false_positives(self, privileged=None):
"""Return the generalized number of false positives, :math:`GFP`, the
weighted sum of predicted scores where true labels are 'favorable',
optionally conditioned on protected attributes.
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.generalized_binary_confusion_matrix(
privileged=privileged)['GFP']
def num_generalized_false_negatives(self, privileged=None):
"""Return the generalized number of false negatives, :math:`GFN`, the
weighted sum of predicted scores where true labels are 'favorable',
optionally conditioned on protected attributes.
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.generalized_binary_confusion_matrix(
privileged=privileged)['GFN']
def num_generalized_true_negatives(self, privileged=None):
"""Return the generalized number of true negatives, :math:`GTN`, the
weighted sum of predicted scores where true labels are 'favorable',
optionally conditioned on protected attributes.
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.generalized_binary_confusion_matrix(
privileged=privileged)['GTN']
def performance_measures(self, privileged=None):
"""Compute various performance measures on the dataset, optionally
conditioned on protected attributes.
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Returns:
dict: True positive rate, true negative rate, false positive rate,
false negative rate, positive predictive value, negative predictive
value, false discover rate, false omission rate, and accuracy
(optionally conditioned).
"""
TP = self.num_true_positives(privileged=privileged)
FP = self.num_false_positives(privileged=privileged)
FN = self.num_false_negatives(privileged=privileged)
TN = self.num_true_negatives(privileged=privileged)
GTP = self.num_generalized_true_positives(privileged=privileged)
GFP = self.num_generalized_false_positives(privileged=privileged)
GFN = self.num_generalized_false_negatives(privileged=privileged)
GTN = self.num_generalized_true_negatives(privileged=privileged)
P = self.num_positives(privileged=privileged)
N = self.num_negatives(privileged=privileged)
return dict(
TPR=TP / P, TNR=TN / N, FPR=FP / N, FNR=FN / P,
GTPR=GTP / P, GTNR=GTN / N, GFPR=GFP / N, GFNR=GFN / P,
PPV=TP / (TP+FP) if (TP+FP) > 0.0 else np.float64(0.0),
NPV=TN / (TN+FN) if (TN+FN) > 0.0 else np.float64(0.0),
FDR=FP / (FP+TP) if (FP+TP) > 0.0 else np.float64(0.0),
FOR=FN / (FN+TN) if (FN+TN) > 0.0 else np.float64(0.0),
ACC=(TP+TN) / (P+N) if (P+N) > 0.0 else np.float64(0.0)
)
def true_positive_rate(self, privileged=None):
"""Return the ratio of true positives to positive examples in the
dataset, :math:`TPR = TP/P`, optionally conditioned on protected
attributes.
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['TPR']
def false_positive_rate(self, privileged=None):
""":math:`FPR = FP/N`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['FPR']
def false_negative_rate(self, privileged=None):
""":math:`FNR = FN/P`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['FNR']
def true_negative_rate(self, privileged=None):
""":math:`TNR = TN/N`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['TNR']
def generalized_true_positive_rate(self, privileged=None):
"""Return the ratio of generalized true positives to positive examples
in the dataset, :math:`GTPR = GTP/P`, optionally conditioned on
protected attributes.
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['GTPR']
def generalized_false_positive_rate(self, privileged=None):
""":math:`GFPR = GFP/N`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['GFPR']
def generalized_false_negative_rate(self, privileged=None):
""":math:`GFNR = GFN/P`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['GFNR']
def generalized_true_negative_rate(self, privileged=None):
""":math:`GTNR = GTN/N`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['GTNR']
def positive_predictive_value(self, privileged=None):
""":math:`PPV = TP/(TP + FP)`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['PPV']
def false_discovery_rate(self, privileged=None):
""":math:`FDR = FP/(TP + FP)`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['FDR']
def false_omission_rate(self, privileged=None):
""":math:`FOR = FN/(TN + FN)`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['FOR']
def negative_predictive_value(self, privileged=None):
""":math:`NPV = TN/(TN + FN)`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['NPV']
def accuracy(self, privileged=None):
""":math:`ACC = (TP + TN)/(P + N)`.
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return self.performance_measures(privileged=privileged)['ACC']
def error_rate(self, privileged=None):
""":math:`ERR = (FP + FN)/(P + N)`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return 1. - self.accuracy(privileged=privileged)
def true_positive_rate_difference(self):
r""":math:`TPR_{D = \text{unprivileged}} - TPR_{D = \text{privileged}}`
"""
return self.difference(self.true_positive_rate)
def false_positive_rate_difference(self):
r""":math:`FPR_{D = \text{unprivileged}} - FPR_{D = \text{privileged}}`
"""
return self.difference(self.false_positive_rate)
def false_negative_rate_difference(self):
r""":math:`FNR_{D = \text{unprivileged}} - FNR_{D = \text{privileged}}`
"""
return self.difference(self.false_negative_rate)
def false_omission_rate_difference(self):
r""":math:`FOR_{D = \text{unprivileged}} - FOR_{D = \text{privileged}}`
"""
return self.difference(self.false_omission_rate)
def false_discovery_rate_difference(self):
r""":math:`FDR_{D = \text{unprivileged}} - FDR_{D = \text{privileged}}`
"""
return self.difference(self.false_discovery_rate)
def false_positive_rate_ratio(self):
r""":math:`\frac{FPR_{D = \text{unprivileged}}}{FPR_{D = \text{privileged}}}`
"""
return self.ratio(self.false_positive_rate)
def false_negative_rate_ratio(self):
r""":math:`\frac{FNR_{D = \text{unprivileged}}}{FNR_{D = \text{privileged}}}`
"""
return self.ratio(self.false_negative_rate)
def false_omission_rate_ratio(self):
r""":math:`\frac{FOR_{D = \text{unprivileged}}}{FOR_{D = \text{privileged}}}`
"""
return self.ratio(self.false_omission_rate)
def false_discovery_rate_ratio(self):
r""":math:`\frac{FDR_{D = \text{unprivileged}}}{FDR_{D = \text{privileged}}}`
"""
return self.ratio(self.false_discovery_rate)
def average_odds_difference(self):
r"""Average of difference in FPR and TPR for unprivileged and privileged
groups:
.. math::
\tfrac{1}{2}\left[(FPR_{D = \text{unprivileged}} - FPR_{D = \text{privileged}})
+ (TPR_{D = \text{unprivileged}} - TPR_{D = \text{privileged}}))\right]
A value of 0 indicates equality of odds.
"""
return 0.5 * (self.difference(self.false_positive_rate)
+ self.difference(self.true_positive_rate))
def average_abs_odds_difference(self):
r"""Average of absolute difference in FPR and TPR for unprivileged and
privileged groups:
.. math::
\tfrac{1}{2}\left[|FPR_{D = \text{unprivileged}} - FPR_{D = \text{privileged}}|
+ |TPR_{D = \text{unprivileged}} - TPR_{D = \text{privileged}}|\right]
A value of 0 indicates equality of odds.
"""
return 0.5 * (np.abs(self.difference(self.false_positive_rate))
+ np.abs(self.difference(self.true_positive_rate)))
def error_rate_difference(self):
r"""Difference in error rates for unprivileged and privileged groups,
:math:`ERR_{D = \text{unprivileged}} - ERR_{D = \text{privileged}}`.
"""
return self.difference(self.error_rate)
def error_rate_ratio(self):
r"""Ratio of error rates for unprivileged and privileged groups,
:math:`\frac{ERR_{D = \text{unprivileged}}}{ERR_{D = \text{privileged}}}`.
"""
return self.ratio(self.error_rate)
def num_pred_positives(self, privileged=None):
r""":math:`\sum_{i=1}^n \mathbb{1}[\hat{y}_i = \text{favorable}]`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
condition = self._to_condition(privileged)
return utils.compute_num_pos_neg(
self.classified_dataset.protected_attributes,
self.classified_dataset.labels,
self.classified_dataset.instance_weights,
self.classified_dataset.protected_attribute_names,
self.classified_dataset.favorable_label,
condition=condition)
def num_pred_negatives(self, privileged=None):
r""":math:`\sum_{i=1}^n \mathbb{1}[\hat{y}_i = \text{unfavorable}]`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
condition = self._to_condition(privileged)
return utils.compute_num_pos_neg(
self.classified_dataset.protected_attributes,
self.classified_dataset.labels,
self.classified_dataset.instance_weights,
self.classified_dataset.protected_attribute_names,
self.classified_dataset.unfavorable_label,
condition=condition)
def selection_rate(self, privileged=None):
r""":math:`Pr(\hat{Y} = \text{favorable})`
Args:
privileged (bool, optional): Boolean prescribing whether to
condition this metric on the `privileged_groups`, if `True`, or
the `unprivileged_groups`, if `False`. Defaults to `None`
meaning this metric is computed over the entire dataset.
Raises:
AttributeError: `privileged_groups` or `unprivileged_groups` must be
must be provided at initialization to condition on them.
"""
return (self.num_pred_positives(privileged=privileged)
/ self.num_instances(privileged=privileged))
def disparate_impact(self):
r"""
.. math::
\frac{Pr(\hat{Y} = 1 | D = \text{unprivileged})}
{Pr(\hat{Y} = 1 | D = \text{privileged})}
"""
return self.ratio(self.selection_rate)
def statistical_parity_difference(self):
r"""
.. math::
Pr(\hat{Y} = 1 | D = \text{unprivileged})
- Pr(\hat{Y} = 1 | D = \text{privileged})
"""
return self.difference(self.selection_rate)
def generalized_entropy_index(self, alpha=2):
r"""Generalized entropy index is proposed as a unified individual and
group fairness measure in [3]_. With :math:`b_i = \hat{y}_i - y_i + 1`:
.. math::
\mathcal{E}(\alpha) = \begin{cases}
\frac{1}{n \alpha (\alpha-1)}\sum_{i=1}^n\left[\left(\frac{b_i}{\mu}\right)^\alpha - 1\right],& \alpha \ne 0, 1,\\
\frac{1}{n}\sum_{i=1}^n\frac{b_{i}}{\mu}\ln\frac{b_{i}}{\mu},& \alpha=1,\\
-\frac{1}{n}\sum_{i=1}^n\ln\frac{b_{i}}{\mu},& \alpha=0.
\end{cases}
Args:
alpha (int): Parameter that regulates the weight given to distances
between values at different parts of the distribution.
References:
.. [3] <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, and <NAME>,
"A Unified Approach to Quantifying Algorithmic Unfairness: Measuring Individual and Group Unfairness via Inequality Indices,"
ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2018.
"""
y_pred = self.classified_dataset.labels.ravel()
y_true = self.dataset.labels.ravel()
y_pred = (y_pred == self.classified_dataset.favorable_label).astype(
np.float64)
y_true = (y_true == self.dataset.favorable_label).astype(np.float64)
b = 1 + y_pred - y_true
if alpha == 1:
# moving the b inside the log allows for 0 values
return np.mean(np.log((b / np.mean(b))**b) / np.mean(b))
elif alpha == 0:
return -np.mean(np.log(b / np.mean(b)) / np.mean(b))
else:
return np.mean((b / np.mean(b))**alpha - 1) / (alpha * (alpha - 1))
def _between_group_generalized_entropy_index(self, groups, alpha=2):
r"""Between-group generalized entropy index is proposed as a group
fairness measure in [2]_ and is one of two terms that the generalized
entropy index decomposes to.
Args:
groups (list): A list of groups over which to calculate this metric.
Groups should be disjoint. By default, this will use the
`privileged_groups` and `unprivileged_groups` as the only two
groups.
alpha (int): See :meth:`generalized_entropy_index`.
References:
.. [2] <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, and <NAME>,
"A Unified Approach to Quantifying Algorithmic Unfairness: Measuring Individual and Group Unfairness via Inequality Indices,"
ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2018.
"""
b = np.zeros(self.dataset.labels.size, dtype=np.float64)
for group in groups:
classified_group = utils.compute_boolean_conditioning_vector(
self.classified_dataset.protected_attributes,
self.classified_dataset.protected_attribute_names,
condition=group)
true_group = utils.compute_boolean_conditioning_vector(
self.dataset.protected_attributes,
self.dataset.protected_attribute_names,
condition=group)
# ignore if there are no members of this group present
if not np.any(true_group):
continue
y_pred = self.classified_dataset.labels[classified_group].ravel()
y_true = self.dataset.labels[true_group].ravel()
y_pred = (y_pred == self.classified_dataset.favorable_label).astype(
np.float64)
y_true = (y_true == self.dataset.favorable_label).astype(np.float64)
b[true_group] = np.mean(1 + y_pred - y_true)
if alpha == 1:
return np.mean(np.log((b / np.mean(b))**b) / | np.mean(b) | numpy.mean |
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Sep 20 18:42:58 2018
@author: owenmadin
"""
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Sep 20 11:33:46 2018
@author: owenmadin
"""
"""
This code performs an RJMC model selection problem over three square regions of uniform probability, defined as squares of side length 1,2 and 5
with one corner at (0,0) and another at (s,s). The uniform probability is defined as positive inside each square, and zero outside each square.
"""
import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
import pandas as pd
import yaml
from LennardJones_correlations import LennardJones
from LennardJones_2Center_correlations import LennardJones_2C
from scipy.stats import distributions
from scipy.stats import linregress
from scipy.optimize import minimize
import random as rm
# Define probabilities for both regions
def test_pdf_1(model,x,y):
if model == 0:
if 0 <= x <= 1 and 0 <= y <= 1:
f=5
else:
f=0
if model == 1:
if 0 <= x <= 2 and 0 <= y <= 2:
f=5
else:
f=0
if model == 2:
if 0 <= x <= 5 and 0 <= y <= 5:
f=5
else:
f=0
return f
def test_pdf_2(model,x,y):
if model == 0:
if 0 <= x <= 1 and 0 <= y <= 1:
f=5
else:
f=0
if model == 1:
if 1 <= x <= 3 and 1 <= y <= 3:
f=5
else:
f=0
if model == 2:
if 3 <= x <= 6 and 3 <= y <= 6:
f=5
else:
f=0
return f
dnorm = distributions.norm.logpdf
dgamma = distributions.gamma.logpdf
duni = distributions.uniform.logpdf
rnorm = np.random.normal
runif = np.random.rand
#Define log priors for the distributions. For now, we will use a uniform prior on (10,10), but we may want to change the prior for different models in the future
def calc_posterior(model,x,y):
logp = 0
logp += duni(x, 0, 10)
logp += duni(y, 0, 10)
#prop_density=test_pdf_1(model,x,y)
prop_density=test_pdf_2(model,x,y)
logp += np.log(prop_density)
return logp
def T_matrix_scale_one():
T_matrix_x_scale=np.ones((3,3))
T_matrix_y_scale=np.ones((3,3))
T_matrix_x_scale[0,1]=3
T_matrix_y_scale[0,1]=3
T_matrix_x_scale[1,0]=1./3
T_matrix_y_scale[1,0]=1./3
T_matrix_x_scale[0,2]=6
T_matrix_y_scale[0,2]=6
T_matrix_x_scale[2,0]=1./6
T_matrix_y_scale[2,0]=1./6
T_matrix_x_scale[1,2]=6./3
T_matrix_y_scale[1,2]=6./3
T_matrix_x_scale[2,1]=3./6
T_matrix_y_scale[2,1]=3./6
return T_matrix_x_scale, T_matrix_y_scale
def T_matrix_scale_two():
T_matrix_x_scale=np.ones((3,3))
T_matrix_y_scale=np.ones((3,3))
T_matrix_x_scale[0,1]=4
T_matrix_x_scale[1,0]=1./4
T_matrix_x_scale[0,2]=9
T_matrix_x_scale[2,0]=1./9
T_matrix_x_scale[1,2]=9/4
T_matrix_x_scale[2,1]=4./9
T_matrix_y_scale[0,1]=4
T_matrix_y_scale[1,0]=1./4
T_matrix_y_scale[0,2]=9
T_matrix_y_scale[2,0]=1./9
T_matrix_y_scale[1,2]=9./4
T_matrix_y_scale[2,1]=4./9
return T_matrix_x_scale, T_matrix_y_scale
def T_matrix_translation():
T_matrix_x=np.zeros((2,2))
T_matrix_y=np.zeros((2,2))
T_matrix_x[0,1]=2
T_matrix_y[0,1]=2
T_matrix_x[1,0]=-2
T_matrix_y[1,0]=-2
return T_matrix_x, T_matrix_y
T_matrix_x_scale_1, T_matrix_y_scale_1 = T_matrix_scale_one()
T_matrix_x_scale_2, T_matrix_y_scale_2 = T_matrix_scale_two()
def RJMC_tuned(calc_posterior,n_iterations, initial_values, prop_var,
tune_for=None, tune_interval=1, map_scale='False'):
n_params = len(initial_values) #One column is the model number
# Initial proposal standard deviations
prop_sd = prop_var
# Initialize trace for parameters
trace = np.zeros((n_iterations+1, n_params)) #n_iterations + 1 to account for guess
logp_trace = np.zeros(n_iterations+1)
# Set initial values
trace[0] = initial_values
# Initialize acceptance counts
accepted = [0]*n_params
rejected = [0]*n_params
model_swaps = 0
model_swap_attempts = 0
swap_freq = 1
swap_flag='False'
# OCM: Currently attempting a model swap every single move, although this can be easily changed. This is something that is not of critical importance now but will be important in the future.
# Calculate joint posterior for initial values
current_log_prob = calc_posterior(*trace[0])
logp_trace[0] = current_log_prob
#OCM: This is just the priors at this point.
if tune_for is None:
tune_for = n_iterations/2
for i in range(n_iterations):
swap_flag='False'
if not i%1000: print('Iteration '+str(i))
# Grab current parameter values
current_params = trace[i].copy()
trace[i+1] = current_params.copy() #Initialize the next step with the current step. Then update if MCMC move is accepted
current_model = int(current_params[0])
logp_trace[i+1] = current_log_prob.copy()
# Loop through model parameters
for j in range(n_params):
# Get current value for parameter j
params = current_params.copy() # This approach updates previous param values
# Propose new values
if j == 0: #If proposing a new model
if not i%swap_freq:
mod_ran = np.random.random()
if mod_ran < 1./3: #Use new models with equal probability
proposed_model = 0
elif mod_ran >= 2./3:
proposed_model = 1
else:
proposed_model = 2
if proposed_model != current_model:
model_swap_attempts += 1
params[0] = proposed_model
if map_scale=='True':
params[1] *= T_matrix_x_scale_1[current_model,proposed_model]
params[2] *= T_matrix_y_scale_1[current_model,proposed_model]
#params[1] *= T_matrix_x_scale_2[current_model,proposed_model]
#params[2] *= T_matrix_y_scale_2[current_model,proposed_model]
'''
else:
params[1] += T_matrix_x[current_model,proposed_model]
params[2] += T_matrix_y[current_model,proposed_model]
# Calculate log posterior with proposed value
'''
proposed_log_prob = calc_posterior(*params)
# Log-acceptance rate
alpha = (proposed_log_prob - current_log_prob) + np.log(T_matrix_x_scale_1[current_model,proposed_model]) + np.log(T_matrix_y_scale_1[current_model,proposed_model])
#alpha = (proposed_log_prob - current_log_prob) + np.log(T_matrix_x_scale_2[current_model,proposed_model]) + np.log(T_matrix_y_scale_2[current_model,proposed_model])
urv = runif()
# Test proposed value
if np.log(urv) < alpha:
# Accept
trace[i+1] = params
logp_trace[i+1] = proposed_log_prob.copy()
current_log_prob = proposed_log_prob.copy()
current_params = params
accepted[j] += 1
if j == 0:
if proposed_model != current_model:
model_swaps += 1
swap_flag = 'True'
else:
if swap_flag=='False':
params[j] = rnorm(current_params[j], prop_sd[j])
# Calculate log posterior with proposed value
proposed_log_prob = calc_posterior(*params)
# Log-acceptance rate
alpha = (proposed_log_prob - current_log_prob)
#OCM: The two components of the acceptance ratio here are the log of the ratio of the probabilities, and the log of the jacobian determinant between the model spaces
# Sample a uniform random variate (urv)
urv = runif()
# Test proposed value
if | np.log(urv) | numpy.log |
import logging
import unittest
import numpy as np
from mne import BaseEpochs
from moabb.datasets.fake import FakeDataset
from moabb.paradigms import (
P300,
SSVEP,
BaseMotorImagery,
BaseP300,
BaseSSVEP,
FilterBankLeftRightImagery,
FilterBankMotorImagery,
FilterBankSSVEP,
LeftRightImagery,
)
log = logging.getLogger(__name__)
log.setLevel(logging.ERROR)
class SimpleMotorImagery(BaseMotorImagery): # Needed to assess BaseImagery
def used_events(self, dataset):
return dataset.event_id
class Test_MotorImagery(unittest.TestCase):
def test_BaseImagery_paradigm(self):
paradigm = SimpleMotorImagery()
dataset = FakeDataset(paradigm="imagery")
X, labels, metadata = paradigm.get_data(dataset, subjects=[1])
# we should have all the same length
self.assertEqual(len(X), len(labels), len(metadata))
# X must be a 3D Array
self.assertEqual(len(X.shape), 3)
# labels must contain 3 values
self.assertEqual(len(np.unique(labels)), 3)
# metadata must have subjets, sessions, runs
self.assertTrue("subject" in metadata.columns)
self.assertTrue("session" in metadata.columns)
self.assertTrue("run" in metadata.columns)
# we should have only one subject in the metadata
self.assertEqual(np.unique(metadata.subject), 1)
# we should have two sessions in the metadata
self.assertEqual(len(np.unique(metadata.session)), 2)
# should return epochs
epochs, _, _ = paradigm.get_data(dataset, subjects=[1], return_epochs=True)
self.assertIsInstance(epochs, BaseEpochs)
def test_BaseImagery_channel_order(self):
"""test if paradigm return correct channel order, see issue #227"""
datasetA = FakeDataset(paradigm="imagery", channels=["C3", "Cz", "C4"])
datasetB = FakeDataset(paradigm="imagery", channels=["Cz", "C4", "C3"])
paradigm = SimpleMotorImagery(channels=["C4", "C3", "Cz"])
ep1, _, _ = paradigm.get_data(datasetA, subjects=[1], return_epochs=True)
ep2, _, _ = paradigm.get_data(datasetB, subjects=[1], return_epochs=True)
self.assertEqual(ep1.info["ch_names"], ep2.info["ch_names"])
def test_BaseImagery_tmintmax(self):
self.assertRaises(ValueError, SimpleMotorImagery, tmin=1, tmax=0)
def test_BaseImagery_filters(self):
# can work with filter bank
paradigm = SimpleMotorImagery(filters=[[7, 12], [12, 24]])
dataset = FakeDataset(paradigm="imagery")
X, labels, metadata = paradigm.get_data(dataset, subjects=[1])
# X must be a 4D Array
self.assertEqual(len(X.shape), 4)
self.assertEqual(X.shape[-1], 2)
# should return epochs
epochs, _, _ = paradigm.get_data(dataset, subjects=[1], return_epochs=True)
self.assertIsInstance(epochs, BaseEpochs)
def test_baseImagery_wrongevent(self):
# test process_raw return empty list if raw does not contain any
# selected event. cetain runs in dataset are event specific.
paradigm = SimpleMotorImagery(filters=[[7, 12], [12, 24]])
dataset = FakeDataset(paradigm="imagery")
raw = dataset.get_data([1])[1]["session_0"]["run_0"]
# add something on the event channel
raw._data[-1] *= 10
self.assertIsNone(paradigm.process_raw(raw, dataset))
# zeros it out
raw._data[-1] *= 0
self.assertIsNone(paradigm.process_raw(raw, dataset))
def test_BaseImagery_noevent(self):
# Assert error if events from paradigm and dataset dont overlap
paradigm = SimpleMotorImagery(events=["left_hand", "right_hand"])
dataset = FakeDataset(paradigm="imagery")
self.assertRaises(AssertionError, paradigm.get_data, dataset)
def test_LeftRightImagery_paradigm(self):
# with a good dataset
paradigm = LeftRightImagery()
dataset = FakeDataset(event_list=["left_hand", "right_hand"], paradigm="imagery")
X, labels, metadata = paradigm.get_data(dataset, subjects=[1])
self.assertEqual(len(np.unique(labels)), 2)
self.assertEqual(list(np.unique(labels)), ["left_hand", "right_hand"])
# should return epochs
epochs, _, _ = paradigm.get_data(dataset, subjects=[1], return_epochs=True)
self.assertIsInstance(epochs, BaseEpochs)
def test_LeftRightImagery_noevent(self):
# we cant pass event to this class
self.assertRaises(ValueError, LeftRightImagery, events=["a"])
def test_LeftRightImagery_badevents(self):
paradigm = LeftRightImagery()
# does not accept dataset with bad event
dataset = FakeDataset(paradigm="imagery")
self.assertRaises(AssertionError, paradigm.get_data, dataset)
def test_FilterBankMotorImagery_paradigm(self):
# can work with filter bank
paradigm = FilterBankMotorImagery()
dataset = FakeDataset(paradigm="imagery")
X, labels, metadata = paradigm.get_data(dataset, subjects=[1])
# X must be a 4D Array
self.assertEqual(len(X.shape), 4)
self.assertEqual(X.shape[-1], 6)
# should return epochs
epochs, _, _ = paradigm.get_data(dataset, subjects=[1], return_epochs=True)
self.assertIsInstance(epochs, BaseEpochs)
def test_FilterBankMotorImagery_moreclassesthanevent(self):
self.assertRaises(
AssertionError, FilterBankMotorImagery, n_classes=3, events=["hands", "feet"]
)
def test_FilterBankLeftRightImagery_paradigm(self):
# can work with filter bank
paradigm = FilterBankLeftRightImagery()
dataset = FakeDataset(event_list=["left_hand", "right_hand"], paradigm="imagery")
X, labels, metadata = paradigm.get_data(dataset, subjects=[1])
# X must be a 4D Array
self.assertEqual(len(X.shape), 4)
self.assertEqual(X.shape[-1], 6)
# should return epochs
epochs, _, _ = paradigm.get_data(dataset, subjects=[1], return_epochs=True)
self.assertIsInstance(epochs, BaseEpochs)
class SimpleP300(BaseP300): # Needed to assess BaseP300
def used_events(self, dataset):
return dataset.event_id
class Test_P300(unittest.TestCase):
def test_BaseP300_paradigm(self):
paradigm = SimpleP300()
dataset = FakeDataset(paradigm="p300", event_list=["Target", "NonTarget"])
X, labels, metadata = paradigm.get_data(dataset, subjects=[1])
# we should have all the same length
self.assertEqual(len(X), len(labels), len(metadata))
# X must be a 3D Array
self.assertEqual(len(X.shape), 3)
# labels must contain 2 values (Target/NonTarget)
self.assertEqual(len(np.unique(labels)), 2)
# metadata must have subjets, sessions, runs
self.assertTrue("subject" in metadata.columns)
self.assertTrue("session" in metadata.columns)
self.assertTrue("run" in metadata.columns)
# we should have only one subject in the metadata
self.assertEqual(np.unique(metadata.subject), 1)
# we should have two sessions in the metadata
self.assertEqual(len(np.unique(metadata.session)), 2)
# should return epochs
epochs, _, _ = paradigm.get_data(dataset, subjects=[1], return_epochs=True)
self.assertIsInstance(epochs, BaseEpochs)
def test_BaseP300_channel_order(self):
"""test if paradigm return correct channel order, see issue #227"""
datasetA = FakeDataset(
paradigm="p300",
channels=["C3", "Cz", "C4"],
event_list=["Target", "NonTarget"],
)
datasetB = FakeDataset(
paradigm="p300",
channels=["Cz", "C4", "C3"],
event_list=["Target", "NonTarget"],
)
paradigm = SimpleP300(channels=["C4", "C3", "Cz"])
ep1, _, _ = paradigm.get_data(datasetA, subjects=[1], return_epochs=True)
ep2, _, _ = paradigm.get_data(datasetB, subjects=[1], return_epochs=True)
self.assertEqual(ep1.info["ch_names"], ep2.info["ch_names"])
def test_BaseP300_tmintmax(self):
self.assertRaises(ValueError, SimpleP300, tmin=1, tmax=0)
def test_BaseP300_filters(self):
# can work with filter bank
paradigm = SimpleP300(filters=[[1, 12], [12, 24]])
dataset = FakeDataset(paradigm="p300", event_list=["Target", "NonTarget"])
X, labels, metadata = paradigm.get_data(dataset, subjects=[1])
# X must be a 4D Array
self.assertEqual(len(X.shape), 4)
self.assertEqual(X.shape[-1], 2)
# should return epochs
epochs, _, _ = paradigm.get_data(dataset, subjects=[1], return_epochs=True)
self.assertIsInstance(epochs, BaseEpochs)
def test_BaseP300_wrongevent(self):
# test process_raw return empty list if raw does not contain any
# selected event. cetain runs in dataset are event specific.
paradigm = SimpleP300(filters=[[1, 12], [12, 24]])
dataset = FakeDataset(paradigm="p300", event_list=["Target", "NonTarget"])
raw = dataset.get_data([1])[1]["session_0"]["run_0"]
# add something on the event channel
raw._data[-1] *= 10
self.assertIsNone(paradigm.process_raw(raw, dataset))
# zeros it out
raw._data[-1] *= 0
self.assertIsNone(paradigm.process_raw(raw, dataset))
def test_P300_specifyevent(self):
# we cant pass event to this class
self.assertRaises(ValueError, P300, events=["a"])
def test_P300_wrongevent(self):
# does not accept dataset with bad event
paradigm = P300()
dataset = FakeDataset(paradigm="p300")
self.assertRaises(AssertionError, paradigm.get_data, dataset)
def test_P300_paradigm(self):
# with a good dataset
paradigm = P300()
dataset = FakeDataset(event_list=["Target", "NonTarget"], paradigm="p300")
X, labels, metadata = paradigm.get_data(dataset, subjects=[1])
self.assertEqual(len(np.unique(labels)), 2)
self.assertEqual(list(np.unique(labels)), sorted(["Target", "NonTarget"]))
# should return epochs
epochs, _, _ = paradigm.get_data(dataset, subjects=[1], return_epochs=True)
self.assertIsInstance(epochs, BaseEpochs)
class Test_SSVEP(unittest.TestCase):
def test_BaseSSVEP_paradigm(self):
paradigm = BaseSSVEP(n_classes=None)
dataset = FakeDataset(paradigm="ssvep")
X, labels, metadata = paradigm.get_data(dataset, subjects=[1])
# Verify that they have the same length
self.assertEqual(len(X), len(labels), len(metadata))
# X must be a 3D array
self.assertEqual(len(X.shape), 3)
# labels must contain 3 values
self.assertEqual(len(np.unique(labels)), 3)
# metadata must have subjets, sessions, runs
self.assertTrue("subject" in metadata.columns)
self.assertTrue("session" in metadata.columns)
self.assertTrue("run" in metadata.columns)
# Only one subject in the metadata
self.assertEqual(np.unique(metadata.subject), 1)
# we should have two sessions in the metadata, n_classes = 2 as default
self.assertEqual(len(np.unique(metadata.session)), 2)
# should return epochs
epochs, _, _ = paradigm.get_data(dataset, subjects=[1], return_epochs=True)
self.assertIsInstance(epochs, BaseEpochs)
def test_BaseSSVEP_channel_order(self):
"""test if paradigm return correct channel order, see issue #227"""
datasetA = FakeDataset(paradigm="ssvep", channels=["C3", "Cz", "C4"])
datasetB = FakeDataset(paradigm="ssvep", channels=["Cz", "C4", "C3"])
paradigm = BaseSSVEP(channels=["C4", "C3", "Cz"])
ep1, _, _ = paradigm.get_data(datasetA, subjects=[1], return_epochs=True)
ep2, _, _ = paradigm.get_data(datasetB, subjects=[1], return_epochs=True)
self.assertEqual(ep1.info["ch_names"], ep2.info["ch_names"])
def test_baseSSVEP_tmintmax(self):
# Verify that tmin < tmax
self.assertRaises(ValueError, BaseSSVEP, tmin=1, tmax=0)
def test_BaseSSVEP_filters(self):
# Accept filters
paradigm = BaseSSVEP(filters=[(10.5, 11.5), (12.5, 13.5)])
dataset = FakeDataset(paradigm="ssvep")
X, labels, metadata = paradigm.get_data(dataset, subjects=[1])
# X must be a 4D array
self.assertEqual(len(X.shape), 4)
# Last dim should be 2 as the number of filters
self.assertEqual(X.shape[-1], 2)
# should return epochs
epochs, _, _ = paradigm.get_data(dataset, subjects=[1], return_epochs=True)
self.assertIsInstance(epochs, BaseEpochs)
def test_BaseSSVEP_nclasses_default(self):
# Default is with 3 classes
paradigm = BaseSSVEP()
dataset = FakeDataset(paradigm="ssvep")
X, labels, metadata = paradigm.get_data(dataset, subjects=[1])
# labels must contain all 3 classes of dataset,
# as n_classes is "None" by default (taking all classes)
self.assertEqual(len( | np.unique(labels) | numpy.unique |
import time
import numpy as np
import multiprocessing as mp
import ctypes
from rlpyt.samplers.base import BaseSampler
from rlpyt.samplers.utils import build_samples_buffer, build_step_buffer
from rlpyt.samplers.parallel_worker import sampling_process
from rlpyt.samplers.gpu.collectors import EvalCollector
from rlpyt.utils.logging import logger
from rlpyt.agents.base import AgentInputs
from rlpyt.utils.collections import AttrDict
EVAL_TRAJ_CHECK = 0.2 # Seconds.
class AsyncGpuSampler(BaseSampler):
###########################################################################
# Master runner methods.
###########################################################################
def master_runner_initialize(self, agent, bootstrap_value=False,
traj_info_kwargs=None):
# Construct an example of each kind of data that needs to be stored.
env = self.EnvCls(**self.env_kwargs)
agent.initialize(env.spaces, share_memory=True) # Actual agent initialization, keep.
samples_pyt, samples_np, examples = build_samples_buffer(agent, env,
self.batch_spec, bootstrap_value, agent_shared=True, env_shared=True,
subprocess=False) # Would like subprocess=True, but might hang?
_, samples_np2, _ = build_samples_buffer(agent, env, self.batch_spec,
bootstrap_value, agent_shared=True, env_shared=True, subprocess=False)
env.close()
del env
if traj_info_kwargs:
for k, v in traj_info_kwargs.items():
setattr(self.TrajInfoCls, "_" + k, v)
self.double_buffer = double_buffer = (samples_np, samples_np2)
self.examples = examples
return double_buffer, examples
###########################################################################
# Sampler runner methods (forked).
###########################################################################
def sample_runner_initialize(self, affinity):
n_server = len(affinity)
n_worker = sum(len(aff["workers_cpus"]) for aff in affinity)
n_envs_list = [self.batch_spec.B // n_worker] * n_worker
if not self.batch_spec.B % n_worker == 0:
logger.log("WARNING: unequal number of envs per process, from "
f"batch_B {self.batch_spec.B} and n_parallel {n_worker} "
"(possible suboptimal speed).")
for b in range(self.batch_spec.B % n_worker):
n_envs_list[b] += 1
if self.eval_n_envs > 0:
eval_n_envs_per = max(1, self.eval_n_envs // len(n_envs_list))
eval_n_envs = eval_n_envs_per * n_worker
logger.log(f"Total parallel evaluation envs: {eval_n_envs}.")
self.eval_max_T = 1 + int(self.eval_max_steps // eval_n_envs)
self.eval_n_envs_per = eval_n_envs_per
else:
self.eval_n_envs_per = 0
self.eval_max_T = 0
ctrl = AttrDict(
quit=mp.RawValue(ctypes.c_bool, False),
barrier_in=mp.Barrier(n_server + n_worker + 1),
barrier_out=mp.Barrier(n_server + n_worker + 1),
do_eval=mp.RawValue(ctypes.c_bool, False),
itr=mp.RawValue(ctypes.c_long, 0),
)
traj_infos_queue = mp.Queue()
common_kwargs = dict(
ctrl=ctrl,
traj_infos_queue=traj_infos_queue,
)
servers_kwargs = assemble_servers_kwargs(affinity, n_envs_list,
self.seed, self.double_buffer)
servers = [mp.Process(target=self.action_server_process,
kwargs=s_kwargs.update(**common_kwargs))
for s_kwargs in servers_kwargs]
for s in servers:
s.start()
self.servers = servers
self.ctrl = ctrl
self.traj_infos_queue = traj_infos_queue
def obtain_samples(self, itr):
self.ctrl.barrier_in.wait()
# Sampling in sub-processes here.
self.ctrl.barrier_out.wait()
traj_infos = list()
while self.traj_infos_queue.qsize():
traj_infos.append(self.traj_infos_queue.get())
return traj_infos
def evaluate_agent(self, itr):
self.ctrl.do_eval = True
self.sync.stop_eval.value = False
self.ctrl.barrier_in.wait()
traj_infos = list()
if self.eval_max_trajectories is not None:
while True:
time.sleep(EVAL_TRAJ_CHECK)
while self.traj_infos_queue.qsize():
traj_infos.append(self.traj_infos_queue.get())
if len(traj_infos) >= self.eval_max_trajectories:
self.sync.stop_eval.value = True
logger.log("Evaluation reached max num trajectories "
f"({self.eval_max_trajectories}).")
break # Stop possibly before workers reach max_T.
if self.ctrl.barrier_out.parties - self.ctrl.barrier_out.n_waiting == 1:
logger.log("Evaluation reached max num time steps "
f"({self.eval_max_T}).")
break # Workers reached max_T.
self.ctrl.barrier_out.wait()
while self.traj_infos_queue.qsize():
traj_infos.append(self.traj_infos_queue.get())
self.ctrl.do_eval.value = False
return traj_infos
def shutdown(self):
self.ctrl.quit.value = True
self.ctrl.barrier_in.wait()
for s in self.servers:
s.join()
###########################################################################
# Methods in forked action server process.
###########################################################################
def action_server_process(self, double_buffer_slice, ctrl, traj_infos_queue,
affinity, seed, n_envs_list):
"""Runs in forked process, inherits from original process, so can easily
pass args to env worker processes, forked from here."""
self.ctrl = ctrl
self.launch_workers(double_buffer_slice, traj_infos_queue, affinity,
seed, n_envs_list)
self.agent.initialize_cuda(cuda_idx=affinity["cuda_idx"], ddp=False)
while True:
self.ctrl.barrier_in.wait()
if self.ctrl.quit.value:
break
self.agent.recv_shared_memory()
if self.ctrl.do_eval.value:
self.agent.eval_mode(self.ctrl.itr.value)
self.serve_actions_evaluation()
else:
self.agent.sample_mode(self.ctrl.itr.value)
self.serve_actions()
self.ctrl.barrier_out.wait()
self.shutdown_workers()
def serve_actions(self):
step_blockers, act_waiters = self.sync.step_blockers, self.sync.act_waiters
step_np, step_pyt = self.step_buffer_np, self.step_buffer_pyt
agent_inputs = AgentInputs(step_pyt.observation, step_pyt.action,
step_pyt.reward) # Fixed buffer objects.
for t in range(self.batch_spec.T):
for b in step_blockers:
b.acquire() # Workers written obs and rew, first prev_act.
if self.mid_batch_reset and np.any(step_np.done):
for b_reset in np.where(step_np.done)[0]:
step_np.action[b_reset] = 0 # Null prev_action into agent.
step_np.reward[b_reset] = 0 # Null prev_reward into agent.
self.agent.reset_one(idx=b_reset)
action, agent_info = self.agent.step(*agent_inputs)
step_np.action[:] = action # Worker applies to env.
step_np.agent_info[:] = agent_info # Worker sends to traj_info.
for w in act_waiters:
w.release() # Signal to worker.
for b in step_blockers:
b.acquire()
if "bootstrap_value" in self.samples_np.agent:
self.samples_np.agent.bootstrap_value[:] = self.agent.value(
*agent_inputs)
if | np.any(step_np.done) | numpy.any |
import itertools
import warnings
from inspect import signature
from timeit import default_timer
from sklearn.preprocessing import normalize
import dask
import numpy as np
try:
import shap
except:
msg = "SHAP not found, therefore using SHAP-values for feature importance not available."
warnings.warn(msg)
shap = None
from dask import delayed
from networkx import NetworkXUnfeasible, find_cycle, topological_sort
from sklearn.ensemble import (
ExtraTreesClassifier,
ExtraTreesRegressor,
RandomForestClassifier,
RandomForestRegressor,
)
from sklearn.impute import SimpleImputer
from sklearn.tree import DecisionTreeClassifier, DecisionTreeRegressor
from ..algo import (
evaluation,
imputation,
inference,
inference_v3,
new_inference,
new_prediction,
selection,
vector_prediction,
)
from ..algo.induction import base_induction_algorithm, expand_induction_algorithm
from ..composition import CompositeModel, NewCompositeModel, o, x
from ..graph import build_diagram, compose_all, get_targ, model_to_graph
from ..utils import (
DESC_ENCODING,
MISS_ENCODING,
TARG_ENCODING,
DecoratedDecisionTreeClassifier,
DecoratedDecisionTreeRegressor,
DecoratedRandomForestClassifier,
DecoratedRandomForestRegressor,
code_to_query,
get_i_o,
query_to_code,
)
from ..visuals import save_diagram, show_diagram
try:
from xgboost import XGBClassifier as XGBC
from xgboost import XGBRegressor as XGBR
except:
XGBC, XGBR = None, None
try:
from lightgbm import LGBMClassifier as LGBMC
from lightgbm import LGBMRegressor as LGBMR
except:
LGBMC, LGBMR = None, None
try:
from catboost import CatBoostClassifier as CBC
from catboost import CatBoostRegressor as CBR
except:
CBC, CBR = None, None
try:
from wekalearn import RandomForestClassifier as WLC
from wekalearn import RandomForestRegressor as WLR
except:
WLC, WLR = None, None
class Mercs(object):
delimiter = "_"
selection_algorithms = dict(
default=selection.base_selection_algorithm,
base=selection.base_selection_algorithm,
random=selection.random_selection_algorithm,
)
induction_algorithms = dict(
base=base_induction_algorithm,
default=base_induction_algorithm,
expand=expand_induction_algorithm,
)
classifier_algorithms = dict(
DT=DecisionTreeClassifier,
DDT=DecoratedDecisionTreeClassifier,
RF=RandomForestClassifier,
DRF=DecoratedRandomForestClassifier,
XGB=XGBC,
xgb=XGBC,
weka=WLC,
LGBM=LGBMC,
lgbm=LGBMC,
CB=CBC,
extra=ExtraTreesClassifier,
)
regressor_algorithms = dict(
DT=DecisionTreeRegressor,
DDT=DecoratedDecisionTreeRegressor,
RF=RandomForestRegressor,
DRF=DecoratedDecisionTreeRegressor,
XGB=XGBR,
xgb=XGBR,
weka=WLR,
LGBM=LGBMR,
lgbm=LGBMR,
CB=CBR,
extra=ExtraTreesRegressor,
)
prediction_algorithms = dict(
mi=vector_prediction.mi,
mrai=vector_prediction.mrai,
it=vector_prediction.it,
rw=vector_prediction.rw,
)
inference_algorithms = dict(
base=inference.base_inference_algorithm,
dask=inference_v3.inference_algorithm,
own=inference_v3.inference_algorithm,
)
imputer_algorithms = dict(
nan=imputation.nan_imputation,
NAN=imputation.nan_imputation,
NaN=imputation.nan_imputation,
null=imputation.nan_imputation,
NULL=imputation.nan_imputation,
skl=imputation.skl_imputation,
base=imputation.skl_imputation,
default=imputation.skl_imputation,
)
evaluation_algorithms = dict(
base=evaluation.base_evaluation,
default=evaluation.base_evaluation,
dummy=evaluation.dummy_evaluation,
)
# Used in parse kwargs to identify parameters. If this identification goes wrong, you are sending settings
# somewhere you do not want them to be. So, this is a tricky part, and moreover hardcoded. In other words:
# this is risky terrain, and should probably be done differently in the future.
configuration_prefixes = dict(
imputation={"imputation", "imp"},
induction={"induction", "ind"},
selection={"selection", "sel"},
prediction={"prediction", "pred", "prd"},
inference={"inference", "infr", "inf"},
classification={"classification", "classifier", "clf"},
regression={"regression", "regressor", "rgr"},
metadata={"metadata", "meta", "mtd"},
evaluation={"evaluation", "evl"},
)
def __init__(
self,
selection_algorithm="base",
induction_algorithm="base",
classifier_algorithm="DT",
regressor_algorithm="DT",
prediction_algorithm="mi",
inference_algorithm="own",
imputer_algorithm="default",
evaluation_algorithm="default",
random_state=42,
**kwargs
):
self.params = dict(
selection_algorithm=selection_algorithm,
induction_algorithm=induction_algorithm,
classifier_algorithm=classifier_algorithm,
regressor_algorithm=regressor_algorithm,
prediction_algorithm=prediction_algorithm,
inference_algorithm=inference_algorithm,
imputer_algorithm=imputer_algorithm,
evaluation_algorithm=evaluation_algorithm,
random_state=random_state,
)
self.params = {**self.params, **kwargs}
self.random_state = random_state
self.selection_algorithm = self.selection_algorithms[selection_algorithm]
# N.b.: First try to look up the key. If the key is not found, we assume the algorithm itself was passed.
self.classifier_algorithm = self.classifier_algorithms.get(
classifier_algorithm, classifier_algorithm
)
self.regressor_algorithm = self.regressor_algorithms.get(
regressor_algorithm, regressor_algorithm
)
self.prediction_algorithm = self.prediction_algorithms[prediction_algorithm]
self.inference_algorithm = self.inference_algorithms[inference_algorithm]
self.induction_algorithm = self.induction_algorithms[
induction_algorithm
] # For now, we only have one.
self.imputer_algorithm = self.imputer_algorithms[imputer_algorithm]
self.evaluation_algorithm = self.evaluation_algorithms[evaluation_algorithm]
# Data-structures
self.m_codes = np.array([])
self.m_list = []
self.c_list = []
self.g_list = []
self.i_list = []
self.m_fimps = np.array([])
self.m_score = np.array([])
self.FI = np.array([])
self.targ_ids = np.array([])
# Query-related things
self.q_code = None
self.q_desc_ids = None
self.q_targ_ids = None
self.q_diagram = None
self.q_compose = None
self.q_methods = []
# Configurations
self.imp_cfg = self._default_config(self.imputer_algorithm)
self.ind_cfg = self._default_config(self.induction_algorithm)
self.sel_cfg = self._default_config(self.selection_algorithm)
self.clf_cfg = self._default_config(self.classifier_algorithm)
self.rgr_cfg = self._default_config(self.regressor_algorithm)
self.prd_cfg = self._default_config(self.prediction_algorithm)
self.inf_cfg = self._default_config(self.inference_algorithm)
self.evl_cfg = self._default_config(self.evaluation_algorithm)
self.configuration = dict(
imputation=self.imp_cfg,
induction=self.ind_cfg,
selection=self.sel_cfg,
classification=self.clf_cfg,
regression=self.rgr_cfg,
prediction=self.prd_cfg,
inference=self.inf_cfg,
) # Collect all configs in one
self._update_config(random_state=random_state, **kwargs)
self.metadata = dict()
self.model_data = dict()
self._extra_checks_on_config()
return
def fit(self, X, y=None, m_codes=None, **kwargs):
assert isinstance(X, np.ndarray)
if y is not None:
assert isinstance(y, np.ndarray)
X = np.c_[X, y]
tic = default_timer()
self.metadata = self._default_metadata(X)
self._update_metadata(**kwargs)
self.i_list = self.imputer_algorithm(X, self.metadata.get("nominal_attributes"))
# N.b.: `random state` parameter is in `self.sel_cfg`
if m_codes is None:
self.m_codes = self.selection_algorithm(self.metadata, **self.sel_cfg)
else:
self.m_codes = m_codes
self.m_list = self.induction_algorithm(
X,
self.m_codes,
self.metadata,
self.classifier_algorithm,
self.regressor_algorithm,
self.clf_cfg,
self.rgr_cfg,
**self.ind_cfg
)
self._filter_m_list_m_codes()
self._consistent_datastructures()
if self.imputer_algorithm == self.imputer_algorithms.get("nan"):
# If you do no have imputers, you cannot use them as a baseline evaluation
self.evl_cfg["consider_imputations"] = False
self.m_score = self.evaluation_algorithm(
X, self.m_codes, self.m_list, self.i_list, **self.evl_cfg
)
toc = default_timer()
self.model_data["ind_time"] = toc - tic
self.metadata["n_component_models"] = len(self.m_codes)
return
def predict(
self,
X,
q_code=None,
inference_algorithm=None,
prediction_algorithm=None,
**kwargs
):
# Update configuration if necessary
if q_code is None:
q_code = self._default_q_code()
if inference_algorithm is not None:
self._reconfig_inference(inference_algorithm=inference_algorithm)
if prediction_algorithm is not None:
self._reconfig_prediction(
prediction_algorithm=prediction_algorithm, **kwargs
)
# Adjust data
self.q_code = q_code
self.q_desc_ids, self.q_targ_ids, _ = code_to_query(
self.q_code, return_list=True
)
# Make query-diagram
tic_prediction = default_timer()
self.m_sel = self.prediction_algorithm(
self.m_codes, self.m_fimps, self.m_score, q_code=self.q_code, **self.prd_cfg
)
toc_prediction = default_timer()
tic_diagram = default_timer()
self.q_diagram = self._build_q_diagram(self.m_list, self.m_sel)
toc_diagram = default_timer()
tic_infalgo = default_timer()
if isinstance(self.q_diagram, tuple):
self.q_diagrams = self.q_diagram
# for d in self.q_diagrams:
# print(d.nodes)
# self.c_list.append(self._build_q_model(X, d))
self.c_list = [self._build_q_model(X, d) for d in self.q_diagrams]
self.c_sel = list(range(len(self.c_list)))
self.c_diagram = self._build_q_diagram(
self.c_list, self.c_sel, composition=True
)
self.q_model = self._build_q_model(X, self.c_diagram)
else:
self.q_model = self._build_q_model(X, self.q_diagram)
toc_infalgo = default_timer()
tic_dask = default_timer()
X = X[:, self.q_model.desc_ids]
result = self.q_model.predict(X)
toc_dask = default_timer()
self.model_data["prd_time"] = toc_prediction - tic_prediction
self.model_data["dia_time"] = toc_diagram - tic_diagram
self.model_data["infalgo_time"] = toc_infalgo - tic_infalgo
self.model_data["dsk_time"] = toc_dask - tic_dask
self.model_data["inf_time"] = toc_dask - tic_prediction
return result
def get_params(self, deep=False):
return self.params
# Diagrams
def _build_q_diagram(self, m_list, m_sel, composition=False):
if isinstance(m_sel, tuple):
diagrams = [
build_diagram(
m_list,
m_sel_instance,
self.q_code,
prune=True,
composition=composition,
)
for m_sel_instance in m_sel
]
return tuple(diagrams)
else:
return build_diagram(
m_list, m_sel, self.q_code, prune=True, composition=composition
)
def show_q_diagram(self, kind="svg", fi=False, ortho=False, index=None, **kwargs):
if isinstance(self.q_diagram, tuple) and index is None:
return show_diagram(self.c_diagram, kind=kind, fi=fi, ortho=ortho, **kwargs)
elif isinstance(self.q_diagram, tuple):
return show_diagram(
self.q_diagram[index], kind=kind, fi=fi, ortho=ortho, **kwargs
)
else:
return show_diagram(self.q_diagram, kind=kind, fi=fi, ortho=ortho, **kwargs)
def save_diagram(self, fname=None, kind="svg", fi=False, ortho=False):
return save_diagram(self.q_diagram, fname, kind=kind, fi=fi, ortho=ortho)
# Inference
def _build_q_model(self, X, diagram):
try:
self.inference_algorithm(
diagram,
self.m_list,
self.i_list,
self.c_list,
X,
self.metadata.get("nominal_attributes"),
)
except NetworkXUnfeasible:
cycle = find_cycle(self.q_diagram, orientation="original")
msg = """
Topological sort failed, investigate diagram to debug.
I will never be able to squeeze a prediction out of a diagram with a loop.
Cycle was: {}
""".format(
cycle
)
raise RecursionError(msg)
n_component_models = self.metadata["n_component_models"]
q_model = NewCompositeModel(
diagram,
nominal_attributes=self.metadata["nominal_attributes"],
n_component_models=n_component_models,
)
return q_model
def _merge_q_models(self, q_models):
q_diagram = build_diagram(self.c_list, self.c_sel, self.q_code, prune=True)
return q_diagram
def merge_models(self, q_models):
types = self._get_types(self.metadata)
walks = [
model_to_graph(m, types, idx=idx, composition=True)
for idx, m in enumerate(q_models)
]
q_diagram = compose_all(walks)
filtered_nodes = self.filter_nodes(q_diagram)
try:
self.inference_algorithm(q_diagram, sorted_nodes=filtered_nodes)
except NetworkXUnfeasible:
cycle = find_cycle(q_diagram, orientation="original")
msg = """
Topological sort failed, investigate diagram to debug.
I will never be able to squeeze a prediction out of a diagram with a loop.
Cycle was: {}
""".format(
cycle
)
raise RecursionError(msg)
q_model = CompositeModel(q_diagram)
return q_diagram, q_model
def _get_q_model(self, q_diagram, X):
self._add_imputer_function(q_diagram)
try:
self.inference_algorithm(q_diagram, X=X)
except NetworkXUnfeasible:
cycle = find_cycle(q_diagram, orientation="original")
msg = """
Topological sort failed, investigate diagram to debug.
I will never be able to squeeze a prediction out of a diagram with a loop.
Cycle was: {}
""".format(
cycle
)
raise RecursionError(msg)
q_model = CompositeModel(q_diagram)
return q_model
# Filter
def _filter_m_list_m_codes(self):
"""Filtering out the failed models.
This happens when TODO: EXPLAIN
"""
fail_m_idxs = [i for i, m in enumerate(self.m_list) if m is None]
self.m_codes = np.delete(self.m_codes, fail_m_idxs, axis=0)
self.m_list = [m for m in self.m_list if m is not None]
return
# Graphs
def _consistent_datastructures(self, binary_scores=False):
self._update_m_codes()
self._update_m_fimps()
return
def _expand_m_list(self):
self.m_list = list(itertools.chain.from_iterable(self.m_list))
return
def _add_model(self, model, binary_scores=False):
self.m_list.append(model)
self._consistent_datastructures(binary_scores=binary_scores)
return
def _update_m_codes(self):
self.m_codes = np.array(
[
query_to_code(
list(model.desc_ids),
list(model.targ_ids),
attributes=self.metadata["attributes"],
)
for model in self.m_list
]
)
return
def _update_m_fimps(self):
init = np.zeros(self.m_codes.shape)
for m_idx, mod in enumerate(self.m_list):
init[m_idx, list(mod.desc_ids)] = mod.feature_importances_
self.m_fimps = init
return
def _update_m_score(self, binary_scores=False):
if binary_scores:
self.m_score = (self.m_codes == TARG_ENCODING).astype(float)
return
# Imputer
def _add_imputer_function(self, g):
for n in g.nodes:
if g.nodes[n]["kind"] == "imputation":
idx = g.nodes[n]["idx"]
f_1 = self._dummy_array # Artificial input
f_2 = self.i_list[idx].transform # Actual imputation
f_3 = np.ravel # Return a vector, not array
g.nodes[n]["function"] = o(f_3, o(f_2, f_1))
return
# Add ids
@staticmethod
def _add_ids(g, desc_ids, targ_ids):
g.graph["desc_ids"] = set(desc_ids)
g.graph["targ_ids"] = set(targ_ids)
return g
# Metadata
def _default_metadata(self, X):
if X.ndim != 2:
X = X.reshape(-1, 1)
n_rows, n_cols = X.shape
types = [X[0, 0].dtype for _ in range(n_cols)]
nominal_attributes = set(
[att for att, typ in enumerate(types) if self._is_nominal(typ)]
)
numeric_attributes = set(
[att for att, typ in enumerate(types) if self._is_numeric(typ)]
)
metadata = dict(
attributes=set(range(n_cols)),
n_attributes=n_cols,
types=types,
nominal_attributes=nominal_attributes,
numeric_attributes=numeric_attributes,
)
return metadata
def _update_metadata(self, **kwargs):
self._update_dictionary(self.metadata, kind="metadata", **kwargs)
# Assure every attribute is `typed`: If not every attribute is here, set to numeric type (default)
numeric = self.metadata["numeric_attributes"]
nominal = self.metadata["nominal_attributes"]
att_ids = self.metadata["attributes"]
# All attributes should be accounted for and none should be double.
if (len(nominal) + len(numeric) - len(att_ids)) != 0:
numeric = att_ids - nominal
self._update_dictionary(
self.metadata, kind="metadata", numeric_attributes=numeric
)
return
# Configuration
def _reconfig_prediction(self, prediction_algorithm="mi", **kwargs):
self.prediction_algorithm = self.prediction_algorithms[prediction_algorithm]
self.prd_cfg = self._default_config(self.prediction_algorithm)
self.configuration["prediction"] = self.prd_cfg
self._update_config(**kwargs)
return
def _reconfig_inference(self, inference_algorithm="own", **kwargs):
self.inference_algorithm = self.inference_algorithms[inference_algorithm]
self.inf_cfg = self._default_config(self.inference_algorithm)
self.configuration["inference"] = self.inf_cfg
self._update_config(**kwargs)
return
@staticmethod
def _default_config(method):
config = {}
sgn = signature(method)
for key, parameter in sgn.parameters.items():
if parameter.default is not parameter.empty:
config[key] = parameter.default
return config
def _update_config(self, **kwargs):
for kind in self.configuration:
self._update_dictionary(self.configuration[kind], kind=kind, **kwargs)
return
def _extra_checks_on_config(self):
self._check_xgb_single_target()
return
def _check_xgb_single_target(self):
nb_targets = self.configuration["selection"]["nb_targets"]
if nb_targets == 1:
return None
else:
if (
self.classifier_algorithm is self.classifier_algorithms["XGB"]
or self.regressor_algorithm is self.regressor_algorithms["XGB"]
):
xgb = True
else:
xgb = False
if xgb:
msg = """
XGBoost cannot deal with multi-target outputs.
Hence, the `nb_targets` parameter is automatically adapted to 1,
so only single-target trees will be learned.
Please take this into account.
"""
warnings.warn(msg)
self.configuration["selection"]["nb_targets"] = 1
return
def _parse_kwargs(self, kind="selection", **kwargs):
prefixes = [e + self.delimiter for e in self.configuration_prefixes[kind]]
parameter_map = {
x.split(prefix)[1]: x
for x in kwargs
for prefix in prefixes
if x.startswith(prefix)
}
return parameter_map
def _update_dictionary(self, dictionary, kind=None, **kwargs):
# Immediate matches
overlap = set(dictionary).intersection(set(kwargs))
for k in overlap:
dictionary[k] = kwargs[k]
if kind is not None:
# Parsed matches
parameter_map = self._parse_kwargs(kind=kind, **kwargs)
overlap = set(dictionary).intersection(set(parameter_map))
for k in overlap:
dictionary[k] = kwargs[parameter_map[k]]
return
# Helpers
def _filter_X(self, X):
# Filter relevant input attributes
if X.shape[1] != len(self.q_compose.desc_ids):
indices = self._overlapping_indices(
self.q_desc_ids, self.q_compose.desc_ids
)
return X[:, indices]
@staticmethod
def _dummy_array(X):
"""
Return an array of np.nan, with the same number of rows as the input array.
Parameters
----------
X: np.ndarray(), n_rows, n_cols = X.shape,
We use the shape of X to deduce shape of our output.
Returns
-------
a: np.ndarray(), shape= (n_rows, 1)
n_rows is the same as the number of rows as X.
"""
n_rows, _ = X.shape
a = np.empty((n_rows, 1))
a.fill(np.nan)
return a
def _default_q_code(self):
q_code = np.zeros(self.metadata["n_attributes"])
q_code[-1] = TARG_ENCODING
return q_code
@staticmethod
def _is_nominal(t):
condition_01 = t == np.dtype(int)
return condition_01
@staticmethod
def _is_numeric(t):
condition_01 = t == np.dtype(float)
return condition_01
@staticmethod
def _get_types(metadata):
nominal = {i: "nominal" for i in metadata["nominal_attributes"]}
numeric = {i: "numeric" for i in metadata["numeric_attributes"]}
return {**nominal, **numeric}
@staticmethod
def _overlapping_indices(a, b):
"""
Given an array a and b, return the indices (in a) of elements that occur in both a and b.
Parameters
----------
a
b
Returns
-------
Examples
--------
a = [4,5,6]
b = [4,6,7]
overlapping_indices(a, b) = [0,2]
"""
return np.nonzero(np.in1d(a, b))[0]
@staticmethod
def filter_nodes(g):
# This is not as safe as it should be
sorted_nodes = list(topological_sort(g))
filtered_nodes = []
for n in reversed(sorted_nodes):
if g.nodes[n]["kind"] == "model":
break
filtered_nodes.append(n)
filtered_nodes = list(reversed(filtered_nodes))
return filtered_nodes
# SYNTH
def autocomplete(self, X, **kwargs):
return
# Legacy (delete when I am sure they can go)
def predict_old(
self, X, q_code=None, prediction_algorithm=None, beta=False, **kwargs
):
# Update configuration if necessary
if q_code is None:
q_code = self._default_q_code()
if prediction_algorithm is not None:
reuse = False
self._reconfig_prediction(
prediction_algorithm=prediction_algorithm, **kwargs
)
# Adjust data
tic_prediction = default_timer()
self.q_code = q_code
self.q_desc_ids, self.q_targ_ids, _ = code_to_query(
self.q_code, return_list=True
)
# Make query-diagram
self.q_diagram = self.prediction_algorithm(
self.g_list, q_code, self.fi, self.t_codes, **self.prd_cfg
)
toc_prediction = default_timer()
tic_dask = default_timer()
toc_dask = default_timer()
tic_compute = default_timer()
res = self.q_model.predict.compute()
toc_compute = default_timer()
# Diagnostics
self.model_data["prd_time"] = toc_prediction - tic_prediction
self.model_data["dsk_time"] = toc_dask - tic_dask
self.model_data["cmp_time"] = toc_compute - tic_compute
self.model_data["inf_time"] = toc_compute - tic_prediction
self.model_data["ratios"] = (
self.model_data["prd_time"] / self.model_data["inf_time"],
self.model_data["dsk_time"] / self.model_data["inf_time"],
self.model_data["cmp_time"] / self.model_data["inf_time"],
)
return res
def _update_g_list(self):
types = self._get_types(self.metadata)
self.g_list = [
model_to_graph(m, types=types, idx=idx) for idx, m in enumerate(self.m_list)
]
return
def _update_t_codes(self):
self.t_codes = (self.m_codes == TARG_ENCODING).astype(int)
return
# AVATAR-TOOLS
def avatar(
self,
explainer_data,
background_data=None,
check_additivity=True,
keep_abs_shaps=False,
**explainer_kwargs
):
assert shap is not None, "SHAP not found, so cannot do anything here."
self._init_avatar()
for m_idx in range(len(self.m_list)):
# Extract tree and m_code
tree = self.m_list[m_idx].model
m_code = self.m_codes[m_idx]
# Filter data
attribute_filter = m_code == DESC_ENCODING
X = explainer_data[:, attribute_filter]
if background_data is not None:
B = background_data[:, attribute_filter]
else:
B = background_data
# Shap Calculation
explainer = shap.TreeExplainer(tree, data=B, **explainer_kwargs)
raw_shaps = explainer.shap_values(X, check_additivity=check_additivity)
# Process Shap values
abs_shaps = self._raw_to_abs_shaps(raw_shaps)
nrm_shaps = self._abs_to_nrm_shaps(abs_shaps)
if keep_abs_shaps:
self.abs_shaps.append(abs_shaps)
self.nrm_shaps.append(nrm_shaps)
self._format_abs_shaps()
self._format_nrm_shaps()
return
@staticmethod
def _raw_to_abs_shaps(raw_shaps):
# Process Shap values
tsr_shaps = np.array(raw_shaps) # tensor
abs_shaps = np.abs(tsr_shaps) # absolute
if len(abs_shaps.shape) == 3:
# In case of nominal target, sum shap values across target classes
abs_shaps = | np.sum(abs_shaps, axis=0) | numpy.sum |
import os
import tempfile
import shutil
import numpy as np
import unittest
import unittest.mock as mock
from gulpio.utils import (check_ffmpeg_exists,
burst_video_into_frames,
resize_by_short_edge,
resize_images,
get_single_video_path,
temp_dir_for_bursting,
DuplicateIdException,
remove_entries_with_duplicate_ids,
_remove_duplicates_in_metadict,
)
from gulpio.fileio import GulpIngestor
from fileio_tests import DummyVideosAdapter
class FSBase(unittest.TestCase):
def setUp(self):
self.temp_dir = tempfile.mkdtemp(prefix='utils-test-')
def tearDown(self):
shutil.rmtree(self.temp_dir)
class TestCheckFFMPEGExists(unittest.TestCase):
@mock.patch('os.system', mock.Mock(return_value=0))
def test_exists(self):
self.assertEqual(True, check_ffmpeg_exists())
@mock.patch('os.system', mock.Mock(return_value=1))
def test_does_not_exists(self):
self.assertEqual(False, check_ffmpeg_exists())
class TestBurstVideoIntoFrames(unittest.TestCase):
def test_mp4(self):
video_path = os.path.join(os.path.dirname(__file__), 'test.mp4')
with temp_dir_for_bursting() as temp_burst_dir:
imgs = burst_video_into_frames(video_path, temp_burst_dir)
# different ffmpeg versions, yield slightly different numbers
self.assertIn(len(imgs), [140, 141])
def test_mp4_with_lower_frame_rate(self):
video_path = os.path.join(os.path.dirname(__file__), 'test.mp4')
with temp_dir_for_bursting() as temp_burst_dir:
imgs = burst_video_into_frames(video_path, temp_burst_dir,
frame_rate=8)
self.assertEqual(39, len(imgs))
def test_webm(self):
video_path = os.path.join(os.path.dirname(__file__), 'test.webm')
with temp_dir_for_bursting() as temp_burst_dir:
imgs = burst_video_into_frames(video_path, temp_burst_dir)
# different ffmpeg versions, yield slightly different numbers
self.assertIn(len(imgs), [140, 141])
def test_webm_with_lower_frame_rate(self):
video_path = os.path.join(os.path.dirname(__file__), 'test.webm')
with temp_dir_for_bursting() as temp_burst_dir:
imgs = burst_video_into_frames(video_path, temp_burst_dir,
frame_rate=8)
self.assertEqual(39, len(imgs))
class TestResizeImages(unittest.TestCase):
@mock.patch('cv2.imread')
@mock.patch('gulpio.utils.resize_by_short_edge')
def test(self, mock_resize, mock_imread):
mock_imread.side_effect = ['READ_IMAGE1',
'READ_IMAGE2',
'READ_IMAGE3']
mock_resize.side_effect = ['RESIZED_IMAGE1',
'RESIZED_IMAGE2',
'RESIZED_IMAGE3']
input_ = ['ANY_IMAGE1',
'ANY_IMAGE2',
'ANY_IMAGE3']
received = list(resize_images(input_, img_size=1))
self.assertEqual(['RESIZED_IMAGE1',
'RESIZED_IMAGE2',
'RESIZED_IMAGE3'],
received)
class TestResizeByShortEdge(unittest.TestCase):
def test_resize_first_edge_shorter(self):
input_image = np.zeros((6, 10))
size = 3
correct_result = np.zeros((3, 5))
result = resize_by_short_edge(input_image, size)
np.testing.assert_array_equal(correct_result, result)
def test_resize_second_edge_shorter(self):
input_image = np.zeros((10, 6))
size = 3
correct_result = np.zeros((5, 3))
result = resize_by_short_edge(input_image, size)
np.testing.assert_array_equal(correct_result, result)
class TestGetSingleVideoPath(FSBase):
def test_video_exists(self):
test_video_path = os.path.join(self.temp_dir, 'test.mp4')
open(test_video_path, 'w').close()
received = get_single_video_path(self.temp_dir)
self.assertEqual(test_video_path, received)
def test_video_doesnt_exists(self):
self.assertRaises(AssertionError, get_single_video_path, 'ANY_PATH')
class TestRemoveEntriesWithDuplicateIds(FSBase):
def test_no_duplicates(self):
adapter = DummyVideosAdapter(3)
output_directory = os.path.join(self.temp_dir, "ANY_OUTPUT_DIR")
ingestor = GulpIngestor(adapter, output_directory, 2, 1)
ingestor()
meta_dict = [{'meta': {'name': 'new_video'},
'frames': [np.ones((4, 1, 3), dtype='uint8')],
'id': 3
}]
new_meta = remove_entries_with_duplicate_ids(
output_directory, meta_dict)
self.assertEqual(meta_dict, new_meta)
def test_one_out_of_one_duplicate(self):
adapter = DummyVideosAdapter(3)
output_directory = os.path.join(self.temp_dir, "ANY_OUTPUT_DIR")
ingestor = GulpIngestor(adapter, output_directory, 2, 1)
ingestor()
meta_dict = [{'meta': {'name': 'new_video'},
'frames': [np.ones((4, 1, 3),
dtype='uint8')],
'id': 1
}]
with self.assertRaises(DuplicateIdException):
remove_entries_with_duplicate_ids(output_directory, meta_dict)
def test_one_out_of_two_duplicate(self):
adapter = DummyVideosAdapter(3)
output_directory = os.path.join(self.temp_dir, "ANY_OUTPUT_DIR")
ingestor = GulpIngestor(adapter, output_directory, 2, 1)
ingestor()
input1 = {'meta': {'name': 'new_video'},
'frames': [np.ones((4, 1, 3), dtype='uint8')],
'id': 1}
input2 = {'meta': {'name': 'new_videoi_2'},
'frames': [np.ones((4, 1, 3), dtype='uint8')],
'id': 3}
meta_dict = [input1, input2]
new_meta = remove_entries_with_duplicate_ids(
output_directory, meta_dict)
self.assertEqual(new_meta, [input2])
class TestRemoveDuplicatesInMetadict(unittest.TestCase):
def test_no_duplicates_in_metadict(self):
input1 = {'meta': {'name': 'new_video'},
'frames': [np.ones((4, 1, 3), dtype='uint8')],
'id': 1}
input2 = {'meta': {'name': 'new_video2'},
'frames': [ | np.ones((4, 1, 3), dtype='uint8') | numpy.ones |
import copy
import os
import sys
import numpy as np
from functools import partial
from matplotlib import patches
import matplotlib.pyplot as plt
sys.path.append(os.path.join(os.path.dirname(__file__), 'pathfind/build'))
import QuoridorUtils
class QuoridorBoard:
def __init__(self, n, board=None):
assert n >= 3
self.n = n
self.history = {}
midpoint_red = self.n // 2 + 1 - n % 2
midpoint_blue = self.n // 2 - 1 + n % 2
lastpoint = self.n - 1
self.red_goal = lastpoint
self.blue_goal = 0
self.is_flipped = False
self.max_walls = (self.n + 1) ** 2 // 10
if board:
self.setBoard(board)
else:
self.v_walls = np.zeros((self.n - 1, self.n - 1), np.int16)
self.h_walls = np.zeros((self.n - 1, self.n - 1), np.int16)
self.draw = False
self.paths_red, self.paths_blue = QuoridorUtils.getPathMatrices(self.v_walls, self.h_walls)
self.legal_vwalls = np.ones((self.n - 1, self.n - 1), np.int16)
self.legal_hwalls = np.ones((self.n - 1, self.n - 1), np.int16)
# red player
self.red_position = (midpoint_red, 0)
self.red_walls = self.max_walls
# blue player
self.blue_position = (midpoint_blue, lastpoint)
self.blue_walls = self.max_walls
self.actions = {
# NORTH
0: partial(self.move, dx=+0, dy=+1),
# SOUTH
1: partial(self.move, dx=+0, dy=-1),
# EAST
2: partial(self.move, dx=+1, dy=+0),
# WEST
3: partial(self.move, dx=-1, dy=+0),
# JN
4: partial(self.move, dx=+0, dy=+2),
# JS
5: partial(self.move, dx=+0, dy=-2),
# JE
6: partial(self.move, dx=+2, dy=+0),
# JW
7: partial(self.move, dx=-2, dy=+0),
# JNE
8: partial(self.move, dx=+1, dy=+1),
# JSW
9: partial(self.move, dx=-1, dy=-1),
# JNW
10: partial(self.move, dx=-1, dy=+1),
# JSE
11: partial(self.move, dx=+1, dy=-1),
# PLACE VERTICAL WALL
'vw': self.placeVerticalWall,
# PLACE HORIZONTAL WALL
'hw': self.placeHorizontalWall,
}
self.convert_action = [1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10] + list(
np.flip(np.arange(12, 12 + (self.n - 1) ** 2).reshape((self.n - 1, self.n - 1)), (0, 1)).ravel()) + list(
np.flip(np.arange(12 + (self.n - 1) ** 2, 12 + 2 * (self.n - 1) ** 2).reshape((self.n - 1, self.n - 1)),
(0, 1)).ravel())
def getGameEnded(self, player):
# endgame_heuristic = True
# if endgame_heuristic:
# dist_red = self.paths_red[self.red_position[0]][self.red_position[1]]
# dist_blue = self.paths_blue[self.blue_position[0]][self.blue_position[1]]
#
# if player == 1 and self.red_walls == 0 and self.blue_walls == 0 and dist_red < dist_blue:
# return player
# if player == -1 and self.red_walls == 0 and self.blue_walls == 0 and dist_blue < dist_red:
# return -player
if self.red_position[1] == self.red_goal:
return player
elif self.blue_position[1] == self.blue_goal:
return -player
elif self.draw:
return -1e-3
return 0
def addToHistory(self):
s = self.getBoardHashable()
if s in self.history:
self.history[s] += 1
else:
self.history[s] = 1
if self.history[s] > 2:
self.draw = True
def getBoard(self):
# Boards
boards = np.zeros((2, self.n, self.n), dtype=int)
# Red position
red_board = np.zeros((self.n, self.n))
red_board[self.red_position[0], self.red_position[1]] = 1
boards[0] = red_board
# Blue position
blue_board = np.zeros((self.n, self.n))
blue_board[self.blue_position[0], self.blue_position[1]] = 1
boards[1] = blue_board
# Walls
walls = np.zeros((2, self.n - 1, self.n - 1), dtype=int)
walls[0] = self.v_walls
walls[1] = self.h_walls
# Values
values = np.append(self.shortestPathActions(),
[self.red_walls / self.max_walls, self.blue_walls / self.max_walls,
((self.n ** 2 + 1) - self.paths_red[self.red_position[0]][self.red_position[1]]) / (
self.n ** 2 + 1),
((self.n ** 2 + 1) - self.paths_blue[self.blue_position[0]][self.blue_position[1]]) / (
self.n ** 2 + 1),
float(self.draw)])
return boards, walls, values
def getBoardFlippedHorizontally(self):
# Boards
boards = np.zeros((2, self.n, self.n), dtype=int)
# Red position
red_board = np.zeros((self.n, self.n))
red_board[(self.n - 1) - self.red_position[0], self.red_position[1]] = 1
boards[0] = red_board
# Blue position
blue_board = np.zeros((self.n, self.n))
blue_board[(self.n - 1) - self.blue_position[0], self.blue_position[1]] = 1
boards[1] = blue_board
# Walls
walls = np.zeros((2, self.n - 1, self.n - 1), dtype=int)
walls[0] = np.flipud(self.v_walls)
walls[1] = | np.flipud(self.h_walls) | numpy.flipud |
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Aug 15 17:01:14 2020
create training files
@author: nel
"""
#%%
import cv2
import os
import matplotlib.pyplot as plt
import numpy as np
import zipfile
import caiman as cm
from caiman.base.rois import nf_read_roi
from caiman.base.rois import nf_read_roi_zip
#%%
img_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/data_voltage/summary_images'
masks_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/labels/combination_v1.2'
#save_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_cross3'
#save_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_L1_6'
#save_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_L1_4'
#save_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_L1_2'
#save_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_L1_1'
#save_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_TEG_2'
#save_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_TEG_1'
#save_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_HPC_8'
#save_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_HPC_4'
#save_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_HPC_2'
#save_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_HPC_1'
save_folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_HPC_4_2'
try:
os.mkdir(save_folder)
os.mkdir(save_folder+'/train')
os.mkdir(save_folder+'/val')
except OSError:
print ("already exist")
else:
print ("make folders" )
files = sorted(os.listdir(img_folder))
files = np.array([file for file in files if '_summary.tif' in file])
#val_set = np.array([0, 3, 8, 10, 12, 15, 18, 21])
#val_set = np.array([1, 4, 7, 9, 13, 16, 19, 22])
#val_set = np.array([2, 5, 6, 11, 14, 17, 20, 23])
#val_set = np.array([3, 8, 10])
#train_set = np.array([4])
#val_set = np.array([0])
#train_set = np.array([1])
val_set = np.array([14, 17, 20, 23])
train_set = np.arange(12, 24)
train_set = np.array(list(set(train_set) - set(val_set)))
#train_set = np.array([22])
train_set = np.array([12, 15, 18, 21])
for file in files:
if file in files[val_set]:
group = 'val'
elif file in files[train_set]:
group = 'train'
else:
group = None
if group is not None:
#else:
# group = 'train'
summary_img = cm.load(os.path.join(img_folder, file))
input_img = summary_img[[0, 0, 1], :, :]
with zipfile.ZipFile(os.path.join(masks_folder, file.split('_summary')[0]+'.zip')) as zf:
names = zf.namelist()
coords = [nf_read_roi(zf.open(n)) for n in names]
if input_img.shape[2] < 128:
for idx, i in enumerate(coords):
coords[idx][:, 1] = list(np.array(i[:, 1]+ int((128-input_img.shape[2])/2)))
aa = coords.copy()
print('hha')
polygons = [{'name': 'polygon','all_points_x':i[:,1],'all_points_y':i[:,0]} for i in coords]
np.savez(save_folder+'/'+group+'/'+file.split('_summary')[0]+'_mask.npz', mask = polygons)
if input_img.shape[2] < 128:
temp = input_img.copy()
a = []
for idx, img in enumerate(temp):
a.append(cv2.copyMakeBorder(img,0, 0, int((128-input_img.shape[2])/2), int((128-input_img.shape[2])/2), borderType=cv2.BORDER_CONSTANT, value=0))
input_img = np.stack(a)
print(input_img.shape)
plt.figure();plt.imshow(input_img[0]);plt.show()
input_img = input_img.transpose([1,2,0])
np.savez(save_folder + '/' + group + '/' + file.split('_summary')[0]+'.npz', img = input_img)
"""
for i in aa:
plt.figure();plt.plot(i[:,0], i[:,1])
import skimage
mask = np.zeros((284, 128, len(polygons)))
for i, p in enumerate(polygons):
# Get indexes of pixels inside the polygon and set them to 1
rr, cc = skimage.draw.polygon(p['all_points_y'], p['all_points_x'])
mask[rr, cc, i] = 1
"""
#%%
folder = '/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_L1_6/train'
files = os.listdir(folder)
files = [file for file in files if 'mask' in file]
for file in files:
m = np.load(os.path.join(folder, file), allow_pickle=True)['mask']
print(file)
print(m.shape)
#%%
m = np.load('/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_L1_1/train/FOV1_35um.npz', allow_pickle=True)['img']
mask = np.load('/home/nel/Code/NEL_LAB/Mask_RCNN/datasets/voltage_v1.2_L1_1/train/FOV1_35um_mask.npz', allow_pickle=True)['mask']
thresh = 296
n = 0
mask_new = []
for mm in mask:
#print(mm)
print(sum(mm['all_points_y']>thresh))
if sum(mm['all_points_y']>thresh) > 15:
n = n + 1
mm['all_points_y'] = mm['all_points_y'] - thresh
mask_new.append(mm)
print(f'number of masks: {n}')
mask_new = | np.array(mask_new) | numpy.array |
# coding=utf-8
# Copyright 2022 The Google Research Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# Lint as: python2, python3
"""Unit tests for layers.py."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
import tensorflow.compat.v1 as tf
from tunas.rematlib import layers
class ScalarMultiplicationLayer(layers.Layer):
def __init__(self, initial_value, regularizer=None, name=None):
super(ScalarMultiplicationLayer, self).__init__()
self._initial_value = initial_value
self._regularizer = regularizer
self._name = name
self._built = False
def build(self, input_shape):
with tf.variable_scope(self._name, 'ScalarMultiplicationLayer') as scope:
self._scope = scope
if not self._built:
self._create_trainable_variable(
name='scalar',
initializer=self._initial_value,
regularizer=self._regularizer)
self._built = True
return input_shape
def apply(self, inputs, training):
del training
assert self._built
with tf.variable_scope(self._scope, reuse=True):
return self._get_trainable_tensor('scalar') * inputs
class Constant(layers.Layer):
def __init__(self, value):
self._value = tf.constant(value, tf.float32)
def build(self, input_shape):
return self._value.shape
def apply(self, inputs, training):
del inputs, training
return self._value
class LayersTest(tf.test.TestCase):
def test_with_data_dependencies(self):
var1 = tf.get_variable(
name='var1',
initializer=0,
dtype=tf.int32,
use_resource=True)
with tf.control_dependencies([var1.assign_add(1)]):
increment_var1 = var1.read_value()
var2 = tf.get_variable(
name='var2',
initializer=[0, 0],
dtype=tf.int32,
use_resource=True)
with tf.control_dependencies([var2.assign_add([1, 1])]):
increment_var2 = var2.read_value()
var3 = tf.get_variable(
name='var3',
initializer=[[0, 0], [0, 0], [0, 0]],
dtype=tf.int32,
use_resource=True)
with tf.control_dependencies([var3.assign_add([[1, 1], [1, 1], [1, 1]])]):
increment_var3 = var3.read_value()
output1 = tf.constant(2.0)
output2 = tf.constant([3.0, 4.0])
output3 = tf.constant([[5.0, 6.0, 7.0], [8.0, 9.0, 10.0]])
tensors = layers.with_data_dependencies(
[increment_var1, increment_var2, increment_var3],
[output1, output2, output3])
self.evaluate(tf.global_variables_initializer())
# Verify that the output values are correct.
arrays = self.evaluate(tensors)
self.assertAllClose(arrays, [
2.0,
[3.0, 4.0],
[[5.0, 6.0, 7.0], [8.0, 9.0, 10.0]],
])
# Verify that the dependencies are evaluated.
self.assertAllClose(self.evaluate(var1), 1)
self.assertAllClose(self.evaluate(var2), [1, 1])
self.assertAllClose(self.evaluate(var3), [[1, 1], [1, 1], [1, 1]])
def test_with_data_dependencies_grads(self):
tensor1 = tf.constant(1.0)
tensor2 = tf.constant(2.0)
outputs = layers.with_data_dependencies([tensor1], [5.0 * tensor2])
self.assertLen(outputs, 1)
grads = tf.gradients(outputs[0], [tensor1, tensor2])
self.assertLen(grads, 2)
self.assertIsNone(grads[0])
self.assertAllClose(self.evaluate(grads[1]), 5.0)
def test_layer_regularization_loss(self):
initial_value = 3.0
l2_weight = 5.0
layer = ScalarMultiplicationLayer(
initial_value=initial_value,
regularizer=tf.keras.regularizers.l2(l2_weight))
inputs = tf.constant(10.0)
layer.build(inputs.shape)
layer.apply(inputs, training=True)
self.evaluate(tf.global_variables_initializer())
self.assertAllClose(
l2_weight * initial_value**2,
self.evaluate(layer.regularization_loss()))
def test_regularization_loss_for_layer_without_variables(self):
layer = layers.Identity()
inputs = tf.constant([1.0, -2.0, 3.0])
layer.build(inputs.shape)
layer.apply(inputs, training=True)
self.assertAllClose(0, self.evaluate(layer.regularization_loss()))
def test_merge_shapes_with_broadcast(self):
self.assertEqual(
layers.merge_shapes_with_broadcast(None, None),
tf.TensorShape(None))
self.assertEqual(
layers.merge_shapes_with_broadcast(None, [1, 3]),
tf.TensorShape([1, 3]))
self.assertEqual(
layers.merge_shapes_with_broadcast([8, 1], None),
tf.TensorShape([8, 1]))
self.assertEqual(
layers.merge_shapes_with_broadcast([8, 1], []),
tf.TensorShape([8, 1]))
self.assertEqual(
layers.merge_shapes_with_broadcast([], [1, 3]),
tf.TensorShape([1, 3]))
self.assertEqual(
layers.merge_shapes_with_broadcast([None], [1]),
tf.TensorShape([1]))
self.assertEqual(
layers.merge_shapes_with_broadcast([1], [None]),
tf.TensorShape([1]))
self.assertEqual(
layers.merge_shapes_with_broadcast([None], [2]),
tf.TensorShape([2]))
self.assertEqual(
layers.merge_shapes_with_broadcast([2], [None]),
tf.TensorShape([2]))
self.assertEqual(
layers.merge_shapes_with_broadcast([1], [1]),
tf.TensorShape([1]))
self.assertEqual(
layers.merge_shapes_with_broadcast([1], [2]),
tf.TensorShape([2]))
self.assertEqual(
layers.merge_shapes_with_broadcast([2], [1]),
tf.TensorShape([2]))
self.assertEqual(
layers.merge_shapes_with_broadcast([2], [2]),
tf.TensorShape([2]))
self.assertEqual(
layers.merge_shapes_with_broadcast(
[2, None, 8, 1, 32],
[None, 4, 8, 16, 32]),
tf.TensorShape([2, 4, 8, 16, 32]))
with self.assertRaisesRegex(ValueError,
'Tensor shapes must have the same rank'):
layers.merge_shapes_with_broadcast([1, 1], [1])
with self.assertRaisesRegex(ValueError, 'Tensor shapes are not compatible'):
layers.merge_shapes_with_broadcast([2], [3])
def test_identity(self):
layer = layers.Identity()
inputs = tf.constant([1.0, -2.0, 3.0])
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), [1.0, -2.0, 3.0])
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_zeros(self):
layer = layers.Zeros()
inputs = tf.constant([1.0, -2.0, 3.0])
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), [0.0, 0.0, 0.0])
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_zeros_with_output_shape(self):
layer = layers.Zeros(output_shape=tf.TensorShape([1, 2]))
inputs = tf.constant([[1.0, -2.0, 3.0]])
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), [[0.0, 0.0]])
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_zeros_with_output_shape_and_unknown_batch_dim(self):
layer = layers.Zeros(output_shape=tf.TensorShape([None, 2]))
inputs = tf.constant([[1.0, -2.0, 3.0]])
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), [[0.0, 0.0]])
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_relu(self):
layer = layers.ReLU()
inputs = tf.constant([1.0, -2.0, 3.0])
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), [1.0, 0.0, 3.0])
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_relu6(self):
layer = layers.ReLU6()
inputs = tf.constant([1.0, -2.0, 3.0, 7.0])
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), [1.0, 0.0, 3.0, 6.0])
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_sigmoid(self):
layer = layers.Sigmoid()
inputs = tf.constant([1.0, -2.0, 3.0])
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
expected_output = tf.nn.sigmoid(inputs)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), self.evaluate(expected_output))
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_swish(self):
layer = layers.Swish()
inputs = tf.constant([1.0, -2.0, 3.0, 7.0])
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
expected_output = tf.nn.swish(inputs)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(
self.evaluate(output),
self.evaluate(expected_output))
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_swish6(self):
layer = layers.Swish6()
inputs = tf.constant([1.0, -2.0, 3.0, 7.0])
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
# Swish6(x) = x * relu6(x + 3) / 6
relu6 = lambda x: max(0, min(x, 6))
expected_output = [
1 * relu6(1 + 3) / 6,
-2 * relu6(-2 + 3) / 6,
3 * relu6(3 + 3) / 6,
7 * relu6(7 + 3) / 6,
]
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), expected_output)
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_elu(self):
layer = layers.ELU()
inputs = tf.constant([1.0, -2.0, 3.0])
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
expected_output = tf.nn.elu(inputs)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), self.evaluate(expected_output))
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_space2depth(self):
layer = layers.SpaceToDepth(block_size=2)
inputs = tf.fill([1, 8, 8, 2], 1.0)
expected_output = tf.fill([1, 4, 4, 8], 1.0)
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output),
self.evaluate(expected_output))
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_space2depth_error(self):
layer = layers.SpaceToDepth(block_size=2)
inputs = tf.fill([1, 5, 5, 2], 1.0)
with self.assertRaisesRegex(ValueError,
'Image height 5 must be a multiple of 2'):
layer.build(inputs.shape)
def test_depth_padding(self):
layer = layers.DepthPadding(filters=4)
inputs = tf.fill([2, 8, 8, 2], 1.0)
expected_output = np.concatenate(
(np.ones((2, 8, 8, 2)),
np.zeros((2, 8, 8, 2))),
axis=3)
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output),
expected_output)
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_depth_padding_wrong_filter(self):
layer = layers.DepthPadding(filters=1)
inputs = tf.fill([2, 8, 8, 2], 1.0)
with self.assertRaisesWithPredicateMatch(
ValueError, 'Output filters is smaller than input filters.'):
layer.build(inputs.shape)
def test_max_pool(self):
layer = layers.MaxPool(kernel_size=(2, 2), strides=2)
inputs = tf.concat(
[
tf.fill([2, 2, 2, 2], 1.0),
tf.fill([2, 2, 2, 2], 0.5),
],
axis=3)
first_row = np.ones((2, 1, 1, 2))
second_row = np.empty((2, 1, 1, 2))
second_row.fill(0.5)
expected_output = np.concatenate(
(first_row,
second_row),
axis=3)
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), expected_output)
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_max_pool_3x3_strides2(self):
layer = layers.MaxPool(kernel_size=(3, 3), strides=2)
inputs = tf.reshape(tf.range(36), [1, 6, 6, 1])
expected_output = [[[[14], [16], [17]], [[26], [28], [29]],
[[32], [34], [35]]]]
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), expected_output)
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_max_pool_3x3_strides2_explicit_padding(self):
layer = layers.MaxPool(
kernel_size=(3, 3), strides=2, use_explicit_padding=True)
inputs = tf.reshape(tf.range(36), [1, 6, 6, 1])
expected_output = [[[[7], [9], [11]], [[19], [21], [23]], [[31], [33],
[35]]]]
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output),
expected_output)
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_avg_pool(self):
layer = layers.AveragePool(kernel_size=(2, 2), strides=2)
inputs = tf.concat(
[
tf.fill([2, 2, 2, 2], 1.0),
tf.fill([2, 2, 2, 2], 0.5),
],
axis=3)
first_row = np.ones((2, 1, 1, 2))
second_row = np.empty((2, 1, 1, 2))
second_row.fill(0.5)
expected_output = np.concatenate(
(first_row,
second_row),
axis=3)
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output),
expected_output.tolist())
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_global_average_pool_no_keepdims(self):
layer = layers.GlobalAveragePool(keepdims=False)
inputs = tf.concat(
[
tf.fill([2, 8, 8, 2], 1.0),
tf.fill([2, 8, 8, 2], 2.0),
tf.fill([2, 8, 8, 2], 3.0),
],
axis=3)
expected_output = [
[1, 1, 2, 2, 3, 3],
[1, 1, 2, 2, 3, 3],
]
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), expected_output)
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_global_average_pool_keepdims_size_1(self):
layer = layers.GlobalAveragePool(keepdims=True)
inputs = tf.concat(
[
tf.fill([2, 1, 1, 2], 1.0),
tf.fill([2, 1, 1, 2], 2.0),
tf.fill([2, 1, 1, 2], 3.0),
],
axis=3)
expected_output = [
[[[1, 1, 2, 2, 3, 3]]],
[[[1, 1, 2, 2, 3, 3]]],
]
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), expected_output)
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_global_average_pool_no_keepdims_size_1(self):
layer = layers.GlobalAveragePool(keepdims=False)
inputs = tf.concat(
[
tf.fill([2, 1, 1, 2], 1.0),
tf.fill([2, 1, 1, 2], 2.0),
tf.fill([2, 1, 1, 2], 3.0),
],
axis=3)
expected_output = [
[1, 1, 2, 2, 3, 3],
[1, 1, 2, 2, 3, 3],
]
output_shape = layer.build(inputs.shape)
output = layer.apply(inputs, training=True)
self.assertEqual(output.shape, output_shape)
self.assertAllClose(self.evaluate(output), expected_output)
self.assertEmpty(layer.trainable_tensors())
self.assertEmpty(layer.trainable_variables())
def test_global_average_pool_no_keepdims_dynamic_shape(self):
layer = layers.GlobalAveragePool(keepdims=False)
inputs = tf.placeholder(dtype=tf.float32, shape=[2, None, None, 6])
inputs_value = np.concatenate(
[
| np.full([2, 8, 8, 2], 1.0) | numpy.full |
# -*- coding: utf-8 -*-
"""Classes and functions to manage the expansion of the electric field in plane wave and spherical wave basis sets."""
import numpy as np
import os
import smuthi.coordinates as coord
import smuthi.vector_wave_functions as vwf
import smuthi.spherical_functions as sf
import smuthi.cuda_sources as cu
try:
import pycuda.autoinit
import pycuda.driver as drv
from pycuda import gpuarray
from pycuda.compiler import SourceModule
import pycuda.cumath
except:
pass
import copy
import math
class FieldExpansion:
"""Base class for field expansions."""
def valid(self, x, y, z):
"""Test if points are in definition range of the expansion. Virtual method to be overwritten in child classes.
Args:
x (numpy.ndarray): x-coordinates of query points
y (numpy.ndarray): y-coordinates of query points
z (numpy.ndarray): z-coordinates of query points
Returns:
numpy.ndarray of bool datatype indicating if points are inside definition domain.
"""
pass
def diverging(self, x, y, z):
"""Test if points are in domain where expansion could diverge. Virtual method to be overwritten in child
classes.
Args:
x (numpy.ndarray): x-coordinates of query points
y (numpy.ndarray): y-coordinates of query points
z (numpy.ndarray): z-coordinates of query points
Returns:
numpy.ndarray of bool datatype indicating if points are inside divergence domain.
"""
pass
def electric_field(self, x, y, z):
"""Evaluate electric field. Virtual method to be overwritten in child classes.
Args:
x (numpy.ndarray): x-coordinates of query points
y (numpy.ndarray): y-coordinates of query points
z (numpy.ndarray): z-coordinates of query points
Returns:
Tuple of (E_x, E_y, E_z) numpy.ndarray objects with the Cartesian coordinates of complex electric field.
"""
pass
class PiecewiseFieldExpansion(FieldExpansion):
r"""Manage a field that is expanded in different ways for different domains, i.e., an expansion of the kind
.. math::
\mathbf{E}(\mathbf{r}) = \sum_{i} \mathbf{E}_i(\mathbf{r}),
where
.. math::
\mathbf{E}_i(\mathbf{r}) = \begin{cases} \tilde{\mathbf{E}}_i(\mathbf{r}) & \text{ if }\mathbf{r}\in D_i \\ 0 & \text{ else} \end{cases}
and :math:`\tilde{\mathbf{E_i}}(\mathbf{r})` is either a plane wave expansion or a spherical wave expansion, and
:math:`D_i` is its domain of validity.
"""
def __init__(self):
self.expansion_list = []
def valid(self, x, y, z):
"""Test if points are in definition range of the expansion.
Args:
x (numpy.ndarray): x-coordinates of query points
y (numpy.ndarray): y-coordinates of query points
z (numpy.ndarray): z-coordinates of query points
Returns:
numpy.ndarray of bool datatype indicating if points are inside definition domain.
"""
vld = np.zeros(x.shape, dtype=bool)
for fex in self.expansion_list:
vld = np.logical_or(vld, fex.valid(x, y, z))
return vld
def diverging(self, x, y, z):
"""Test if points are in domain where expansion could diverge.
Args:
x (numpy.ndarray): x-coordinates of query points
y (numpy.ndarray): y-coordinates of query points
z (numpy.ndarray): z-coordinates of query points
Returns:
numpy.ndarray of bool datatype indicating if points are inside divergence domain.
"""
dvg = np.zeros(x.shape, dtype=bool)
for fex in self.expansion_list:
dvg = np.logical_and(dvg, fex.diverging(x, y, z))
return dvg
def electric_field(self, x, y, z):
"""Evaluate electric field.
Args:
x (numpy.ndarray): x-coordinates of query points
y (numpy.ndarray): y-coordinates of query points
z (numpy.ndarray): z-coordinates of query points
Returns:
Tuple of (E_x, E_y, E_z) numpy.ndarray objects with the Cartesian coordinates of complex electric field.
"""
x, y, z = np.array(x), np.array(y), np.array(z)
ex = np.zeros(x.shape, dtype=complex)
ey = np.zeros(x.shape, dtype=complex)
ez = np.zeros(x.shape, dtype=complex)
for fex in self.expansion_list:
dex, dey, dez = fex.electric_field(x, y, z)
ex, ey, ez = ex + dex, ey + dey, ez + dez
return ex, ey, ez
def compatible(self, other):
"""Returns always true, because any field expansion can be added to a piecewise field expansion."""
return True
def __add__(self, other):
"""Addition of expansion objects.
Args:
other (FieldExpansion): expansion object to add to this object
Returns:
PiecewiseFieldExpansion object as the sum of this expansion and the other
"""
# todo: testing
pfe_sum = PiecewiseFieldExpansion()
if type(other).__name__ == "PiecewiseFieldExpansion":
added = [False for other_fex in other.expansion_list]
for self_fex in self.expansion_list:
fex = copy.deepcopy(self_fex)
for i, other_fex in enumerate(other.expansion_list):
if (not added[i]) and self_fex.compatible(other_fex):
fex = fex + other_fex
added[i] = True
pfe_sum.expansion_list.append(fex)
for i, other_fex in enumerate(other.expansion_list):
if not added[i]:
pfe_sum.expansion_list.append(other_fex)
else:
added = False
for self_fex in self.expansion_list:
fex = copy.deepcopy(self_fex)
if (not added) and fex.compatible(other):
pfe_sum.expansion_list.append(fex + other)
added = True
else:
pfe_sum.expansion_list.append(fex)
if not added:
pfe_sum.expansion_list.append(other)
return pfe_sum
class SphericalWaveExpansion(FieldExpansion):
r"""A class to manage spherical wave expansions of the form
.. math::
\mathbf{E}(\mathbf{r}) = \sum_{\tau=1}^2 \sum_{l=1}^\infty \sum_{m=-l}^l a_{\tau l m}
\mathbf{\Psi}^{(\nu)}_{\tau l m}(\mathbf{r} - \mathbf{r}_i)
for :math:`\mathbf{r}` located in a layer defined by :math:`z\in [z_{min}, z_{max}]`
and where :math:`\mathbf{\Psi}^{(\nu)}_{\tau l m}` are the SVWFs, see
:meth:`smuthi.vector_wave_functions.spherical_vector_wave_function`.
Internally, the expansion coefficients :math:`a_{\tau l m}` are stored as a 1-dimensional array running over a multi
index :math:`n` subsumming over the SVWF indices :math:`(\tau,l,m)`. The mapping from the SVWF indices to the multi
index is organized by the function :meth:`multi_to_single_index`.
Args:
k (float): wavenumber in layer where expansion is valid
l_max (int): maximal multipole degree :math:`l_\mathrm{max}\geq 1` where to truncate the expansion.
m_max (int): maximal multipole order :math:`0 \leq m_\mathrm{max} \leq l_\mathrm{max}` where to truncate the
expansion.
kind (str): 'regular' for :math:`\nu=1` or 'outgoing' for :math:`\nu=3`
reference_point (list or tuple): [x, y, z]-coordinates of point relative to which the spherical waves are
considered (e.g., particle center).
lower_z (float): the expansion is valid on and above that z-coordinate
upper_z (float): the expansion is valid below that z-coordinate
inner_r (float): radius inside which the expansion diverges (e.g. circumscribing sphere of particle)
outer_r (float): radius outside which the expansion diverges
Attributes:
coefficients (numpy ndarray): expansion coefficients :math:`a_{\tau l m}` ordered by multi index n
"""
def __init__(self, k, l_max, m_max=None, kind=None, reference_point=None, lower_z=-np.inf, upper_z=np.inf,
inner_r=0, outer_r=np.inf):
self.k = k
self.l_max = l_max
if m_max is not None:
self.m_max = m_max
else:
self.m_max = l_max
self.coefficients = np.zeros(blocksize(self.l_max, self.m_max), dtype=complex)
self.kind = kind # 'regular' or 'outgoing'
self.reference_point = reference_point
self.lower_z = lower_z
self.upper_z = upper_z
self.inner_r = inner_r
self.outer_r = outer_r
def valid(self, x, y, z):
"""Test if points are in definition range of the expansion.
Args:
x (numpy.ndarray): x-coordinates of query points
y (numpy.ndarray): y-coordinates of query points
z (numpy.ndarray): z-coordinates of query points
Returns:
numpy.ndarray of bool datatype indicating if points are inside definition domain.
"""
return np.logical_and(z >= self.lower_z, z < self.upper_z)
def diverging(self, x, y, z):
"""Test if points are in domain where expansion could diverge.
Args:
x (numpy.ndarray): x-coordinates of query points
y (numpy.ndarray): y-coordinates of query points
z (numpy.ndarray): z-coordinates of query points
Returns:
numpy.ndarray of bool datatype indicating if points are inside divergence domain.
"""
r = np.sqrt((x - self.reference_point[0])**2 + (y - self.reference_point[1])**2
+ (z - self.reference_point[2])**2)
if self.kind == 'regular':
return r >= self.outer_r
if self.kind == 'outgoing':
return r <= self.inner_r
else:
return None
def coefficients_tlm(self, tau, l, m):
"""SWE coefficient for given (tau, l, m)
Args:
tau (int): SVWF polarization (0 for spherical TE, 1 for spherical TM)
l (int): SVWF degree
m (int): SVWF order
Returns:
SWE coefficient
"""
n = multi_to_single_index(tau, l, m, self.l_max, self.m_max)
return self.coefficients[n]
def electric_field(self, x, y, z):
"""Evaluate electric field.
Args:
x (numpy.ndarray): x-coordinates of query points
y (numpy.ndarray): y-coordinates of query points
z (numpy.ndarray): z-coordinates of query points
Returns:
Tuple of (E_x, E_y, E_z) numpy.ndarray objects with the Cartesian coordinates of complex electric field.
"""
x = np.array(x)
y = np.array(y)
z = np.array(z)
xr = x[self.valid(x, y, z)] - self.reference_point[0]
yr = y[self.valid(x, y, z)] - self.reference_point[1]
zr = z[self.valid(x, y, z)] - self.reference_point[2]
ex = | np.zeros(x.shape, dtype=complex) | numpy.zeros |
"""
Loads spike data, bins and smoothes.
@author: bartulem
"""
import os
import sys
import sparse
import warnings
import matplotlib.pyplot as plt
from numba import njit
import numpy as np
from scipy.ndimage.filters import gaussian_filter1d
import sessions2load
import quantify_ratemaps
import decode_events
warnings.simplefilter('ignore')
def gaussian_smoothing(array, sigma=1, axis=1):
"""
Parameters
----------
array : np.ndarray
The input array to be smoothed.
sigma : int
The SD of the smoothing window; defaults to 1 (bin).
axis : int
The filter smooths in 1D, so you choose the axis; defaults to 1.
----------
Returns
----------
smoothed_array : np.ndarray
The 1D smoothed input array.
----------
"""
return gaussian_filter1d(input=array, sigma=sigma, axis=axis)
@njit(parallel=False)
def get_shuffling_shifts(number_of_shuffles=1000, shuffle_range=(20, 60)):
"""
Parameters
----------
number_of_shuffles : int
How many times to shuffle; defaults to 1000.
shuffle_range : tuple
Minimum and maximum number of seconds to shift the spike train; defaults to (20, 60).
----------
Returns
----------
seed_value : int64
The specific seed for generating this set of random numbers.
shuffle_shifts : np.ndarray
The pseudorandom shifts for generating shuffled spike trains.
----------
"""
# create a seed & seed the random number generator
seed_value = np.random.randint(0, 2 ** 32 - 1)
np.random.seed(seed_value)
# get time shifts for every shuffle
shuffle_shifts = np.random.uniform(shuffle_range[0], shuffle_range[1], size=(number_of_shuffles,))
return seed_value, shuffle_shifts
@njit(parallel=False)
def purge_spikes_beyond_tracking(spike_train, tracking_ts, full_purge=True):
"""
Parameters
----------
spike_train : np.ndarray
Spike times in seconds.
tracking_ts : np.ndarray (2, )
The start and end of tracking relative to sessions start.
full_purge : bool
Remove spikes before and after tracking; defaults to True.
----------
Returns
----------
purged_spike_train : np.ndarray
The spike train without spikes that precede or succeed tracking, relative to tracking start.
----------
"""
if full_purge:
# re-calculate spike times relative to tracking start
purged_spike_train = spike_train - tracking_ts[0]
# remove spikes that precede or succeed tracking
purged_spike_train = purged_spike_train[(purged_spike_train >= 0) & (purged_spike_train < tracking_ts[1] - tracking_ts[0])]
else:
# remove spikes that succeed tracking
purged_spike_train = spike_train[spike_train < tracking_ts[1] - tracking_ts[0]]
return purged_spike_train
@njit(parallel=False)
def convert_spikes_to_frame_events(purged_spike_train, frames_total, camera_framerate=120.):
"""
Parameters
----------
purged_spike_train : np.ndarray
Spike times in seconds (relative to tracking start).
frames_total : int
The total number of tracking frames in the recording.
camera_framerate : np.float64
The sampling frequency of the tracking system; defaults to 120.
----------
Returns
----------
spikes_frames : np.ndarray (frames_total, )
How many spikes happened in each frame of tracking.
----------
"""
# initialize an array of zeros with the size of the number of frames
spikes_frames = np.zeros(frames_total)
# convert spike times to frames when they happened
spikes_tracking = purged_spike_train * camera_framerate
spikes_tracking = np.floor(spikes_tracking, np.empty_like(spikes_tracking))
# categorize spikes
for frame in spikes_tracking:
spikes_frames[int(frame)] += 1
return spikes_frames
@njit(parallel=False)
def condense_frame_arrays(frame_array, camera_framerate=120.,
bin_size_ms=100, arr_type=True,
sound=True):
"""
Parameters
----------
frame_array : np.ndarray (frames_total, )
The input frame array.
bin_size_ms : int
The bin size of the PETH; defaults to 100 (ms).
camera_framerate : np.float64
The sampling frequency of the tracking system; defaults to 120.
arr_type : bool
True if it's a spike array, False if it's some other array; defaults to True.
sound : bool
If true, it's the sound array, if false - it's a variable; defaults to True.
----------
Returns
----------
new_arr : np.ndarray
The frame array with the reduced shape.
----------
"""
total_frames = frame_array.shape[0]
# calculate size of new frame
step = int(camera_framerate * (bin_size_ms / 1000))
new_shape = total_frames // step
new_arr = np.zeros(new_shape)
# fill it in
ls_iter = list(range(0, new_shape * step, step))
for idx, one_bin in enumerate(ls_iter):
array_excerpt = frame_array[one_bin:one_bin + step]
if arr_type:
new_arr[idx] = array_excerpt.sum()
else:
if sound:
new_arr[idx] = 1 if array_excerpt.sum() >= (step / 2) else 0
else:
new_arr[idx] = np.nanmean(array_excerpt)
return new_arr
@njit(parallel=False)
def shuffle_spike_train(spike_train, random_shifts):
"""
Parameters
----------
spike_train : np.ndarray (number_of_spikes, )
Spike times in seconds (relative to tracking start).
random_shifts : np.ndarray (number_of_shuffles, )
The pseudorandom shifts for generating shuffled spike trains.
----------
Returns
----------
shuffled_spike_train : np.ndarray (number_of_shuffles, number_of_spikes)
The shuffled spike trains without spikes that precede or succeed tracking, relative to tracking start.
----------
"""
# create array of zeroed values to store shuffled spikes in
shuffled_spike_train_sec = np.zeros((random_shifts.shape[0], spike_train.shape[0]))
# get shuffled spike time values
for shuffle_idx in range(random_shifts.shape[0]):
shuffled_spike_train_sec[shuffle_idx, :] = spike_train + random_shifts[shuffle_idx]
return shuffled_spike_train_sec
@njit(parallel=False)
def find_event_starts(event_array, return_all=True,
camera_framerate=120.,
expected_event_duration=5.,
min_inter_event_interval=10.):
"""
Parameters
----------
event_array : np.ndarray (frames_total, )
The array of events (should be binary, i.e. 0/1).
return_all : bool
Return all event starts, irrespective of duration; defaults to True.
camera_framerate : np.float64
The sampling frequency of the tracking system; defaults to 120.
expected_event_duration : int/float
The expected duration of the designated event; defaults to 5 (seconds).
min_inter_event_interval : int/float
The minimum interval between any two adjacent events; defaults to 10 (seconds).
----------
Returns
----------
event_start_frames: np.ndarray
Every frame ON (1) start in the input array.
----------
"""
event_change_points = np.where(np.roll(event_array, 1) != event_array)[0]
event_start_frames = event_change_points[::2]
if not return_all:
# this returns only events that satisfy: expected_event_duration - .1 < duration < expected_event_duration + .1
event_end_frames = event_change_points[1::2]
event_durations = (event_end_frames - event_start_frames) / camera_framerate
inter_event_intervals = np.concatenate((np.array([min_inter_event_interval + .1]),
(event_start_frames[1:] - event_start_frames[:-1]) / camera_framerate))
event_start_frames = event_start_frames[(event_durations > (expected_event_duration - .1))
& (event_durations < (expected_event_duration + .1))
& (inter_event_intervals > min_inter_event_interval)]
return event_start_frames
@njit(parallel=False)
def calculate_peth(input_array, event_start_frames,
bin_size_ms=50, window_size=10,
camera_framerate=120.,
behavior_input=False):
"""
Parameters
----------
input_array : np.ndarray
Arrays with spikes/behavior allocated to tracking frames.
event_start_frames : np.ndarray
Every frame ON (1) start in the session.
bin_size_ms : int
The bin size of the PETH; defaults to 50 (ms).
window_size : int
The unilateral window size; defaults to 10 (seconds).
camera_framerate : np.float64
The sampling frequency of the tracking system; defaults to 120.
behavior_input : bool
Whether or not the input array is behavioral; defaults to False.
----------
Returns
----------
peth_array : np.ndarray (epoch_num, total_window)
Peri-event time histogram.
----------
"""
# convert bin size to seconds
bin_size = bin_size_ms / 1e3
# get bin step (number of frames in each bin)
bin_step = int(round(camera_framerate * bin_size))
# get total window
window_one_side = int(round((window_size / bin_size)))
total_window = 2 * window_one_side
# calculate PETH
peth_array = np.zeros((event_start_frames.shape[0], total_window))
for epoch in range(event_start_frames.shape[0]):
window_start_bin = int(round(event_start_frames[epoch] - (bin_step * window_one_side)))
for one_bin in range(total_window):
if behavior_input:
if window_start_bin < 0:
peth_array[epoch, one_bin] = np.nan
else:
peth_array[epoch, one_bin] = np.nanmean(input_array[window_start_bin:window_start_bin + bin_step])
else:
if window_start_bin < 0:
peth_array[epoch, one_bin] = np.nan
else:
peth_array[epoch, one_bin] = np.sum(input_array[window_start_bin:window_start_bin + bin_step]) / bin_size
window_start_bin += bin_step
return peth_array
@njit(parallel=False)
def calculate_discontinuous_peth(input_array_lst, esf, event_number,
bin_size_ms=50, window_size=6,
camera_framerate=120.):
"""
Parameters
----------
input_array_lst : list
List of session arrays with spikes allocated to tracking frames.
esf : list
List of session behavior arrays.
event_number : int
Number of events to consider.
bin_size_ms : int
The bin size of the PETH; defaults to 50 (ms).
window_size : int
The complete window size; defaults to 6 (seconds).
camera_framerate : np.float64
The sampling frequency of the tracking system; defaults to 120.
----------
Returns
----------
peth_array : np.ndarray (event_number, total_window)
Peri-event time histogram.
----------
"""
# convert bin size to seconds
bin_size = bin_size_ms / 1e3
# get bin step (number of frames in each bin)
bin_step = int(round(camera_framerate * bin_size))
# get total window
total_window = int(round((window_size / bin_size)))
switch_points = np.arange(0, total_window, total_window // 3)
# calculate PETH
peth_array = np.zeros((event_number, total_window))
for arr_idx, arr in enumerate(input_array_lst):
for epoch in range(event_number):
window_start_bin = int(round(esf[arr_idx][epoch]))
for one_bin in range(total_window // 3):
real_bin = one_bin + switch_points[arr_idx]
peth_array[epoch, real_bin] = np.sum(arr[window_start_bin:window_start_bin + bin_step]) / bin_size
window_start_bin += bin_step
return peth_array
@njit(parallel=False)
def raster_preparation(purged_spike_train, event_start_frames,
camera_framerate=120., window_size=10):
"""
Parameters
----------
purged_spike_train : np.ndarray
The spike train without spikes that precede or succeed tracking, relative to tracking start.
event_start_frames : np.ndarray
Every frame ON (1) start in the session.
camera_framerate : np.float64
The sampling frequency of the tracking system; defaults to 120.
window_size : int
The unilateral window size; defaults to 10 (seconds).
----------
Returns
----------
raster_list : list
List of raster events (np.ndarrays) for that spike train.
----------
"""
raster_list = []
for event in event_start_frames:
window_start_seconds = (event / camera_framerate) - window_size
window_centered_spikes = purged_spike_train[(purged_spike_train >= window_start_seconds)
& (purged_spike_train < window_start_seconds + (window_size * 2))] - window_start_seconds
raster_list.append(window_centered_spikes[window_centered_spikes > 0])
return raster_list
def discontinuous_raster_preparation(purged_spike_arr, event_start_arr, event_number,
camera_framerate_arr, window_size=2):
"""
Parameters
----------
purged_spike_arr : np.ndarray
An array of spike trains without spikes that precede or succeed tracking, relative to tracking start.
event_start_arr : np.ndarray
An array of every start frame of speed within a specified range.
event_number : int
Number of events to consider.
camera_framerate_arr : np.ndarray
An array with camera sampling frequencies for all sessions.
window_size : int
The unilateral window size; defaults to 2 (seconds).
----------
Returns
----------
raster_list : list
List of raster events (np.ndarrays) for that spike train.
----------
"""
raster_list = []
for event_idx in range(event_number):
temp_raster_list = []
for session_idx, session in enumerate(event_start_arr):
if len(purged_spike_arr[session_idx]) > 0:
purged_spike_train = purged_spike_arr[session_idx]
window_start_seconds = (session[event_idx] / camera_framerate_arr[session_idx])
window_centered_spikes = purged_spike_train[(purged_spike_train >= window_start_seconds)
& (purged_spike_train < window_start_seconds + window_size)] - window_start_seconds + (session_idx * 2)
for spike in window_centered_spikes:
temp_raster_list.append(spike)
raster_list.append(np.array(temp_raster_list))
return raster_list
@njit(parallel=False)
def find_variable_sequences(variable, threshold_low=0., threshold_high=5.,
min_seq_duration=2, camera_framerate=120.):
"""
Parameters
----------
variable : np.ndarray
The spike train without spikes that precede or succeed tracking, relative to tracking start.
threshold_low : int/float
Value above which variable should be considered; defaults to 0.
threshold_high : int/float
Value above which variable should not be considered; defaults to 5.
min_seq_duration : int/float
The minimum duration for chosen sequences; defaults to 2 (seconds).
camera_framerate : np.float64
The sampling frequency of the tracking system; defaults to 120.
----------
Returns
----------
seq_starts : np.ndarray
An array of sequence starts for the designated variable.
----------
"""
# transform sequence duration to bins
min_seq_duration = int(round(min_seq_duration * camera_framerate))
indices_above_threshold = np.where((threshold_low <= variable) & (variable <= threshold_high))[0]
seq_starts = []
for idx, item in enumerate(indices_above_threshold):
# both idx and item need to be below array length minus min_seq_duration
idx_truth = idx <= indices_above_threshold.shape[0] - min_seq_duration
item_truth = item <= variable.shape[0] - min_seq_duration
if idx_truth and item_truth \
and (np.arange(item, item + min_seq_duration, 1) == indices_above_threshold[idx:idx + min_seq_duration]).all():
if len(seq_starts) == 0:
seq_starts.append(item)
else:
if item > seq_starts[-1] + (min_seq_duration * 2):
seq_starts.append(item)
return np.array(seq_starts).astype(np.int32)
class Spikes:
# get shuffling shifts
shuffle_seed, shuffle_shifts = get_shuffling_shifts()
print(f"The pseudorandom number generator was seeded at {shuffle_seed}.")
def __init__(self, input_file='', purged_spikes_dictionary='', input_012=['', '', ''],
cluster_groups_dir='/.../cluster_groups_info',
sp_profiles_csv='/.../spiking_profiles.csv',
pkl_files_dir='/.../data_files'):
self.input_file = input_file
self.purged_spikes_dictionary = purged_spikes_dictionary
self.input_012 = input_012
self.cluster_groups_dir = cluster_groups_dir
self.sp_profiles_csv = sp_profiles_csv
self.pkl_files_dir = pkl_files_dir
def get_baseline_firing_rates(self, **kwargs):
"""
Description
----------
This method calculates the baseline firing rates for all selected clusters, where
the baseline rate is defined as the number of spikes divided by the length of
the tracking period.
----------
Parameters
----------
**kwargs (dictionary)
get_clusters (str / int / list)
Cluster IDs to extract (if int, takes first n clusters; if 'all', takes all); defaults to 'all'.
----------
Returns
----------
file_info (str)
The shortened version of the file name.
baseline_activity_dictionary (dict)
A dictionary with the baseline firing rates for all desired clusters.
----------
"""
get_clusters = kwargs['get_clusters'] if 'get_clusters' in kwargs.keys() \
and (kwargs['get_clusters'] == 'all' or type(kwargs['get_clusters']) == int or type(kwargs['get_clusters']) == list) else 'all'
# get spike data in seconds and tracking start and end time
file_id, extracted_data = sessions2load.Session(session=self.input_file).data_loader(extract_clusters=get_clusters,
extract_variables=['tracking_ts'])
# get baseline rates
baseline_activity_dictionary = {}
track_ts = extracted_data['tracking_ts']
recording_len = track_ts[1] - track_ts[0]
extracted_activity = extracted_data['cluster_spikes']
for cl_id, spikes in extracted_activity.items():
# eliminate spikes that happen prior to and post tracking
purged_spikes_sec = purge_spikes_beyond_tracking(spike_train=spikes, tracking_ts=track_ts)
baseline_activity_dictionary[cl_id] = round(purged_spikes_sec.shape[0] / recording_len, 2)
return file_id, baseline_activity_dictionary
def convert_activity_to_frames_with_shuffles(self, **kwargs):
"""
Description
----------
This method converts cluster spiking activity into trains that match the tracking
resolution, as spikes are allocated to appropriate frames. It returns such spike
trains both for true and shuffled data.
----------
Parameters
----------
**kwargs (dictionary)
get_clusters (str / int / list)
Cluster IDs to extract (if int, takes first n clusters; if 'all', takes all); defaults to 'all'.
to_shuffle (bool)
Yey or ney on shuffling; defaults to False.
condense_arr (bool)
Yey or ney on the condensing (reducing the number of bins); defaults to False.
----------
Returns
----------
file_info (str)
The shortened version of the file name.
activity_dictionary (dict)
A dictionary with frame-converted cluster activity and shuffled data.
----------
"""
get_clusters = kwargs['get_clusters'] if 'get_clusters' in kwargs.keys() \
and (kwargs['get_clusters'] == 'all' or type(kwargs['get_clusters']) == int or type(kwargs['get_clusters']) == list) else 'all'
to_shuffle = kwargs['to_shuffle'] if 'to_shuffle' in kwargs.keys() and type(kwargs['to_shuffle']) == bool else False
condense_arr = kwargs['condense_arr'] if 'condense_arr' in kwargs.keys() and type(kwargs['condense_arr']) == bool else False
condense_bin_ms = kwargs['condense_bin_ms'] if 'condense_bin_ms' in kwargs.keys() and type(kwargs['condense_bin_ms']) == int else 100
# get spike data in seconds and tracking start and end time
file_id, extracted_data = sessions2load.Session(session=self.input_file).data_loader(extract_clusters=get_clusters,
extract_variables=['tracking_ts', 'framerate', 'total_frame_num'])
# convert spike arrays to frame arrays
activity_dictionary = {}
purged_spikes_dictionary = {}
track_ts = extracted_data['tracking_ts']
extracted_activity = extracted_data['cluster_spikes']
empirical_camera_fr = extracted_data['framerate']
total_frame_num = extracted_data['total_frame_num']
for cell_id, spikes in extracted_activity.items():
activity_dictionary[cell_id] = {}
# eliminate spikes that happen prior to and post tracking
purged_spikes_sec = purge_spikes_beyond_tracking(spike_train=spikes, tracking_ts=track_ts)
purged_spikes_dictionary[cell_id] = purged_spikes_sec
# covert spikes to frame arrays
cell_id_activity = convert_spikes_to_frame_events(purged_spike_train=purged_spikes_sec,
frames_total=total_frame_num,
camera_framerate=empirical_camera_fr)
if not condense_arr:
activity_dictionary[cell_id]['activity'] = sparse.COO(cell_id_activity).astype(np.int16)
else:
activity_dictionary[cell_id]['activity'] = sparse.COO(condense_frame_arrays(frame_array=cell_id_activity,
bin_size_ms=condense_bin_ms)).astype(np.int16)
if to_shuffle:
activity_dictionary[cell_id]['shuffled'] = {}
# shuffle the purged spike train N times
shuffled_spikes_sec = shuffle_spike_train(purged_spikes_sec, Spikes.shuffle_shifts)
# convert shuffles to frame arrays
for shuffle_idx in range(shuffled_spikes_sec.shape[0]):
purged_shuffle = purge_spikes_beyond_tracking(spike_train=shuffled_spikes_sec[shuffle_idx, :], tracking_ts=track_ts, full_purge=False)
shuffle_cell_id = convert_spikes_to_frame_events(purged_spike_train=purged_shuffle,
frames_total=total_frame_num,
camera_framerate=empirical_camera_fr)
if not condense_arr:
activity_dictionary[cell_id]['shuffled'][shuffle_idx] = sparse.COO(shuffle_cell_id).astype(np.int16)
else:
activity_dictionary[cell_id]['shuffled'][shuffle_idx] = sparse.COO(condense_frame_arrays(frame_array=shuffle_cell_id)).astype(np.int16)
return file_id, activity_dictionary, purged_spikes_dictionary
def get_peths(self, **kwargs):
"""
Description
----------
This method converts cluster spiking activity into peri-event time histograms (PETHs),
where you have the option to define bin and window size. NB: As of yet, it is NOT set
to do the same for shuffled spike data (but it's a simple fix).
Details: Each spike train is zeroed to tracking start and purged of spikes that exceed
those boundaries. The spike train is then binned to match the tracking resolution, and
spike counts are allocated to the appropriate frames. These spike counts are further
binned (50 ms) to encompass a window (10 s) before and after every event onset (the
start of the white noise stimulation). Rates are calculated and smoothed with a 3 bin
Gaussian kernel. Raster arrays are prepared by zeroing spike times to each start of the
trial window. Behavioral peths bin and compute the status of any given behavioral feature
around relevant events (NB: works only for speed as of yet).
----------
Parameters
----------
**kwargs (dictionary)
get_clusters (str / int / list)
Cluster IDs to extract (if int, takes first n clusters; if 'all', takes all); defaults to 'all'.
bin_size_ms (int)
The bin size of the PETH; defaults to 50 (ms).
window_size (int / float)
The unilateral window size; defaults to 10 (seconds).
return_all (bool)
Return all event starts, irrespective of duration; defaults to True.
expected_event_duration (int / float)
The expected duration of the designated event; defaults to 5 (seconds).
min_inter_event_interval (int / float)
The minimum interval between any two adjacent events; defaults to 10 (seconds).
smooth (bool)
Smooth PETHs; defaults to False.
smooth_sd (int)
The SD of the smoothing window; defaults to 1 (bin).
smooth_axis (int)
The smoothing axis in a 2D array; defaults to 1 (smooths within rows).
raster (bool)
Prepare arrays from making raster plots; defaults to False.
beh_raster (str / bool)
Prepare behavior arrays from making raster plots; defaults to False.
----------
Returns
----------
peth_dictionary (dict)
Peri-event time histogram for all clusters (np.ndarray (epoch_num, total_window)).
raster_dictionary (dict)
Raster arrays for all clusters zeroed to window start.
peth_beh (np.ndarray)
Peri-event time histogram for the designated behavioral feature (np.ndarray (epoch_num, total_window)).
----------
"""
get_clusters = kwargs['get_clusters'] if 'get_clusters' in kwargs.keys() \
and (kwargs['get_clusters'] == 'all' or type(kwargs['get_clusters']) == int or type(kwargs['get_clusters']) == list) else 'all'
bin_size_ms = kwargs['bin_size_ms'] if 'bin_size_ms' in kwargs.keys() and type(kwargs['bin_size_ms']) == int else 50
window_size = kwargs['window_size'] if 'window_size' in kwargs.keys() and (type(kwargs['window_size']) == int or type(kwargs['window_size']) == float) else 10
return_all = kwargs['return_all'] if 'return_all' in kwargs.keys() and type(kwargs['return_all']) == bool else True
expected_event_duration = kwargs['expected_event_duration'] if 'expected_event_duration' in kwargs.keys() \
and (type(kwargs['expected_event_duration']) == int or type(kwargs['expected_event_duration']) == float) else 5
min_inter_event_interval = kwargs['min_inter_event_interval'] if 'min_inter_event_interval' in kwargs.keys() \
and (type(kwargs['min_inter_event_interval']) == int or type(kwargs['min_inter_event_interval']) == float) else 10
smooth = kwargs['smooth'] if 'smooth' in kwargs.keys() and type(kwargs['smooth']) == bool else False
smooth_sd = kwargs['smooth_sd'] if 'smooth_sd' in kwargs.keys() and type(kwargs['smooth_sd']) == int else 1
smooth_axis = kwargs['smooth_axis'] if 'smooth_axis' in kwargs.keys() and type(kwargs['smooth_axis']) == int else 1
raster = kwargs['raster'] if 'raster' in kwargs.keys() and type(kwargs['raster']) == bool else False
beh_raster = kwargs['beh_raster'] if 'beh_raster' in kwargs.keys() and (type(kwargs['beh_raster']) == str or type(kwargs['beh_raster']) == bool) else False
# extract relevant variables / clusters from session data
get_variables = ['imu_sound', 'framerate']
if type(beh_raster) == str:
get_variables.append(beh_raster)
ses_name, session_vars = sessions2load.Session(session=self.input_file).data_loader(extract_variables=get_variables)
# get activity converted to frames
file_id, activity_dictionary, purged_spikes_dictionary = self.convert_activity_to_frames_with_shuffles(get_clusters=get_clusters)
# get event start frames
event_start_frames = find_event_starts(session_vars['imu_sound'],
return_all=return_all,
camera_framerate=session_vars['framerate'],
expected_event_duration=expected_event_duration,
min_inter_event_interval=min_inter_event_interval)
# get raster plot
if raster:
raster_dictionary = {}
for cell_id, purged_spikes in purged_spikes_dictionary.items():
if cell_id in get_clusters:
raster_dictionary[cell_id] = raster_preparation(purged_spike_train=purged_spikes,
event_start_frames=event_start_frames,
camera_framerate=session_vars['framerate'],
window_size=window_size)
# get PETHs for each cluster and smooth if necessary
peth_dictionary = {}
for cell_id in activity_dictionary.keys():
peth_dictionary[cell_id] = {}
peth_array = calculate_peth(input_array=activity_dictionary[cell_id]['activity'].todense().astype(np.float32),
event_start_frames=event_start_frames,
bin_size_ms=bin_size_ms,
window_size=window_size,
camera_framerate=session_vars['framerate'])
if smooth:
peth_dictionary[cell_id]['peth'] = gaussian_smoothing(array=peth_array, sigma=smooth_sd, axis=smooth_axis)
else:
peth_dictionary[cell_id]['peth'] = peth_array
# get behavior for raster (nb: currently only works for speed)
if type(beh_raster) == str:
peth_beh = calculate_peth(input_array=session_vars[beh_raster][:, 3],
event_start_frames=event_start_frames,
bin_size_ms=bin_size_ms,
window_size=window_size,
camera_framerate=session_vars['framerate'],
behavior_input=True)
if smooth:
peth_beh = gaussian_smoothing(array=peth_beh, sigma=smooth_sd, axis=smooth_axis)
if raster and beh_raster is not False:
return ses_name, peth_dictionary, raster_dictionary, peth_beh
elif raster and beh_raster is False:
return ses_name, peth_dictionary, raster_dictionary
else:
return ses_name, peth_dictionary
def get_discontinuous_peths(self, **kwargs):
"""
Description
----------
This method converts cluster spiking activity into peri-event time histograms (PETHs),
where you have the option to define bin and window size. It should be used to construct
PETHs whose trial parts come from different sessions.
Details: Each session spike train is zeroed to tracking start and purged of spikes that exceed
those boundaries. The spike train is then binned to match the tracking resolution, and
spike counts are allocated to the appropriate frames. These spike counts are further
binned (50 ms) to encompass a window (2 s) after every event onset (NB: which for our purpose
is a 2s window where the speed of the animal was < 5 cm/s) Rates are calculated and smoothed
with a 3 bin Gaussian kernel for each session segment separately. Raster arrays are prepared
by zeroing spike times to each start of the trial window.
----------
Parameters
----------
**kwargs (dictionary)
get_clusters (str / int / list)
Cluster IDs to extract (if int, takes first n clusters; if 'all', takes all); defaults to 'all'.
decode_what (str)
What are you decoding; defaults to 'luminance'.
cluster_areas (list)
Cluster area(s) of choice; defaults to ['A'].
cluster_type (str)
Cluster type of choice; defaults to True.
speed_threshold_low (int/float)
Value above which variable should be considered; defaults to 0.
speed_threshold_high (int/float)
Value below which variable should not be considered; defaults to 5.
speed_min_seq_duration (int/float)
The minimum duration for chosen sequences; defaults to 2 (seconds).
discontinuous_raster (bool)
Prepare arrays from making raster plots; defaults to False.
bin_size_ms (int)
The bin size of the PETH; defaults to 50 (ms).
window_size (int / float)
The unilateral window size; defaults to 10 (seconds).
smooth (bool)
Smooth PETHs; defaults to False.
smooth_sd (int)
The SD of the smoothing window; defaults to 1 (bin).
----------
Returns
----------
peth_dictionary (dict)
Peri-event time histogram for all clusters (np.ndarray (epoch_num, total_window)).
raster_dictionary (dict)
Raster arrays for all clusters zeroed to window start.
----------
"""
get_clusters = kwargs['get_clusters'] if 'get_clusters' in kwargs.keys() \
and (kwargs['get_clusters'] == 'all' or type(kwargs['get_clusters']) == int or type(kwargs['get_clusters']) == list) else 'all'
decode_what = kwargs['decode_what'] if 'decode_what' in kwargs.keys() and type(kwargs['decode_what']) == str else 'luminance'
cluster_areas = kwargs['cluster_areas'] if 'cluster_areas' in kwargs.keys() and type(kwargs['cluster_areas']) == list else ['A']
cluster_type = kwargs['cluster_type'] if 'cluster_type' in kwargs.keys() and type(kwargs['cluster_type']) == str else True
speed_threshold_high = kwargs['speed_threshold_high'] if 'speed_threshold_high' in kwargs.keys() and (
type(kwargs['speed_threshold_high']) == int or type(kwargs['speed_threshold_high']) == float) else 5.
speed_threshold_low = kwargs['speed_threshold_low'] if 'speed_threshold_low' in kwargs.keys() and (
type(kwargs['speed_threshold_low']) == int or type(kwargs['speed_threshold_low']) == float) else 0.
speed_min_seq_duration = kwargs['speed_min_seq_duration'] if 'speed_min_seq_duration' in kwargs.keys() \
and (type(kwargs['speed_min_seq_duration']) == int or type(kwargs['speed_min_seq_duration']) == float) else 2.
discontinuous_raster = kwargs['discontinuous_raster'] if 'discontinuous_raster' in kwargs.keys() and type(kwargs['discontinuous_raster']) == bool else False
bin_size_ms = kwargs['bin_size_ms'] if 'bin_size_ms' in kwargs.keys() and type(kwargs['bin_size_ms']) == int else 50
window_size = kwargs['window_size'] if 'window_size' in kwargs.keys() and (type(kwargs['window_size']) == int or type(kwargs['window_size']) == float) else 6
to_smooth = kwargs['to_smooth'] if 'to_smooth' in kwargs.keys() and type(kwargs['to_smooth']) == bool else False
smooth_sd = kwargs['smooth_sd'] if 'smooth_sd' in kwargs.keys() and type(kwargs['smooth_sd']) == int else 1
# choose clusters for PETHs
all_clusters, chosen_clusters, extra_chosen_clusters, cluster_dict = decode_events.choose_012_clusters(the_input_012=self.input_012,
cl_gr_dir=self.cluster_groups_dir,
sp_prof_csv=self.sp_profiles_csv,
cl_areas=cluster_areas,
cl_type=cluster_type,
dec_type=decode_what,
desired_profiles=True)
# check if cluster(s) exist in the input sessions
for cluster in get_clusters:
if cluster not in all_clusters:
print(f"Sorry, cluster {cluster} not in the input files!")
sys.exit()
# get activity dictionary
zero_first_second_activity = {0: {}, 1: {}, 2: {}}
zero_first_second_purged_spikes = {0: {}, 1: {}, 2: {}}
for cluster in get_clusters:
for file_idx, one_file in enumerate(self.input_012):
if cluster in cluster_dict[file_idx]:
file_id, activity_dictionary, purged_spikes_dictionary = Spikes(input_file=one_file).convert_activity_to_frames_with_shuffles(get_clusters=cluster,
to_shuffle=False)
zero_first_second_activity[file_idx][cluster] = activity_dictionary[cluster]
zero_first_second_purged_spikes[file_idx][cluster] = purged_spikes_dictionary[cluster]
# get behavior onsets
session_variables = {0: {}, 1: {}, 2: {}}
zero_first_second_behavior = {0: [], 1: [], 2: []}
for file_idx, one_file in enumerate(self.input_012):
ses_name, session_vars = sessions2load.Session(session=one_file).data_loader(extract_variables=['speeds', 'framerate'])
session_variables[file_idx] = session_vars
zero_first_second_behavior[file_idx] = find_variable_sequences(variable=session_vars['speeds'][:, 3],
threshold_low=speed_threshold_low,
threshold_high=speed_threshold_high,
min_seq_duration=speed_min_seq_duration,
camera_framerate=session_variables[file_idx]['framerate'])
# find session with least events and get that number
max_event_num_all_sessions = min([len(list(value)) for value in zero_first_second_behavior.values()])
# get raster plot
if discontinuous_raster:
raster_dictionary = {}
for cluster in get_clusters:
pu_sp_tr_lst = []
es_lst = []
cam_fr = []
for session_idx in range(len(self.input_012)):
cam_fr.append(session_variables[session_idx]['framerate'])
es_lst.append(zero_first_second_behavior[session_idx])
if cluster in zero_first_second_purged_spikes[session_idx].keys():
pu_sp_tr_lst.append(zero_first_second_purged_spikes[session_idx][cluster])
else:
pu_sp_tr_lst.append(np.empty(1))
raster_dictionary[cluster] = discontinuous_raster_preparation(purged_spike_arr=np.array(pu_sp_tr_lst),
event_start_arr=np.array(es_lst),
event_number=max_event_num_all_sessions,
camera_framerate_arr=np.array(cam_fr),
window_size=speed_min_seq_duration)
# get PETHs for each cluster and smooth if necessary
peth_dictionary = {}
for cluster in get_clusters:
peth_dictionary[cluster] = {}
input_arr_ls = []
esf_lst = []
for session in zero_first_second_activity.keys():
esf_lst.append(zero_first_second_behavior[session])
if cluster in zero_first_second_activity[session].keys():
input_arr_ls.append(zero_first_second_activity[session][cluster]['activity'].todense().astype(np.float32))
else:
input_arr_ls.append(np.zeros(session_variables[session]['total_frame_num']).astype(np.float32))
peth_array = calculate_discontinuous_peth(input_array_lst=input_arr_ls,
esf=esf_lst,
event_number=max_event_num_all_sessions,
bin_size_ms=bin_size_ms,
window_size=window_size)
# smooth every sequence separately
if to_smooth:
total_window = int(round((window_size / (bin_size_ms / 1e3))))
switch_points = np.arange(0, total_window, total_window // 3)
for epoch in range(max_event_num_all_sessions):
for sp_idx, sp in enumerate(switch_points):
peth_array[epoch, sp:sp + (total_window // 3)] = gaussian_smoothing(array=peth_array[epoch, sp:sp + (total_window // 3)], sigma=smooth_sd, axis=0)
peth_dictionary[cluster]['discontinuous_peth'] = peth_array
if discontinuous_raster:
return peth_dictionary, raster_dictionary
else:
return peth_dictionary
def correlate_activity(self, **kwargs):
"""
Description
----------
This method correlates spiking activity between different clusters within a recording
condition and then compares how it differs across conditions (e.g. light/dark).
----------
Parameters
----------
**kwargs (dictionary)
to_corr (bool)
To correlate or use covariance; defaults to True.
condense_bin_ms (int)
The size of bin for spikes; defaults to 100 (ms).
specific_date (dict)
Selected dates for specific animals; defaults to *see below*.
corr_input_dict (dict)
Parameters that find appropriate clusters; defaults to *see below*.
----------
Returns
----------
activity_correlation (fig)
A figure of activity correlations.
----------
"""
to_corr = kwargs['to_corr'] if 'to_corr' in kwargs.keys() and type(kwargs['to_corr']) == bool else True
condense_bin_ms = kwargs['condense_bin_ms'] if 'condense_bin_ms' in kwargs.keys() and type(kwargs['condense_bin_ms']) == int else 100
specific_date = kwargs['specific_date'] if 'specific_date' in kwargs.keys() and type(kwargs['specific_date']) == dict else {'bruno': ['020520', '030520'],
'roy': True,
'jacopo': True,
'crazyjoe': True,
'frank': True,
'johnjohn': ['210520', '220520'],
'kavorka': True}
corr_input_dict = kwargs['corr_input_dict'] if 'corr_input_dict' in kwargs.keys() and type(kwargs['corr_input_dict']) == dict else {'light1': {'area_filter': 'V',
'animal_filter': True,
'profile_filter': True,
'session_id_filter': 's1',
'session_non_filter': True,
'session_type_filter': True,
'cluster_type_filter': 'good',
'specific_date': None},
'dark': {'area_filter': 'V',
'animal_filter': True,
'profile_filter': True,
'session_id_filter': True,
'session_non_filter': True,
'session_type_filter': ['dark'],
'cluster_type_filter': 'good',
'specific_date': None}}
cluster_dict = {}
for session_type in corr_input_dict.keys():
cluster_dict[session_type] = quantify_ratemaps.RatemapCharacteristics(pkl_sessions_dir=self.pkl_files_dir,
area_filter=corr_input_dict[session_type]['area_filter'],
animal_filter=corr_input_dict[session_type]['animal_filter'],
profile_filter=corr_input_dict[session_type]['profile_filter'],
session_id_filter=corr_input_dict[session_type]['session_id_filter'],
session_non_filter=corr_input_dict[session_type]['session_non_filter'],
session_type_filter=corr_input_dict[session_type]['session_type_filter'],
cluster_type_filter=corr_input_dict[session_type]['cluster_type_filter'],
cluster_groups_dir=self.cluster_groups_dir,
sp_profiles_csv=self.sp_profiles_csv,
specific_date=corr_input_dict[session_type]['specific_date']).file_finder(return_clusters=True,
sort_ch_num=True)
# get clusters that are present in both sessions
acceptable_cluster_dict = {}
for st_idx, session_type in enumerate(cluster_dict.keys()):
if st_idx == 0:
for animal in cluster_dict[session_type].keys():
for bank in cluster_dict[session_type][animal].keys():
for cl in cluster_dict[session_type][animal][bank]:
if cl in cluster_dict[list(cluster_dict.keys())[1]][animal][bank]:
if session_type not in acceptable_cluster_dict.keys():
acceptable_cluster_dict[session_type] = {}
if animal not in acceptable_cluster_dict[session_type].keys():
acceptable_cluster_dict[session_type][animal] = {}
if bank not in acceptable_cluster_dict[session_type][animal].keys():
acceptable_cluster_dict[session_type][animal][bank] = []
acceptable_cluster_dict[session_type][animal][bank].append(cl)
# get activity for each cluster
activity_dict = {}
for session_type in acceptable_cluster_dict.keys():
for animal in acceptable_cluster_dict[session_type].keys():
activity_dict[animal] = {}
for bank in acceptable_cluster_dict[session_type][animal].keys():
activity_dict[animal][bank] = {key: {} for key in cluster_dict.keys()}
for pkl_file in os.listdir(self.pkl_files_dir):
first_for_loop = False
if (specific_date[animal] is True or any(one_date in pkl_file for one_date in specific_date[animal])) and \
animal in pkl_file and \
bank in pkl_file and \
(corr_input_dict[session_type]['session_id_filter'] is True or corr_input_dict[session_type]['session_id_filter'] in pkl_file) and \
(corr_input_dict[session_type]['session_non_filter'] is True or corr_input_dict[session_type]['session_non_filter'] not in pkl_file) and \
(corr_input_dict[session_type]['session_type_filter'] is True or any(
one_word in pkl_file for one_word in corr_input_dict[session_type]['session_type_filter']) in pkl_file):
for pkl_file2 in os.listdir(self.pkl_files_dir):
if (specific_date[animal] is True or any(one_date in pkl_file2 for one_date in specific_date[animal])) and \
animal in pkl_file2 and \
bank in pkl_file2 and \
(corr_input_dict[list(cluster_dict.keys())[1]]['session_id_filter'] is True or corr_input_dict[list(cluster_dict.keys())[1]][
'session_id_filter'] in pkl_file2) and \
(corr_input_dict[list(cluster_dict.keys())[1]]['session_non_filter'] is True or corr_input_dict[list(cluster_dict.keys())[1]][
'session_non_filter'] not in pkl_file2) and \
(corr_input_dict[list(cluster_dict.keys())[1]]['session_type_filter'] is True or any(
one_word in pkl_file2 for one_word in corr_input_dict[list(cluster_dict.keys())[1]]['session_type_filter'])):
print(pkl_file, pkl_file2)
file_id, \
activity_dictionary, \
purged_spikes_dictionary = Spikes(input_file=f'{self.pkl_files_dir}{os.sep}{pkl_file}').convert_activity_to_frames_with_shuffles(
get_clusters=acceptable_cluster_dict[session_type][animal][bank],
to_shuffle=False,
condense_arr=True,
condense_bin_ms=condense_bin_ms)
file_id2, \
activity_dictionary2, \
purged_spikes_dictionary2 = Spikes(input_file=f'{self.pkl_files_dir}{os.sep}{pkl_file2}').convert_activity_to_frames_with_shuffles(
get_clusters=acceptable_cluster_dict[session_type][animal][bank],
to_shuffle=False,
condense_arr=True,
condense_bin_ms=condense_bin_ms)
activity_dict[animal][bank][session_type] = activity_dictionary
activity_dict[animal][bank][list(cluster_dict.keys())[1]] = activity_dictionary2
first_for_loop = True
break
if first_for_loop:
break
# place activity in arrays
rearranged_activity_dict = {}
for animal in activity_dict.keys():
rearranged_activity_dict[animal] = {}
for bank in activity_dict[animal].keys():
rearranged_activity_dict[animal][bank] = {}
for session_type in cluster_dict.keys():
for cl_idx, cl in enumerate(activity_dict[animal][bank][session_type].keys()):
if cl_idx == 0:
arr_len = np.shape(activity_dict[animal][bank][session_type][cl]['activity'].todense())[0]
break
rearranged_activity_dict[animal][bank][session_type] = np.zeros((len(activity_dict[animal][bank][session_type].keys()), arr_len))
for cl_idx, cl in enumerate(activity_dict[animal][bank][session_type].keys()):
rearranged_activity_dict[animal][bank][session_type][cl_idx, :] = activity_dict[animal][bank][session_type][cl]['activity'].todense()
# calculate corr/cov and plot
for animal in rearranged_activity_dict.keys():
for bank in rearranged_activity_dict[animal].keys():
results = {}
for session_type in rearranged_activity_dict[animal][bank].keys():
if to_corr:
results[session_type] = | np.corrcoef(x=rearranged_activity_dict[animal][bank][session_type]) | numpy.corrcoef |
# Copyright (c) 2017 The Khronos Group Inc.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from __future__ import division
import sys
import os
import shutil
import tarfile
import inspect
import traceback
import numpy as np
import tensorflow as tf
if sys.version_info[0] < 3:
from Queue import Queue
else:
from queue import Queue
from tensorflow.python.ops import gen_math_ops as tf_ops
from tensorflow.contrib.layers.python.layers import layers as tf_layers
from tensorflow.python.layers import utils
RedText = "\x1b[31m"
ResetStyle = "\x1b[0m"
def tf_version_greater(major, minor):
str = tf.__version__
i = str.index('.')
j = str.index('.', i+1)
return (int(str[:i]), int(str[i+1:j])) >= (major, minor)
def print_error(msg, stack):
sys.stderr.write("%sError: %s%s\n" % (RedText, msg, ResetStyle))
if stack is not None:
traceback.print_list(stack)
def print_warning(msg):
sys.stderr.write("%sWarning: %s%s\n" % (RedText, msg, ResetStyle))
def undecorate(decorated, orig_name=None):
if orig_name is None:
orig_name = decorated.__name__
if not hasattr(decorated, "__closure__") or not decorated.__closure__:
return decorated
for obj in (c.cell_contents for c in decorated.__closure__):
if hasattr(obj, "__name__") and obj.__name__ == orig_name:
return obj
if hasattr(obj, "__closure__") and obj.__closure__:
found = undecorate(obj, orig_name)
if found:
return found
return None
class InvocationTrace:
def __init__(self, functions, handler):
self.frame = None
self.invocations = list()
self.handler = handler
self.func_names = set()
self.qualified = {}
for func in functions:
undecorated = undecorate(func)
self.func_names.add(undecorated.__name__)
self.qualified[undecorated.__module__ + '.' + undecorated.__name__] = func
def __call__(self, frame, event, result):
func_name = frame.f_code.co_name
if func_name == '__init__':
result = frame.f_locals.get('self')
if result is not None:
func_name = result.__class__.__name__
if func_name not in self.func_names:
return
mod = inspect.getmodule(frame)
if mod is None:
return
func_name = mod.__name__ + '.' + func_name
if event == 'call':
if self.frame is None:
func = self.qualified.get(func_name)
if func is not None:
arg_values = inspect.getargvalues(frame)
self.frame = frame
self.func = func
self.args = {key: value for (key,value) in arg_values.locals.items() if key in arg_values.args}
elif event == 'return':
if self.frame == frame and result is not None:
if isinstance(result, (list, dict)):
result = result.copy()
results = result if isinstance(result, tuple) else (result, )
stack = traceback.extract_stack(frame.f_back)
self.invocations.append((self.func, self.args, results, stack))
if self.handler:
self.handler(self.func, self.args, results, stack)
self.frame = None
return self
class TF2NNEFConverter:
def __init__(self, producers, exporters, reader, output_path):
self.producers = producers
self.exporters = exporters
self.reader = reader
self.consumrs = {}
self.tensor_names = {}
self.tensor_counts = {}
self.activations = []
self.output_path = output_path
self.fused = set()
for invocation in producers.values():
args = invocation[1]
for arg in args.values():
if isinstance(arg, (tf.Tensor, tf.Variable)):
self.consumrs.setdefault(arg, []).append(invocation)
def producer(self, tensor):
return self.producers.get(tensor)
def consumers(self, tensor):
return self.consumrs.get(tensor)
def consumer(self, tensor):
consumers = self.consumrs.get(tensor)
return consumers[0] if consumers is not None and len(consumers) == 1 else None
def exporter(self, func):
item = self.exporters.get(func)
return item[0] if isinstance(item, tuple) else item
def make_fused(self, tensor):
self.fused.add(tensor)
def is_fused(self, tensor):
return tensor in self.fused
def make_constant(self, tf_tensor, nnef_value):
self.tensor_names[tf_tensor] = nnef_value
def make_tensor(self, tf_tensor, nnef_name, indexed=True):
name = self.tensor_names.get(tf_tensor)
if name is not None:
return name
if indexed:
count = self.tensor_counts.get(nnef_name, 1)
self.tensor_counts[nnef_name] = count + 1
indexed_name = nnef_name + str(count)
else:
indexed_name = nnef_name
self.tensor_names[tf_tensor.value() if isinstance(tf_tensor, tf.Variable) else tf_tensor] = indexed_name
self.activations.append((tf_tensor, indexed_name))
return indexed_name
def make_passthrough_tensor(self, tf_tensor_in, tf_tensor_out):
variable = isinstance(tf_tensor_out, tf.Variable)
self.tensor_names[tf_tensor_out.value() if variable else tf_tensor_out] = self.nnef_tensor(tf_tensor_in)
def nnef_tensor(self, tf_tensor):
if isinstance(tf_tensor, (float, int)):
return str(float(tf_tensor))
elif isinstance(tf_tensor, tf.Variable):
return self.tensor_names[tf_tensor.value()]
else:
return self.tensor_names[tf_tensor]
def nnef_op(self, func):
item = self.exporters.get(func)
return item[1] if isinstance(item, tuple) else None
@staticmethod
def nnef_shape(shape, stack=None, is_filter=False, is_broadcast=False):
if isinstance(shape, tf.Tensor):
shape = tf.contrib.util.constant_value(shape)
if shape is None:
print_error('cannot handle dynamic tensor shape', stack)
return []
if isinstance(shape, tf.TensorShape):
shape = shape.as_list()
if not isinstance(shape, list):
shape = list(shape)
shape = [s.value if isinstance(s, tf.Dimension) else int(s) for s in shape]
if len(shape) == 0:
return []
elif len(shape) == 1:
return [1, shape[0]] if is_broadcast else [shape[0]]
elif len(shape) == 2:
return shape
else:
if is_filter:
return [shape[-1], shape[-2]] + shape[:-2]
else:
return [shape[0], shape[-1]] + shape[1:-1]
@staticmethod
def nnef_axis(axis, rank):
if axis < 0:
axis = rank + axis
if rank == 1:
return 1
elif rank == 2:
return axis
else:
if axis == 0:
return 0
elif axis == rank - 1:
return 1
else:
return axis + 1
@staticmethod
def nnef_axes(axis, rank):
if isinstance(axis, (list, tuple)):
return [TF2NNEFConverter.nnef_axis(a, rank) for a in axis]
else:
return [TF2NNEFConverter.nnef_axis(axis, rank)]
@staticmethod
def nnef_bool(value):
if value is None:
value = False
return 'true' if value else 'false'
@staticmethod
def nnef_array(value, rank):
if isinstance(value, list):
return value
elif isinstance(value, tuple):
return list(value)
else:
return [value] * rank
@staticmethod
def nnef_padding(padding, rank):
return [] if padding.upper() == 'SAME' else [(0, 0)] * rank
@staticmethod
def nnef_padding_ex(padding, input_sizes, filter_sizes, strides):
def same_padding(input_size, filter_size, stride):
output_size = int(np.ceil(float(input_size) / float(stride)))
pad_total = (output_size - 1) * stride + filter_size - input_size
if pad_total >= 0:
pad_front = pad_total // 2
pad_back = pad_total - pad_front
return (pad_front, pad_back)
else:
return (0, pad_total)
def valid_padding(input_size, filter_size, stride):
output_size = int(np.ceil(float(input_size - filter_size + 1) / float(stride)))
pad_total = (output_size - 1) * stride + filter_size - input_size
return (0, pad_total)
return [same_padding(input_size, filter_size, stride) if padding.upper() == 'SAME' else valid_padding(input_size, filter_size, stride)
for (input_size, filter_size, stride) in zip(input_sizes, filter_sizes, strides)]
@staticmethod
def nnef_tensor_shuffle_dims(tensor, is_filter, is_broadcast):
rank = tensor.ndim
if rank == 0:
return tensor
elif rank == 1:
return np.expand_dims(tensor, axis=0) if is_broadcast else tensor
elif rank == 2:
return tensor
else:
axes = [rank-1, rank-2] + list(range(rank-2)) if is_filter else [0, rank-1] + list(range(1,rank-1))
return np.transpose(tensor, axes)
@staticmethod
def nnef_ids(ids):
return "[" + ", ".join(map(str, ids)) + "]"
@staticmethod
def dilated_size(size, dilation):
return [(s - 1) * d + 1 for (s, d) in zip(size, dilation)]
def propagate_padding(self, input, padding, border, spatial, stack):
producer = self.producer(input)
if producer is not None and producer[0] == tf.pad:
if len(padding) == 0:
print_error("only 'VALID' padding is accepted after an explicit 'pad' operation", stack)
args = producer[1]
border = args['mode'].lower()
if border == 'symmetric':
border = 'reflect-even'
paddings = args['paddings']
paddings = paddings[1:-1] if spatial else [paddings[0], paddings[-1]] + paddings[1:-1]
padding = [tuple(p) for p in paddings]
return padding, border
def propagate_space_to_batch(self, input, dilation, padding):
producer = self.producer(input)
if producer is not None and (producer[0] == tf.space_to_batch_nd or producer[0] == tf.space_to_batch):
args = producer[1]
input = args['input']
dilation = args['block_shape'].tolist()
padding = 'SAME' if args['paddings'].any() else 'VALID'
return input, dilation, padding
def propagate_batch_to_space(self, output):
consumer = self.consumer(output)
if consumer is not None and (consumer[0] == tf.batch_to_space_nd or consumer[0] == tf.batch_to_space):
results = consumer[2]
return results[0]
return output
def is_binary_op(self, func):
return self.exporter(func) == export_binary
def is_broadcast(self, tensor):
shape = tensor.shape
if isinstance(shape, tf.TensorShape):
shape = shape.dims
if len(shape) != 1:
return False
consumers = self.consumers(tensor)
if consumers is None:
return False
for invocation in consumers:
func, args = invocation[:2]
if self.is_binary_op(func):
x = args['x']
other = args['y'] if tensor == x else x
elif func == tf.nn.bias_add:
other = args['value']
elif func == tf.nn.batch_normalization or func == tf.nn.fused_batch_norm:
other = args['x']
else:
return False
if isinstance(other, tf.Variable):
other = other.value()
if not isinstance(other, tf.Tensor):
return False
if other.shape[-1] != tensor.shape[0]:
return False
return True
def is_filter(self, tensor):
consumers = self.consumers(tensor)
if consumers is not None:
for invocation in consumers:
func, args = invocation[:2]
if func in [tf.nn.conv1d, tf.nn.atrous_conv2d, tf.nn.atrous_conv2d_transpose] \
and args['filters'] == tensor:
return True
elif func in [tf.nn.conv2d, tf.nn.conv3d, tf.nn.convolution,
tf.nn.conv2d_transpose, tf.nn.conv3d_transpose,
tf.nn.depthwise_conv2d, tf.nn.depthwise_conv2d_native,
tf.nn.depthwise_conv2d_native_backprop_input] \
and args['filter'] == tensor:
return True
elif func == tf.nn.separable_conv2d:
if args['depthwise_filter'] == tensor or args['pointwise_filter'] == tensor:
return True
return False
def is_depthwise(self, tensor):
consumers = self.consumers(tensor)
if consumers is not None:
for invocation in consumers:
func, args = invocation[:2]
if func in [tf.nn.depthwise_conv2d, tf.nn.depthwise_conv2d_native,
tf.nn.depthwise_conv2d_native_backprop_input] \
and args['filter'] == tensor:
return True
elif func == tf.nn.separable_conv2d:
if args['depthwise_filter'] == tensor:
return True
return False
def export_skip(func, args, results, stack, converter):
return None
def export_passthrough(func, args, results, stack, converter):
arg = converter.exporters.get(func)[1]
converter.make_passthrough_tensor(args[arg], results[0])
return None
def export_placeholder(func, args, results, stack, converter):
result = results[0]
shape = converter.nnef_shape(args['shape'], stack=stack, is_broadcast=converter.is_broadcast(result))
name = args['name']
if name is not None:
output = converter.make_tensor(result, name, indexed=False)
else:
output = converter.make_tensor(result, 'input')
return "{} = external(shape = {})".format(output, shape)
def export_variable(func, args, results, stack, converter):
name = args['name']
if name is None or name == '':
print_error("non-empty 'name' argument must be provided for {}".
format("tf.Variable()" if func == tf.Variable else "tf.get_variable()"), stack)
return None
if func == tf.get_variable:
initializer = args.get('initializer')
if isinstance(initializer, np.ndarray):
shape = initializer.shape
elif isinstance(initializer, (int, float)):
shape = [1,1]
else:
shape = args['shape']
else:
shape = tf.convert_to_tensor(args['initial_value']).shape
result = results[0]
is_filter = converter.is_filter(result)
is_depthwise = converter.is_depthwise(result)
is_broadcast = converter.is_broadcast(result)
shape = converter.nnef_shape(shape, stack=stack, is_filter=is_filter, is_broadcast=is_broadcast)
pos = name.rfind('/')
output = converter.make_tensor(result, name[pos + 1:] if pos != -1 else name)
if is_filter and is_depthwise:
shape[0] *= shape[1]
shape[1] = 1
if converter.reader:
key = result.name[:-2]
if converter.reader.has_tensor(key):
tensor = converter.reader.get_tensor(key)
if is_filter and is_depthwise:
tensor = np.reshape(tensor, newshape = tensor.shape[:-2] + (1, tensor.shape[-2] * tensor.shape[-1]))
filename = converter.output_path + '/' + name + '.dat'
write_nnef_tensor(filename, tensor, is_filter=is_filter, is_broadcast=is_broadcast)
else:
print_error("variable '{}' not found in checkpoint".format(key), stack)
return "{} = variable(shape = {}, label = '{}')".format(output, shape, name)
def export_constant(func, args, results, stack, converter):
shape = args['shape']
value = args['value']
result = results[0]
singular = True
if shape is not None:
for s in shape:
if s != 1:
singular = False
if not isinstance(value, (np.ndarray, list, tuple)) and singular:
converter.make_constant(results[0], float(value))
return None
if not isinstance(value, np.ndarray):
value = np.array(value, dtype=np.float32)
if value.size == 1 and singular:
converter.make_constant(results[0], value.flatten()[0])
return None
if shape is None:
shape = list(value.shape)
is_broadcast = converter.is_broadcast(result)
shape = converter.nnef_shape(shape, stack=stack, is_broadcast=is_broadcast)
value = converter.nnef_tensor_shuffle_dims(value, is_filter=False, is_broadcast=is_broadcast).flatten().tolist()
output = converter.make_tensor(results[0], 'const')
return '{} = constant(shape = {}, value = {})'.format(output, shape, value)
def export_conv(func, args, results, stack, converter):
kernel = args['filter']
if isinstance(kernel, tf.Variable):
kernel = kernel.value()
value = args.get('input')
if value is None:
value = args['value']
input = converter.nnef_tensor(value)
filter = converter.nnef_tensor(kernel)
size = kernel.shape.as_list()[:-2]
strides = list(args['strides'])[1:-1]
rate = args.get('rate', args.get('dilation_rate'))
rate = list(rate) if rate else [1] * len(size)
filter_sizes = converter.dilated_size(size, rate)
padding = args['padding']
border = 'constant'
value, rate, padding = converter.propagate_space_to_batch(value, rate, padding)
result = converter.propagate_batch_to_space(results[0])
bias = 0.0
consumers = converter.consumers(result)
if consumers is not None and len(consumers) == 1:
invocation = consumers[0]
_func, _args, _res = invocation[:3]
if _func == tf.nn.bias_add and _args["value"] == result:
bias = converter.nnef_tensor(_args["bias"])
result = _res[0]
converter.make_fused(result)
elif _func in [tf.add, tf_ops.add]:
if _args["x"] == result:
bias = converter.nnef_tensor(_args["y"])
elif _args["y"] == result:
bias = converter.nnef_tensor(_args["x"])
result = _res[0]
converter.make_fused(result)
output_shape = args.get('output_shape')
if output_shape is not None:
if isinstance(output_shape, tf.Tensor):
output_shape = tf.contrib.util.constant_value(output_shape)
if output_shape is None:
output_shape = result.get_shape()
if output_shape is not None:
output_shape = output_shape.as_list()
if None in output_shape:
output_shape = None
if output_shape is None:
print_warning("dynamic 'output_shape' cannot be evaluated, reverting to default")
value_shape = value.shape.as_list()[1:-1]
input_shape = output_shape[1:-1] if output_shape is not None else \
[utils.deconv_output_length(value_shape[i], filter_sizes[i], padding.lower(), strides[i]) for i in range(len(value_shape))]
padding = converter.nnef_padding_ex(padding, input_shape, filter_sizes, strides)
else:
padding = converter.nnef_padding(padding, len(size))
padding, border = converter.propagate_padding(value, padding, border, spatial=True, stack=stack)
op = converter.nnef_op(func)
output = converter.make_tensor(result, 'conv' if op == 'planewise_conv' else op)
return "{} = {}({}, {}, {}, padding = {}, border = '{}', stride = {}, dilation = {})" \
.format(output, op, input, filter, bias, padding, border, strides, rate)
def export_convolution(func, args, results, stack, converter):
args['strides'] = [1] + list(args['strides']) + [1]
return export_conv(func, args, results, stack, converter)
def export_separable_conv(func, args, results, stack, converter):
value = args['input']
depth_kernel = args['depthwise_filter']
point_kernel = args['pointwise_filter']
if isinstance(depth_kernel, tf.Variable):
depth_kernel = depth_kernel.value()
if isinstance(point_kernel, tf.Variable):
point_kernel = point_kernel.value()
input = converter.nnef_tensor(value)
depth_filter = converter.nnef_tensor(depth_kernel)
point_filter = converter.nnef_tensor(point_kernel)
size = depth_kernel.shape.as_list()[:-2]
strides = converter.nnef_array(args['strides'][1:-1], 2)
rate = converter.nnef_array(args['rate'], 2)
padding = converter.nnef_padding(args['padding'], len(size))
border = 'constant'
padding, border = converter.propagate_padding(value, padding, border, spatial=True, stack=stack)
output = converter.make_tensor(results[0], 'conv')
return "{} = separable_conv({}, plane_filter = {}, point_filter = {}, padding = {}, border = '{}', stride = {}, dilation = {})" \
.format(output, input, depth_filter, point_filter, padding, border, strides, rate)
def export_pool(func, args, results, stack, converter):
value = args['value']
input = converter.nnef_tensor(value)
size = converter.nnef_shape(args['ksize'], stack=stack)
strides = converter.nnef_shape(args['strides'], stack=stack)
padding = converter.nnef_padding(args['padding'], len(size))
border = 'ignore'
padding, border = converter.propagate_padding(value, padding, border, spatial=False, stack=stack)
op = converter.nnef_op(func)
output = converter.make_tensor(results[0], 'pool')
return "{} = {}({}, size = {}, padding = {}, border = '{}', stride = {})".format(output, op, input, size, padding, border, strides)
def export_activation(func, args, results, stack, converter):
x = converter.nnef_tensor(args['features'])
op = converter.nnef_op(func)
output = converter.make_tensor(results[0], op)
return '{} = {}({})'.format(output, op, x)
def export_unary(func, args, results, stack, converter):
x = converter.nnef_tensor(args['x'])
op = converter.nnef_op(func)
output = converter.make_tensor(results[0], op)
return '{} = {}({})'.format(output, op, x)
def export_binary(func, args, results, stack, converter):
x = converter.nnef_tensor(args['x'])
y = converter.nnef_tensor(args['y'])
op = converter.nnef_op(func)
output = converter.make_tensor(results[0], op)
return '{} = {}({}, {})'.format(output, op, x, y)
def export_squared_diff(func, args, results, stack, converter):
x = converter.nnef_tensor(args['x'])
y = converter.nnef_tensor(args['y'])
output = converter.make_tensor(results[0], 'diff')
return '{} = sqr({} - {})'.format(output, x, y)
def export_where(func, args, results, stack, converter):
c = converter.nnef_tensor(args['condition'])
x = converter.nnef_tensor(args['x'])
y = converter.nnef_tensor(args['y'])
if x is None or y is None:
print_error("arguments must not be None in tf.where() operation", stack)
return None
output = converter.make_tensor(results[0], 'select')
return '{} = select({}, {}, {})'.format(output, c, x, y)
def export_reduce(func, args, results, stack, converter):
tensor = args['input_tensor']
input = converter.nnef_tensor(tensor)
rank = len(tensor.shape.as_list())
axis = args['axis']
axes = sorted(converter.nnef_axes(axis, rank)) if axis else list(range(rank))
op = converter.nnef_op(func)
output = converter.make_tensor(results[0], 'reduce')
return '{} = {}({}, axes = {})'.format(output, op, input, axes)
def export_lrn(func, args, results, stack, converter):
input = converter.nnef_tensor(args['input'])
depth_radius = args['depth_radius']
depth_size = 2 * depth_radius + 1
bias = float(args['bias'])
alpha = float(args['alpha'] * depth_size)
beta = float(args['beta'])
size = [1, depth_size, 1, 1]
output = converter.make_tensor(results[0], 'norm')
return '{} = local_response_normalization({}, size = {}, alpha = {}, beta = {}, bias = {})'\
.format(output, input, size, alpha, beta, bias)
def export_batch_normalization(func, args, results, stack, converter):
input = converter.nnef_tensor(args['x'])
mean = converter.nnef_tensor(args['mean'])
variance = converter.nnef_tensor(args['variance'])
offset = converter.nnef_tensor(args['offset']) if args.get('offset') is not None else float(0)
scale = converter.nnef_tensor(args['scale']) if args.get('scale') is not None else float(1)
epsilon = float(args.get('variance_epsilon', args.get('epsilon')))
output = converter.make_tensor(results[0], 'norm')
return '{} = batch_normalization({}, mean = {}, variance = {}, offset = {}, scale = {}, epsilon = {})'\
.format(output, input, mean, variance, offset, scale, epsilon)
def export_l2_normalization(func, args, results, stack, converter):
input = converter.nnef_tensor(args['x'])
axes = sorted(converter.nnef_axes(args['dim']))
epsilon = float(args.get('epsilon'))
output = converter.make_tensor(results[0], 'norm')
return "{} = l2_normalization({}, axes = {}, bias = {})".format(output, input, axes, epsilon)
def export_matmul(func, args, results, stack, converter):
A = converter.nnef_tensor(args['a'])
B = converter.nnef_tensor(args['b'])
trA = converter.nnef_bool(args['transpose_a'])
trB = converter.nnef_bool(args['transpose_b'])
output = converter.make_tensor(results[0], 'matmul')
return '{} = matmul({}, {}, trA = {}, trB = {})'.format(output, A, B, trA, trB)
def export_assign(func, args, results, stack, converter):
ref = converter.nnef_tensor(args['ref'])
value = converter.nnef_tensor(args['value'])
output = converter.make_tensor(results[0], 'assign')
return '{} = update({}, {})'.format(output, ref, value)
def export_add_n(func, args, results, stack, converter):
inputs = args['inputs']
value = converter.nnef_ids([converter.nnef_tensor(input) for input in inputs])
output = converter.make_tensor(results[0], 'add')
return '{} = add_n({})'.format(output, value)
def export_bias_add(func, args, results, stack, converter):
input = converter.nnef_tensor(args['value'])
bias = converter.nnef_tensor(args['bias'])
output = converter.make_tensor(results[0], 'add')
return '{} = add({}, {})'.format(output, input, bias)
def export_concat(func, args, results, stack, converter):
values = args['values']
rank = values[0].shape.ndims
axis = converter.nnef_axis(args['axis'], rank)
parts = converter.nnef_ids([converter.nnef_tensor(value) for value in values])
output = converter.make_tensor(results[0], 'concat')
return '{} = concat({}, axis = {})'.format(output, parts, axis)
def export_split(func, args, results, stack, converter):
value = args['value']
whole = converter.nnef_tensor(value)
num_or_sizes = args['num_or_size_splits']
ratios = num_or_sizes if isinstance(num_or_sizes, list) else [1] * num_or_sizes
rank = value.shape.ndims
axis = converter.nnef_axis(args['axis'], rank)
output = converter.nnef_ids([converter.make_tensor(result, 'split') for result in results[0]])
return '{} = split({}, axis = {}, ratios = {})'.format(output, whole, axis, ratios)
def export_softmax(func, args, results, stack, converter):
logits = args['logits']
rank = len(logits.shape.as_list())
axis = sorted(converter.nnef_axes(args.get('dim', -1), rank))
parts = converter.nnef_tensor(logits)
output = converter.make_tensor(results[0], 'softmax')
return '{} = softmax({}, axes = {})'.format(output, parts, axis)
def export_moments(func, args, results, stack, converter):
value = args['x']
input = converter.nnef_tensor(value)
rank = value.shape.ndims
axes = sorted(converter.nnef_axes(args['axes'], rank))
mean = converter.make_tensor(results[0], 'mean')
variance = converter.make_tensor(results[1], 'variance')
return "{}, {} = moments({}, axes = {})".format(mean, variance, input, axes)
def export_reshape(func, args, results, stack, converter):
input = converter.nnef_tensor(args['tensor'])
shape = converter.nnef_shape(args['shape'], stack=stack)
output = converter.make_tensor(results[0], 'reshape')
return '{} = reshape({}, shape = {})'.format(output, input, shape)
def export_flatten(func, args, results, stack, converter):
value = args['inputs']
input = converter.nnef_tensor(value)
output = converter.make_tensor(results[0], 'reshape')
return '{} = reshape({}, shape = [0, -1])'.format(output, input)
def export_expand_dims(func, args, results, stack, converter):
value = args['input']
rank = value.shape.ndims
input = converter.nnef_tensor(value)
axis = args['axis']
if axis is None:
axis = rank
shape = value.shape.as_list()
shape.insert(axis, 1)
shape = converter.nnef_shape(shape)
output = converter.make_tensor(results[0], 'reshape')
return '{} = reshape({}, shape = {})'.format(output, input, shape)
def export_squeeze(func, args, results, stack, converter):
value = args['input']
input = converter.nnef_tensor(value)
axis = args['axis']
if axis is not None:
axis = sorted(axis)
else:
shape = value.shape.as_list()
axis = [i for i in range(len(shape)) if shape[i] == 1]
rank = value.shape.ndims
if axis == list(range(rank - 1)) or axis == list(range(1,rank - 1)):
converter.make_passthrough_tensor(value, results[0])
return None
axes = converter.nnef_axes(axis, rank)
shape = ''
for a in range(0,rank):
if a not in axes:
if len(shape) != 0:
shape += ', '
shape += 'shape_of({})[{}]'.format(input, a)
output = converter.make_tensor(results[0], 'reshape')
return '{} = reshape({}, shape = [{}])'.format(output, input, shape)
def export_transpose(func, args, results, stack, converter):
value = args['a']
input = converter.nnef_tensor(value)
rank = value.shape.ndims
perm = args['perm']
if perm is None:
perm = list(reversed(range(rank)))
perm = converter.nnef_axes(perm, rank)
p = list(perm)
for i in range(len(perm)):
perm[converter.nnef_axis(i, rank)] = p[i]
output = converter.make_tensor(results[0], 'trans')
return '{} = transpose({}, perm = {})'.format(output, input, perm)
def export_resize_images(func, args, results, stack, converter):
value = args['images']
input = converter.nnef_tensor(value)
size = args['size']
method = args['method']
aligned = args['align_corners']
if isinstance(size, tf.Tensor):
print_error('cannot handle dynamic target size in tf.image.resize()', stack)
return None
input_size = [s.value if isinstance(s,tf.Dimension) else int(s) for s in value.shape[1:-1]]
size = [s.value if isinstance(s, tf.Dimension) else int(s) for s in size]
if size[0] == input_size[0] and size[1] == input_size[1]:
converter.make_passthrough_tensor(value, results[0])
return None
if (size[0] > input_size[0] and size[1] < input_size[1]) or (size[0] < input_size[0] and size[1] > input_size[1]):
print_error("resize must be up or down-sampling", stack)
return None
if size[0] > input_size[0]:
if size[0] % input_size[0] or size[1] % input_size[1]:
print_error('only integer factor resize allowed', stack)
return None
factor = [size[0] // input_size[0], size[1] // input_size[1]]
output = converter.make_tensor(results[0], 'upsample')
if method == tf.image.ResizeMethod.BILINEAR:
return "{} = multilinear_upsample({}, factor = {}, method = '{}', border = 'replicate')"\
.format(output, input, factor, 'aligned' if aligned else 'asymmetric')
elif method == tf.image.ResizeMethod.NEAREST_NEIGHBOR:
return "{} = nearest_upsample({}, factor = {})".format(output, input, factor)
else:
print_error("unsupported upsample method '{}'".format(method), stack)
return None
else:
if input_size[0] % size[0] or input_size[1] % size[1]:
print_error('only integer factor resize allowed', stack)
return None
factor = [input_size[0] // size[0], input_size[1] // size[1]]
output = converter.make_tensor(results[0], 'downsample')
if method == tf.image.ResizeMethod.AREA:
return "{} = area_downsample({}, factor = {})".format(output, input, factor)
elif method == tf.image.ResizeMethod.NEAREST_NEIGHBOR:
return "{} = nearest_downsample({}, factor = {})".format(output, input, factor)
else:
print_error("unsupported downsample method '{}'".format(method), stack)
return None
def export_resize_bilinear(func, args, results, stack, converter):
args['method'] = tf.image.ResizeMethod.BILINEAR
return export_resize_images(func, args, results, stack, converter)
def export_resize_bicubic(func, args, results, stack, converter):
args['method'] = tf.image.ResizeMethod.BICUBIC
return export_resize_images(func, args, results, stack, converter)
def export_resize_nearest(func, args, results, stack, converter):
args['method'] = tf.image.ResizeMethod.NEAREST_NEIGHBOR
return export_resize_images(func, args, results, stack, converter)
def export_resize_area(func, args, results, stack, converter):
args['method'] = tf.image.ResizeMethod.AREA
return export_resize_images(func, args, results, stack, converter)
def export_space_to_batch(func, args, results, stack, converter):
input = converter.nnef_tensor(args['input'])
block_shape = args['block_shape']
paddings = args['paddings']
output = converter.make_tensor(results[0], 'space2batch')
return "{} = space2batch({}, block_shape = {}, paddings = {})".format(output, input, block_shape, paddings)
def export_batch_to_space(func, args, results, stack, converter):
input = converter.nnef_tensor(args['input'])
block_shape = args['block_shape']
output = converter.make_tensor(results[0], 'batch2space')
return "{} = batch2space({}, block_shape = {})".format(output, input, block_shape)
DefaultExporters =\
{
tf.Variable: (export_variable, 'variable'),
tf.get_variable: (export_variable, 'variable'),
tf.placeholder: (export_placeholder, 'external'),
tf.constant: (export_constant, 'constant'),
tf.identity: (export_passthrough, 'input'),
tf.concat: (export_concat, 'concat'),
tf.split: (export_split, 'split'),
tf.reshape: (export_reshape, 'reshape'),
tf.squeeze: (export_squeeze, 'reshape'),
tf.expand_dims: (export_expand_dims, 'reshape'),
tf.transpose: (export_transpose, 'transpose'),
tf.stop_gradient: (export_passthrough, 'input'),
tf.cast: (export_passthrough, 'x'),
tf.pad: (export_passthrough, 'tensor'),
tf.add: (export_binary, 'add'),
tf.subtract: (export_binary, 'sub'),
tf.multiply: (export_binary, 'mul'),
tf.divide: (export_binary, 'div'),
tf.pow: (export_binary, 'pow'),
tf.squared_difference: (export_squared_diff, 'sqr'),
tf.logical_and: (export_binary, 'and'),
tf.logical_or: (export_binary, 'or'),
tf.negative: (export_unary, 'neg'),
tf.logical_not: (export_unary, 'not'),
tf.abs: (export_unary, 'abs'),
tf.sign: (export_unary, 'sign'),
tf.exp: (export_unary, 'exp'),
tf.log: (export_unary, 'log'),
tf.sqrt: (export_unary, 'sqrt'),
tf.rsqrt: (export_unary, 'rsqrt'),
tf.square: (export_unary, 'sqr'),
tf.floor: (export_unary, 'floor'),
tf.ceil: (export_unary, 'ceil'),
tf.round: (export_unary, 'round'),
tf.where: (export_where, 'select'),
tf.greater: (export_binary, 'gt'),
tf.greater_equal: (export_binary, 'ge'),
tf.less: (export_binary, 'lt'),
tf.less_equal: (export_binary, 'le'),
tf.equal: (export_binary, 'eq'),
tf.not_equal: (export_binary, 'ne'),
tf.minimum: (export_binary, 'min'),
tf.maximum: (export_binary, 'max'),
tf.assign: (export_assign, 'update'),
tf_ops.add: (export_binary, 'add'),
tf_ops.sub: (export_binary, 'sub'),
tf_ops.mul: (export_binary, 'mul'),
tf_ops.div: (export_binary, 'div'),
tf_ops.real_div: (export_binary, 'div'),
tf_ops._pow: (export_binary, 'pow'),
tf_ops.logical_and: (export_binary, 'and'),
tf_ops.logical_or: (export_binary, 'or'),
tf_ops.neg: (export_unary, 'neg'),
tf_ops.reciprocal: (export_unary, 'rcp'),
tf_ops.logical_not: (export_unary, 'not'),
tf_ops._abs: (export_unary, 'abs'),
tf_ops.sign: (export_unary, 'sign'),
tf_ops.exp: (export_unary, 'exp'),
tf_ops.log: (export_unary, 'log'),
tf_ops.square: (export_unary, 'sqr'),
tf_ops.floor: (export_unary, 'floor'),
tf_ops.ceil: (export_unary, 'ceil'),
tf_ops.round: (export_unary, 'round'),
tf_ops.greater: (export_binary, 'gt'),
tf_ops.greater_equal: (export_binary, 'ge'),
tf_ops.less: (export_binary, 'lt'),
tf_ops.less_equal: (export_binary, 'le'),
tf_ops.equal: (export_binary, 'eq'),
tf_ops.not_equal: (export_binary, 'ne'),
tf_ops.sqrt: (export_unary, 'sqrt'),
tf_ops.rsqrt: (export_unary, 'rsqrt'),
tf.sigmoid: (export_unary, 'sigmoid'),
tf.tanh: (export_unary, 'tanh'),
tf.reduce_sum: (export_reduce, 'sum_reduce'),
tf.reduce_mean: (export_reduce, 'mean_reduce'),
tf.reduce_max: (export_reduce, 'max_reduce'),
tf.matmul: (export_matmul, 'matmul'),
tf.add_n: (export_add_n, 'add_n'),
tf.nn.sigmoid: (export_unary, 'sigmoid'),
tf.nn.tanh: (export_unary, 'tanh'),
tf.nn.elu: (export_activation, 'elu'),
tf.nn.relu: (export_activation, 'relu'),
tf.nn.softsign: (export_activation, 'softsign'),
tf.nn.softplus: (export_activation, 'softplus'),
tf.nn.conv1d: (export_conv, 'conv'),
tf.nn.conv2d: (export_conv, 'conv'),
tf.nn.conv3d: (export_conv, 'conv'),
tf.nn.convolution: (export_convolution, 'conv'),
tf.nn.conv2d_transpose: (export_conv, 'deconv'),
tf.nn.conv3d_transpose: (export_conv, 'deconv'),
tf.nn.depthwise_conv2d: (export_conv, 'planewise_conv'),
tf.nn.depthwise_conv2d_native: (export_conv, 'planewise_conv'),
tf.nn.separable_conv2d: (export_separable_conv, 'conv'),
tf.nn.max_pool: (export_pool, 'max_pool'),
tf.nn.max_pool_with_argmax: (export_pool, 'max_pool_with_indices'),
tf.nn.avg_pool: (export_pool, 'avg_pool'),
tf.nn.dropout: (export_passthrough, 'x'),
tf.nn.bias_add: (export_bias_add, 'add'),
tf.nn.lrn: (export_lrn, 'local_response_normalization'),
tf.nn.local_response_normalization: (export_lrn, 'local_response_normalization'),
tf.nn.batch_normalization: (export_batch_normalization, 'batch_normalization'),
tf.nn.fused_batch_norm: (export_batch_normalization, 'batch_normalization'),
tf.nn.l2_normalize: (export_l2_normalization, 'l2_normalization'),
tf.nn.softmax: (export_softmax, 'softmax'),
tf.nn.moments: (export_moments, 'moments'),
tf.image.resize_images: export_resize_images,
tf.image.resize_bilinear: export_resize_bilinear,
tf.image.resize_nearest_neighbor: export_resize_nearest,
tf.image.resize_bicubic: export_resize_bicubic,
tf.image.resize_area: export_resize_area,
tf.space_to_batch: (export_passthrough, 'input'),
tf.space_to_batch_nd: (export_passthrough, 'input'),
tf.batch_to_space: export_skip,
tf.batch_to_space_nd: export_skip,
tf_layers.softmax: (export_softmax, 'softmax'),
tf_layers.flatten: (export_flatten, 'reshape'),
}
if tf_version_greater(1,3):
DefaultExporters.update(
{
tf.sinh: (export_unary, 'sinh'),
tf.cosh: (export_unary, 'cosh')
})
def unrolled_rnn(cell, inputs, sequence_length=None, initial_state=None, dtype=tf.float32, scope=None):
if sequence_length is None:
sequence_length = tf.constant(shape=[inputs.shape[0]], value=[float(inputs.shape[1])], dtype=tf.float32)
split_inputs = tf.split(inputs, axis=1, num_or_size_splits=inputs.shape[1])
if initial_state is not None:
c, h = initial_state
else:
c = tf.zeros(shape=[inputs.shape[0], inputs.shape[2]], dtype=dtype)
h = tf.zeros(shape=[inputs.shape[0], inputs.shape[2]], dtype=dtype)
_c = c
_h = h
output_list = []
with tf.variable_scope(scope or "rnn"):
for index, input in enumerate(split_inputs):
output, (c, h) = cell(tf.squeeze(input, axis=[1]), (c, h))
output_list.append(output)
condition = tf.equal(sequence_length, index + 1)
_c = tf.where(condition, c, _c)
_h = tf.where(condition, h, _h)
outputs = tf.concat(output_list, axis=1)
return outputs, (_c, _h)
def trace_invocations(func, functions, handler=None):
systrace = sys.gettrace()
trace = InvocationTrace(functions, handler)
sys.settrace(trace)
results = func()
sys.settrace(systrace)
if isinstance(results, (tf.Tensor, tf.Variable)):
outputs = { 'output': results }
elif isinstance(results, (list, tuple)):
outputs = {}
for i, result in enumerate(results):
if isinstance(result, (tf.Tensor, tf.Variable)):
outputs['output' + str(i+1)] = result
elif isinstance(results, dict):
outputs = {}
for name, result in results.items():
if isinstance(result, (tf.Tensor, tf.Variable)):
outputs[name] = result
return trace.invocations, outputs
def enumerate_dependencies(dependencies, targets, exclusions):
q = Queue()
s = set()
def insert(tensor,func,stack):
if tensor not in s:
if isinstance(tensor, tf.Variable):
tensor = tensor.value()
q.put((tensor,func,stack))
s.add(tensor)
for target in targets:
insert(target,None,None)
while not q.empty():
tensor, func, stack = q.get()
invocation = dependencies.get(tensor)
if invocation is None:
if func:
op = func.__module__ + '.' + func.__name__
print_error("tensor '{}' used by operation {} is not the result of any exported operation".format(tensor.name, op), stack)
else:
print_error("output tensor '{}' is not the result of any exported operation".format(tensor.name), stack)
continue
func, args, results, stack = invocation
exc = exclusions.get(func)
for key, arg in args.items():
if exc is not None and key in exc:
continue
if isinstance(arg, (list, tuple)):
for a in arg:
if isinstance(a, (tf.Tensor, tf.Variable)):
insert(a, func, stack)
elif isinstance(arg, (tf.Tensor, tf.Variable)):
insert(arg, func, stack)
return s
def write_nnef_version(file, major, minor):
np.asarray([0x4E, 0xEF], dtype=np.uint8).tofile(file)
| np.asarray([major,minor], dtype=np.uint8) | numpy.asarray |
#!/usr/bin/env python
#
# timeresp_test.py - test time response functions
# RMM, 17 Jun 2011 (based on TestMatlab from v0.4c)
#
# This test suite just goes through and calls all of the MATLAB
# functions using different systems and arguments to make sure that
# nothing crashes. It doesn't test actual functionality; the module
# specific unit tests will do that.
import unittest
import numpy as np
from control.timeresp import *
from control.statesp import *
from control.xferfcn import TransferFunction, _convert_to_transfer_function
from control.dtime import c2d
from control.exception import slycot_check
class TestTimeresp(unittest.TestCase):
def setUp(self):
"""Set up some systems for testing out MATLAB functions"""
A = np.matrix("1. -2.; 3. -4.")
B = np.matrix("5.; 7.")
C = np.matrix("6. 8.")
D = np.matrix("9.")
self.siso_ss1 = StateSpace(A, B, C, D)
# Create some transfer functions
self.siso_tf1 = TransferFunction([1], [1, 2, 1])
self.siso_tf2 = _convert_to_transfer_function(self.siso_ss1)
# Create MIMO system, contains ``siso_ss1`` twice
A = np.matrix("1. -2. 0. 0.;"
"3. -4. 0. 0.;"
"0. 0. 1. -2.;"
"0. 0. 3. -4. ")
B = np.matrix("5. 0.;"
"7. 0.;"
"0. 5.;"
"0. 7. ")
C = np.matrix("6. 8. 0. 0.;"
"0. 0. 6. 8. ")
D = np.matrix("9. 0.;"
"0. 9. ")
self.mimo_ss1 = StateSpace(A, B, C, D)
# Create discrete time systems
self.siso_dtf1 = TransferFunction([1], [1, 1, 0.25], True)
self.siso_dtf2 = TransferFunction([1], [1, 1, 0.25], 0.2)
self.siso_dss1 = tf2ss(self.siso_dtf1)
self.siso_dss2 = tf2ss(self.siso_dtf2)
self.mimo_dss1 = StateSpace(A, B, C, D, True)
self.mimo_dss2 = c2d(self.mimo_ss1, 0.2)
def test_step_response(self):
# Test SISO system
sys = self.siso_ss1
t = np.linspace(0, 1, 10)
youttrue = np.array([9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776])
# SISO call
tout, yout = step_response(sys, T=t)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# Play with arguments
tout, yout = step_response(sys, T=t, X0=0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
X0 = np.array([0, 0])
tout, yout = step_response(sys, T=t, X0=X0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
tout, yout, xout = step_response(sys, T=t, X0=0, return_x=True)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# Test MIMO system, which contains ``siso_ss1`` twice
sys = self.mimo_ss1
_t, y_00 = step_response(sys, T=t, input=0, output=0)
_t, y_11 = step_response(sys, T=t, input=1, output=1)
np.testing.assert_array_almost_equal(y_00, youttrue, decimal=4)
np.testing.assert_array_almost_equal(y_11, youttrue, decimal=4)
# Make sure continuous and discrete time use same return conventions
sysc = self.mimo_ss1
sysd = c2d(sysc, 1) # discrete time system
Tvec = np.linspace(0, 10, 11) # make sure to use integer times 0..10
Tc, youtc = step_response(sysc, Tvec, input=0)
Td, youtd = step_response(sysd, Tvec, input=0)
np.testing.assert_array_equal(Tc.shape, Td.shape)
np.testing.assert_array_equal(youtc.shape, youtd.shape)
def test_step_info(self):
# From matlab docs:
sys = TransferFunction([1,5,5],[1,1.65,5,6.5,2])
Strue = {
'RiseTime': 3.8456,
'SettlingTime': 27.9762,
'SettlingMin': 2.0689,
'SettlingMax': 2.6873,
'Overshoot': 7.4915,
'Undershoot': 0,
'Peak': 2.6873,
'PeakTime': 8.0530
}
S = step_info(sys)
# Very arbitrary tolerance because I don't know if the
# response from the MATLAB is really that accurate.
# maybe it is a good idea to change the Strue to match
# but I didn't do it because I don't know if it is
# accurate either...
rtol = 2e-2
np.testing.assert_allclose(
S.get('RiseTime'),
Strue.get('RiseTime'),
rtol=rtol)
np.testing.assert_allclose(
S.get('SettlingTime'),
Strue.get('SettlingTime'),
rtol=rtol)
np.testing.assert_allclose(
S.get('SettlingMin'),
Strue.get('SettlingMin'),
rtol=rtol)
np.testing.assert_allclose(
S.get('SettlingMax'),
Strue.get('SettlingMax'),
rtol=rtol)
np.testing.assert_allclose(
S.get('Overshoot'),
Strue.get('Overshoot'),
rtol=rtol)
np.testing.assert_allclose(
S.get('Undershoot'),
Strue.get('Undershoot'),
rtol=rtol)
np.testing.assert_allclose(
S.get('Peak'),
Strue.get('Peak'),
rtol=rtol)
np.testing.assert_allclose(
S.get('PeakTime'),
Strue.get('PeakTime'),
rtol=rtol)
np.testing.assert_allclose(
S.get('SteadyStateValue'),
2.50,
rtol=rtol)
def test_impulse_response(self):
# Test SISO system
sys = self.siso_ss1
t = np.linspace(0, 1, 10)
youttrue = np.array([86., 70.1808, 57.3753, 46.9975, 38.5766, 31.7344,
26.1668, 21.6292, 17.9245, 14.8945])
tout, yout = impulse_response(sys, T=t)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# Play with arguments
tout, yout = impulse_response(sys, T=t, X0=0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
X0 = np.array([0, 0])
tout, yout = impulse_response(sys, T=t, X0=X0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
tout, yout, xout = impulse_response(sys, T=t, X0=0, return_x=True)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# Test MIMO system, which contains ``siso_ss1`` twice
sys = self.mimo_ss1
_t, y_00 = impulse_response(sys, T=t, input=0, output=0)
_t, y_11 = impulse_response(sys, T=t, input=1, output=1)
np.testing.assert_array_almost_equal(y_00, youttrue, decimal=4)
np.testing.assert_array_almost_equal(y_11, youttrue, decimal=4)
# Test MIMO system, as mimo, and don't trim outputs
sys = self.mimo_ss1
_t, yy = impulse_response(sys, T=t, input=0)
np.testing.assert_array_almost_equal(
yy, np.vstack((youttrue, np.zeros_like(youttrue))), decimal=4)
def test_initial_response(self):
# Test SISO system
sys = self.siso_ss1
t = np.linspace(0, 1, 10)
x0 = np.array([[0.5], [1]])
youttrue = np.array([11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391])
tout, yout = initial_response(sys, T=t, X0=x0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# Play with arguments
tout, yout, xout = initial_response(sys, T=t, X0=x0, return_x=True)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# Test MIMO system, which contains ``siso_ss1`` twice
sys = self.mimo_ss1
x0 = np.matrix(".5; 1.; .5; 1.")
_t, y_00 = initial_response(sys, T=t, X0=x0, input=0, output=0)
_t, y_11 = initial_response(sys, T=t, X0=x0, input=1, output=1)
np.testing.assert_array_almost_equal(y_00, youttrue, decimal=4)
np.testing.assert_array_almost_equal(y_11, youttrue, decimal=4)
def test_initial_response_no_trim(self):
# test MIMO system without trimming
t = np.linspace(0, 1, 10)
x0 = np.matrix(".5; 1.; .5; 1.")
youttrue = np.array([11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391])
sys = self.mimo_ss1
_t, yy = initial_response(sys, T=t, X0=x0)
np.testing.assert_array_almost_equal(
yy, np.vstack((youttrue, youttrue)),
decimal=4)
def test_forced_response(self):
t = np.linspace(0, 1, 10)
# compute step response - test with state space, and transfer function
# objects
u = np.array([1., 1, 1, 1, 1, 1, 1, 1, 1, 1])
youttrue = np.array([9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776])
tout, yout, _xout = forced_response(self.siso_ss1, t, u)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
_t, yout, _xout = forced_response(self.siso_tf2, t, u)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
# test with initial value and special algorithm for ``U=0``
u = 0
x0 = np.matrix(".5; 1.")
youttrue = np.array([11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391])
_t, yout, _xout = forced_response(self.siso_ss1, t, u, x0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
# Test MIMO system, which contains ``siso_ss1`` twice
# first system: initial value, second system: step response
u = np.array([[0., 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1., 1, 1, 1, 1, 1, 1, 1, 1, 1]])
x0 = np.array([[.5], [1], [0], [0]])
youttrue = np.array([[11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391],
[9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776]])
_t, yout, _xout = forced_response(self.mimo_ss1, t, u, x0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
# Test discrete MIMO system to use correct convention for input
sysc = self.mimo_ss1
dt=t[1]-t[0]
sysd = c2d(sysc, dt) # discrete time system
Tc, youtc, _xoutc = forced_response(sysc, t, u, x0)
Td, youtd, _xoutd = forced_response(sysd, t, u, x0)
np.testing.assert_array_equal(Tc.shape, Td.shape)
np.testing.assert_array_equal(youtc.shape, youtd.shape)
np.testing.assert_array_almost_equal(youtc, youtd, decimal=4)
# Test discrete MIMO system without default T argument
u = np.array([[0., 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1., 1, 1, 1, 1, 1, 1, 1, 1, 1]])
x0 = np.array([[.5], [1], [0], [0]])
youttrue = np.array([[11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391],
[9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776]])
_t, yout, _xout = forced_response(sysd, U=u, X0=x0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
def test_lsim_double_integrator(self):
# Note: scipy.signal.lsim fails if A is not invertible
A = np.mat("0. 1.;0. 0.")
B = np.mat("0.; 1.")
C = np.mat("1. 0.")
D = 0.
sys = StateSpace(A, B, C, D)
def check(u, x0, xtrue):
_t, yout, xout = forced_response(sys, t, u, x0)
np.testing.assert_array_almost_equal(xout, xtrue, decimal=6)
ytrue = np.squeeze(np.asarray(C.dot(xtrue)))
np.testing.assert_array_almost_equal(yout, ytrue, decimal=6)
# test with zero input
npts = 10
t = np.linspace(0, 1, npts)
u = np.zeros_like(t)
x0 = np.array([2., 3.])
xtrue = np.zeros((2, npts))
xtrue[0, :] = x0[0] + t * x0[1]
xtrue[1, :] = x0[1]
check(u, x0, xtrue)
# test with step input
u = np.ones_like(t)
xtrue = np.array([0.5 * t**2, t])
x0 = np.array([0., 0.])
check(u, x0, xtrue)
# test with linear input
u = t
xtrue = np.array([1./6. * t**3, 0.5 * t**2])
check(u, x0, xtrue)
def test_discrete_initial(self):
h1 = TransferFunction([1.], [1., 0.], 1.)
t, yout = impulse_response(h1, np.arange(4))
np.testing.assert_array_equal(yout, [0., 1., 0., 0.])
@unittest.skipIf(not slycot_check(), "slycot not installed")
def test_step_robustness(self):
"Unit test: https://github.com/python-control/python-control/issues/240"
# Create 2 input, 2 output system
num = [ [[0], [1]], [[1], [0]] ]
den1 = [ [[1], [1,1]], [[1,4], [1]] ]
sys1 = TransferFunction(num, den1)
den2 = [ [[1], [1e-10, 1, 1]], [[1,4], [1]] ] # slight perturbation
sys2 = TransferFunction(num, den2)
# Compute step response from input 1 to output 1, 2
t1, y1 = step_response(sys1, input=0)
t2, y2 = step_response(sys2, input=0)
np.testing.assert_array_almost_equal(y1, y2)
def test_time_vector(self):
"Unit test: https://github.com/python-control/python-control/issues/239"
# Discrete time simulations with specified time vectors
Tin1 = np.arange(0, 5, 1) # matches dtf1, dss1; multiple of 0.2
Tin2 = np.arange(0, 5, 0.2) # matches dtf2, dss2
Tin3 = np.arange(0, 5, 0.5) # incompatible with 0.2
# Initial conditions to use for the different systems
siso_x0 = [1, 2]
mimo_x0 = [1, 2, 3, 4]
#
# Easy cases: make sure that output sample time matches input
#
# No timebase in system => output should match input
#
# Initial response
tout, yout = initial_response(self.siso_dtf1, Tin2, siso_x0,
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin2)
# Impulse response
tout, yout = impulse_response(self.siso_dtf1, Tin2,
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin2)
# Step response
tout, yout = step_response(self.siso_dtf1, Tin2,
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin2)
# Forced response with specified time vector
tout, yout, xout = forced_response(self.siso_dtf1, Tin2, np.sin(Tin2),
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin2)
# Forced response with no time vector, no sample time (should use 1)
tout, yout, xout = forced_response(self.siso_dtf1, None, np.sin(Tin1),
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin1)
# MIMO forced response
tout, yout, xout = forced_response(self.mimo_dss1, Tin1,
(np.sin(Tin1), np.cos(Tin1)),
mimo_x0)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
self.assertEqual(np.shape(tout), np.shape(yout[1,:]))
np.testing.assert_array_equal(tout, Tin1)
# Matching timebase in system => output should match input
#
# Initial response
tout, yout = initial_response(self.siso_dtf2, Tin2, siso_x0,
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin2)
# Impulse response
tout, yout = impulse_response(self.siso_dtf2, Tin2,
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin2)
# Step response
tout, yout = step_response(self.siso_dtf2, Tin2,
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin2)
# Forced response
tout, yout, xout = forced_response(self.siso_dtf2, Tin2, np.sin(Tin2),
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin2)
# Forced response with no time vector, use sample time
tout, yout, xout = forced_response(self.siso_dtf2, None, np.sin(Tin2),
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin2)
# Compatible timebase in system => output should match input
#
# Initial response
tout, yout = initial_response(self.siso_dtf2, Tin1, siso_x0,
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin1)
# Impulse response
tout, yout = impulse_response(self.siso_dtf2, Tin1,
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin1)
# Step response
tout, yout = step_response(self.siso_dtf2, Tin1,
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin1)
# Forced response
tout, yout, xout = forced_response(self.siso_dtf2, Tin1, np.sin(Tin1),
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
np.testing.assert_array_equal(tout, Tin1)
#
# Interpolation of the input (to match scipy.signal.dlsim)
#
# Initial response
tout, yout, xout = forced_response(self.siso_dtf2, Tin1,
np.sin(Tin1), interpolate=True,
squeeze=False)
self.assertEqual(np.shape(tout), np.shape(yout[0,:]))
self.assertTrue(np.allclose(tout[1:] - tout[:-1], self.siso_dtf2.dt))
#
# Incompatible cases: make sure an error is thrown
#
# System timebase and given time vector are incompatible
#
# Initial response
with self.assertRaises(Exception) as context:
tout, yout = initial_response(self.siso_dtf2, Tin3, siso_x0,
squeeze=False)
self.assertTrue(isinstance(context.exception, ValueError))
def test_discrete_time_steps(self):
"""Make sure rounding errors in sample time are handled properly"""
# See https://github.com/python-control/python-control/issues/332)
#
# These tests play around with the input time vector to make sure that
# small rounding errors don't generate spurious errors.
# Discrete time system to use for simulation
# self.siso_dtf2 = TransferFunction([1], [1, 1, 0.25], 0.2)
# Set up a time range and simulate
T = np.arange(0, 100, 0.2)
tout1, yout1 = step_response(self.siso_dtf2, T)
# Simulate every other time step
T = | np.arange(0, 100, 0.4) | numpy.arange |
import numpy as np
def normalize_to_range(array, R):
"""Returns array normalized to range R."""
array = array - | np.min(array) | numpy.min |
import numpy as np
from scipy.signal import filtfilt
class LaneLocalizer():
def __init__(self, lane_xs, lane_ys, lane_yaws, lane_vs, s_resolution=0.5):
# Make sure yaw angles are within bounds:
lane_ss = self._get_cumulative_distances(lane_xs, lane_ys)
lane_yaws = self._bound_angle_within_pi(lane_yaws)
s_interp = np.arange(0., lane_ss[-1] + s_resolution/2., s_resolution)
x_interp = np.interp(s_interp, lane_ss, lane_xs)
y_interp = np.interp(s_interp, lane_ss, lane_ys)
yaw_interp = np.interp(s_interp, lane_ss, np.unwrap(lane_yaws))
v_interp = np.interp(s_interp, lane_ss, lane_vs)
curv_interp = self._get_curvatures(s_interp, yaw_interp)
yaw_interp = self._bound_angle_within_pi(yaw_interp)
self.lane_arr = np.column_stack((s_interp, x_interp, y_interp, yaw_interp, v_interp, curv_interp))
self.lane_length = s_interp[-1]
@staticmethod
def _bound_angle_within_pi(angle):
""" Given an angle, adjusts it to lie within a +/- PI range """
return (angle + np.pi) % (2 * np.pi) - np.pi # https://stackoverflow.com/questions/15927755/opposite-of-numpy-unwrap
@staticmethod
def _get_cumulative_distances(xs, ys):
# Arclength/progress estimation.
lane_xy = np.column_stack((xs, ys))
lane_ss = np.cumsum( np.linalg.norm( np.diff(lane_xy, axis=0), axis=1 ) )
lane_ss = np.insert(lane_ss, 0, [0.0])
return lane_ss
@staticmethod
def _get_curvatures(ss, yaws):
# Curvature estimation.
curv_raw = LaneLocalizer._bound_angle_within_pi(np.diff(yaws)) / np.diff(ss)
if len(curv_raw) < 10:
curv_filt = curv_raw
else:
curv_filt = filtfilt(np.ones((3,))/3, 1, curv_raw)
curv_filt = np.append(curv_filt, curv_filt[-1])
return curv_filt
def get_reference_speed_and_curvature(self, s):
closest_index = np.argmin( np.abs(self.lane_arr[:,0] - s) )
v_waypoint = self.lane_arr[closest_index, 4]
curv_waypoint = self.lane_arr[closest_index, 5]
return v_waypoint, curv_waypoint
def convert_global_to_frenet_coords(self, x, y, psi, extrapolate_s = False):
xy_traj = self.lane_arr[:,1:3]
xy_query = np.array([x, y])
closest_index = np.argmin( np.linalg.norm(xy_traj - xy_query, axis=1) )
# Note: Can do some smarter things here, like linear interpolation.
# If s_K+1 - s_k is reasonably small, we can assume s of the waypoint
# and s of the query point are the same for simplicity.
s_waypoint = self.lane_arr[closest_index, 0]
xy_waypoint = self.lane_arr[closest_index, 1:3]
psi_waypoint = self.lane_arr[closest_index, 3]
rot_global_to_frenet = np.array([[ np.cos(psi_waypoint), np.sin(psi_waypoint)], \
[-np.sin(psi_waypoint), np.cos(psi_waypoint)]])
# Error_xy = xy deviation (global frame)
# Error_frenet = e_s, e_y deviation (Frenet frame)
error_xy = xy_query - xy_waypoint
error_frenet = rot_global_to_frenet @ error_xy
# e_psi
error_psi = self._bound_angle_within_pi(psi - psi_waypoint)
if extrapolate_s:
if closest_index == 0 or closest_index == self.lane_arr.shape[0]-1:
s_waypoint += error_frenet[0] # Add "e_s" at the endpoints to extrapolate the lane.
return s_waypoint, error_frenet[1], error_psi # s, ey, epsi
def convert_frenet_to_global_coords(self, s, ey, epsi):
s_traj = self.lane_arr[:,0]
# Handle "closest waypoint" differently based on s_query:
if s < s_traj[0]:
# NOTE: This can be problematic if s_query is really far away from the start.
# Not handling this but intuitively, need to do some extrapolation.
x_waypoint = self.lane_arr[0, 1]
y_waypoint = self.lane_arr[0, 2]
psi_waypoint = self.lane_arr[0, 3]
elif s > s_traj[-1]:
# NOTE: This can be problematic if s_query is really far away from the end.
# Not handling this but intuitively, need to do some extrapolation.
x_waypoint = self.lane_arr[-1, 1]
y_waypoint = self.lane_arr[-1, 2]
psi_waypoint = self.lane_arr[-1, 3]
else:
# NOTE: keeping this simple and using the closest waypoint, in place of more
# complex and possibly error-prone interpolation strategies.
closest_index = np.argmin( np.abs( s_traj - s) )
x_waypoint = self.lane_arr[closest_index, 1]
y_waypoint = self.lane_arr[closest_index, 2]
psi_waypoint = self.lane_arr[closest_index, 3]
rot_frenet_to_global = np.array([[np.cos(psi_waypoint), -np.sin(psi_waypoint)], \
[np.sin(psi_waypoint), np.cos(psi_waypoint)]])
error_global = rot_frenet_to_global @ np.array([0, ey]) # assuming "e_s" is 0.
x_global = x_waypoint + error_global[0]
y_global = y_waypoint + error_global[1]
psi_global = self._bound_angle_within_pi(psi_waypoint + epsi)
return x_global, y_global, psi_global
def get_lane_measurement(self, x, y):
# Similar to conversion to Frenet coords but getting the actual waypoint / local rotation matrix.
xy_traj = self.lane_arr[:,1:3]
xy_query = np.array([x, y])
closest_index = np.argmin( np.linalg.norm(xy_traj - xy_query, axis=1) )
xy_waypoint = self.lane_arr[closest_index, 1:3]
psi_waypoint = self.lane_arr[closest_index, 3]
pose_waypoint = np.append(xy_waypoint, psi_waypoint)
rot_frenet_to_global = np.array([[np.cos(psi_waypoint), - | np.sin(psi_waypoint) | numpy.sin |
from typing import List
import numpy as np
import tensorflow as tf
class AutoRegressive:
"""Auto regressive, it is used to generate text"""
def beam_search(self, inputs: List[np.ndarray], **kwargs) -> np.ndarray:
"""
Beam search
:param inputs: a list contain input ids or input masks or segment ids for 1 sample
:return: 1 axis list, each elements is vocab id
"""
top_k = self.top_k
output_ids = np.empty((1, 0), dtype=int) if self.start_id is None else np.array([[self.start_id]])
output_scores = np.zeros(1)
for step in range(self.max_len):
scores = self.next_token_scores(inputs, output_ids).numpy()
if step == 0:
inputs = [np.repeat(_input, top_k, axis=0) for _input in inputs]
scores = output_scores.reshape((-1, 1)) + scores
indices = scores.argpartition(-top_k, axis=None)[-top_k:]
indices_1 = indices // scores.shape[1]
indices_2 = (indices % scores.shape[1]).reshape((-1, 1))
output_ids = np.concatenate([output_ids[indices_1], indices_2], 1)
output_scores = np.take_along_axis(scores, indices, axis=None)
end_counts = (output_ids == self.end_id).sum(1)
if output_ids.shape[1] >= self.min_len:
best_one = output_scores.argmax()
if end_counts[best_one] == self.min_ends: # 如果已经终止
return output_ids[best_one][:-1]
else: # 否则，只保留未完成部分, 未完成部分还没有结束标志
flag = (end_counts < self.min_ends) # 标记未完成序列
if not flag.all(): # 如果有已完成的
inputs = [_input[flag] for _input in inputs] # 扔掉已完成序列
output_ids = output_ids[flag] # 扔掉已完成序列
output_scores = output_scores[flag] # 扔掉已完成序列
top_k = flag.sum() # top_k相应变化
return output_ids[output_scores.argmax()]
def random_sample(self, inputs: List[np.ndarray], **kwargs) -> np.ndarray:
"""
Random sample
:param inputs: a list contain input ids or input masks or segment ids for 1 sample
:return: 2 axis list, each list contains all token ids of each sentence
"""
output_ids = np.empty((1, 0), dtype=int) if self.start_id is None else np.array([[self.start_id]])
results = []
for step in range(self.max_len):
probas = self.next_token_prob(inputs, output_ids).numpy()
p_indices = None
k_indices = None
probas /= probas.sum(axis=1, keepdims=True) # normalization
if step == 0:
probas = | np.repeat(probas, self.num_samples, axis=0) | numpy.repeat |
# -*- coding: utf-8 -*-
# MegEngine is Licensed under the Apache License, Version 2.0 (the "License")
#
# Copyright (c) 2014-2021 Megvii Inc. All rights reserved.
#
# Unless required by applicable law or agreed to in writing,
# software distributed under the License is distributed on an
# "AS IS" BASIS, WITHOUT ARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
import itertools
import numpy as np
import megengine as mge
import megengine.autodiff as ad
import megengine.functional as F
from megengine import Tensor
from megengine.core._imperative_rt.core2 import (
_set_drop_flag,
_set_swap_flag,
get_option,
set_option,
)
from megengine.module import Linear, Module
from megengine.optimizer import SGD
batch_size = 64
data_shape = (batch_size, 2)
label_shape = (batch_size,)
def minibatch_generator():
while True:
inp_data = np.zeros((batch_size, 2))
label = np.zeros(batch_size, dtype=np.int32)
for i in range(batch_size):
# [x0, x1], sampled from U[-1, 1]
inp_data[i, :] = np.random.rand(2) * 2 - 1
label[i] = 0 if np.prod(inp_data[i]) < 0 else 1
yield inp_data.astype(np.float32), label.astype(np.int32)
def calculate_precision(data: np.ndarray, pred: np.ndarray) -> float:
""" Calculate precision for given data and prediction.
:type data: [[x, y], ...]
:param data: Input data
:type pred: [[x_pred, y_pred], ...]
:param pred: Network output data
"""
correct = 0
assert len(data) == len(pred)
for inp_data, pred_output in zip(data, pred):
label = 0 if np.prod(inp_data) < 0 else 1
pred_label = | np.argmax(pred_output) | numpy.argmax |
import numpy
'''
compute angle (in degrees) for p0p1p2 corner
Inputs:
p0,p1,p2 - points in the form of [x,y]
'''
def calc_angle(p0, p1, p2):
v0 = numpy.array(p0) - | numpy.array(p1) | numpy.array |
#!/usr/bin/env python
"""
Portierung der Matlab-Skripts zu Python-Funktionen
Matlab-Code Prof. Dr. <NAME>, <EMAIL>
Portierung zu Python 8/2017 <NAME>, <EMAIL>
Teil des Praktikums zur Vorlesung Quellen- und Kanalcodierung
"""
import numpy as np, matplotlib.pyplot as plt
from ipywidgets import interact
import ipywidgets as widgets
def my_range(start, end, step):
"""
range for a loop with decimal incrementation
stepsize step in range of [start, end]
"""
while start <= end:
yield start
start += step
def reconprk_old():
"""
Version ohne ipython-Widget
"""
T = 1 # T ist die Zeitkonstante der raised cosine function
T_s = 0.5 * T # für alpha=0.5 beträgt die Bandbreite zwar nur 1.5/T, es wird aber trotzdem mit T_s=0.5T (über-)abgetastet.
alpha = 0.499 # Roll-Off Faktor
amp_si = (1 + alpha) / T * T_s # Amplitudenfaktor =2f_g*T_s
t = np.linspace(-4, 4, 81) # Betrachteter Ausschnitt des Signals
x = np.sinc(t / T) * | np.cos(np.pi * alpha * t / T) | numpy.cos |
"""
Functions that used in data preprocessing.
"""
import torch
import numpy as np
from tqdm import tqdm
from collections import Counter
from .dict_utils import counter2ordered_dict
from common.constants import NLP, SPM
from allennlp.modules.elmo import batch_to_ids
def text2tokens(sentence):
"""
Transform text to tokens list.
:param sentence: input text
:return: list of token texts
"""
doc = NLP(sentence)
return [token.text for token in doc]
def get_token_char_level_spans(text, tokens):
"""
Get tokens' char-level [) spans in text.
:param text: input text
:param tokens: list of token texts
:return: list of tokens' char-level [) spans in text,
each span is a tuple
"""
current = 0
spans = []
for token in tokens:
current = text.find(token, current)
if current < 0:
print("Token {} cannot be found".format(token))
raise Exception()
spans.append((current, current + len(token)))
current += len(token)
return spans
def spacydoc2tokens(doc):
"""
Transform spaCy doc to tokens list.
:param doc: spaCy doc
:return: list of token texts
"""
return [token.text for token in doc]
def word2wid(word, word2id_dict, OOV="<oov>"):
"""
Transform single word to word index.
:param word: a word
:param word2id_dict: a dict map words to indexes
:param OOV: a token that represents Out-of-Vocabulary words
:return: int index of the word
"""
for each in (word, word.lower(), word.capitalize(), word.upper()):
if each in word2id_dict:
return word2id_dict[each]
return word2id_dict[OOV]
def char2cid(char, char2id_dict, OOV="<oov>"):
"""
Transform single character to character index.
:param char: a character
:param char2id_dict: a dict map characters to indexes
:param OOV: a token that represents Out-of-Vocabulary characters
:return: int index of the character
"""
if char in char2id_dict:
return char2id_dict[char]
return char2id_dict[OOV]
def spacydoc2wids(spacy_doc, word2id_dict, sent_length,
PAD="<pad>", OOV="<oov>"):
"""
Transform spaCy doc to padded word indexes list.
:param spacy_doc: a spaCy doc
:param word2id_dict: a dict map words to indexes
:param sent_length: maximum length (number of words) of input text
:param PAD: a token that represents pad
:param OOV: a token that represents Out-of-Vocabulary words
:return: list of word indexes
"""
word_ids = np.ones(sent_length, dtype=np.int32) * word2id_dict[PAD]
words = [token.text for token in spacy_doc]
for i, token in enumerate(words):
if i == sent_length:
break
word_ids[i] = word2wid(token, word2id_dict, OOV)
return word_ids
def spacydoc2cids(spacy_doc, char2id_dict, sent_length, word_length,
PAD="<pad>", OOV="<oov>"):
"""
Transform spaCy doc to padded character indexes 2D list.
:param spacy_doc: a spaCy doc
:param char2id_dict: a dict map characters to indexes
:param sent_length: maximum length (number of words) of input text
:param word_length: maximum length (number of characters) of words
:param PAD: a token that represents pad
:param OOV: a token that represents Out-of-Vocabulary words
:return: 2D list of character indexes
"""
char_ids = np.ones(
[sent_length, word_length], dtype=np.int32) * char2id_dict[PAD]
words = [token.text for token in spacy_doc]
chars = [list(token) for token in words]
for i, token in enumerate(chars):
if i == sent_length:
break
for j, char in enumerate(token):
if j == word_length:
break
char_ids[i, j] = char2cid(char, char2id_dict, OOV)
return char_ids
def spacydoc2tagids(spacy_doc, tag_type, tag2id_dict, sent_length,
PAD="<pad>", OOV="<oov>"):
"""
Transform spaCy doc to padded tag indexes list.
:param spacy_doc: a spaCy doc
:param tag_type: type of tag, currently support "pos", "ner", "iob", "dep"
:param tag2id_dict: a dict map words to tags
:param sent_length: maximum length (number of words) of input text
:param PAD: a token that represents pad
:param OOV: a token that represents Out-of-Vocabulary words
:return: list of tag indexes
"""
tag_ids = np.ones(sent_length, dtype=np.int32) * tag2id_dict[PAD]
if tag_type == "pos":
tags = [token.tag_ for token in spacy_doc]
elif tag_type == "ner":
tags = [token.ent_type_ for token in spacy_doc]
elif tag_type == "iob":
tags = [token.ent_iob_ for token in spacy_doc]
elif tag_type == "dep":
tags = [token.dep_ for token in spacy_doc]
else:
print("tag_type must be POS, NER, IOB or DEP.")
for i, token in enumerate(tags):
if i == sent_length:
break
tag_ids[i] = char2cid(token, tag2id_dict, OOV)
return tag_ids
def spacydoc2features(spacy_doc, feature_type, sent_length):
"""
Transform spaCy doc to padded tokens feature list.
:param spacy_doc: a spaCy doc
:param feature_type: type of features
:param sent_length: maximum length (number of words) of input text
:return: list of token feature values
"""
features_padded = | np.zeros([sent_length], dtype=np.float32) | numpy.zeros |
#!/usr/bin/env python
""" Convert a svg file into 2D triangle mesh.
"""
import argparse
import logging
import pymesh
import numpy as np
from numpy.linalg import norm
import os.path
from subprocess import check_call
from time import time
def parse_args():
parser = argparse.ArgumentParser(__doc__);
parser.add_argument("--engine", help="Triangulation engine", choices=(
"triangle_conforming_delaunay",
"triangle_constrained_delaunay",
"cgal_constrained_delaunay",
"cgal_conforming_delaunay",
"geogram_delaunay",
"jigsaw_frontal_delaunay",
"mmg_delaunay", "triwild"),
default="triangle_conforming_delaunay");
parser.add_argument("--resolve-self-intersection", "-r", action="store_true");
parser.add_argument("--with-frame", '-f', action="store_true");
parser.add_argument("--with-cell-label", "-l", action="store_true");
parser.add_argument("--with-cleanup", "-c", action="store_true");
parser.add_argument("--with-triangulation", "-t", action="store_true");
parser.add_argument("--stage", type=int, default=1);
parser.add_argument("--epsilon", type=float, default=1e-3);
parser.add_argument("--log", type=str, help="Logging level",
choices=["DEBUG", "INFO", "WARNING", "ERROR", "CRITICAL"],
default="INFO");
parser.add_argument("--with-features", '-F', action="store_true",
help="TriWild specific option to preserve features");
parser.add_argument("input_svg");
parser.add_argument("output_mesh");
return parser.parse_args();
def get_logger(level):
numeric_level = getattr(logging, level, None);
if not isinstance(numeric_level, int):
raise ValueError('Invalid log level: {}'.format(level));
logging.basicConfig(level=numeric_level);
return logging.getLogger("PyMesh.Triangulation");
def drop_zero_dim(wires):
# Trim zero dimension.
if wires.dim == 3:
vertices = wires.vertices;
assert(np.all(vertices[:,2] == 0));
vertices = vertices[:, [0,1]];
wires.load(vertices, wires.edges);
return wires;
def cleanup(wires, logger):
if wires.num_vertices == 0:
return wires;
start_time = time();
tol = 1e-6;
vertices, edges, __ = pymesh.remove_duplicated_vertices_raw(
wires.vertices, wires.edges, tol);
# Remove duplicated edges.
ordered_edges = np.sort(edges, axis=1);
__, unique_edge_ids, __ = pymesh.unique_rows(ordered_edges);
edges = edges[unique_edge_ids, :];
wires.load(vertices, edges);
# Remove topologically degenerate edges.
is_not_topologically_degenerate = edges[:,0] != edges[:,1];
if not np.all(is_not_topologically_degenerate):
wires.filter_edges(is_not_topologically_degenerate);
finish_time = time();
t = finish_time - start_time;
logger.info("Cleanup running time: {}".format(t));
return wires;
def add_frame(wires):
if wires.num_vertices == 0:
return wires;
vertices = wires.vertices;
edges = wires.edges;
bbox_min = np.amin(vertices, axis=0);
bbox_max = np.amax(vertices, axis=0);
bbox_center = 0.5 * (bbox_min + bbox_max);
diag_len = norm(bbox_max - bbox_min);
offset = np.ones(2) * diag_len / 20;
bbox_min -= offset;
bbox_max += offset;
frame_vertices = np.array([
[bbox_min[0], bbox_min[1]],
[bbox_max[0], bbox_min[1]],
[bbox_max[0], bbox_max[1]],
[bbox_min[0], bbox_max[1]],
]);
frame_edges = np.array([
[0, 1],
[1, 2],
[2, 3],
[3, 0],
]) + wires.num_vertices;
vertices = np.vstack([vertices, frame_vertices]);
edges = np.vstack([edges, frame_edges]);
wires.load(vertices, edges);
return wires;
def resolve_self_intersection(wires, logger):
if wires.num_vertices == 0:
return wires;
bbox_min, bbox_max = wires.bbox;
tol = norm(bbox_max - bbox_min) / 1000;
start_time = time();
vertices, edges = pymesh.snap_rounding(wires.vertices, wires.edges, tol);
finish_time = time();
t = finish_time - start_time;
logger.info("Snap rounding running time: {}".format(t));
wires.load(vertices, edges);
return wires;
def triangulate(wires, engine, stage, eps, logger, wire_file, json_file):
if wires.num_vertices == 0:
return pymesh.form_mesh(np.zeros((0, 2)), np.zeros((0,3)));
basename = os.path.splitext(wire_file)[0];
if engine == "triwild":
out_mesh = "{}_linear.msh".format(basename);
log_file = "{}_triwild.log".format(basename);
if json_file is not None:
command = "TriWild --mute-log --feature-envelope-r {} --stage {} --log-file {} --feature-input {} --output-linear-mesh --skip-eps --input {} --output {}".format(
eps, stage, log_file, json_file, wire_file, basename);
else:
command = "TriWild --mute-log --feature-envelope-r {} --stage {} --log-file {} --output-linear-mesh --skip-eps --input {} --output {}".format(
eps, stage, log_file, wire_file, basename);
print(command);
start_time = time();
check_call(command.split());
finish_time = time();
t = finish_time - start_time;
mesh = pymesh.load_mesh(out_mesh, drop_zero_dim=True);
else:
mesh, t = pymesh.triangulate_beta(wires.vertices, wires.edges,
engine=engine, with_timing=True);
logger.info("Triangulation running time: {}".format(t));
return mesh;
def compute_cell_labels(wires, mesh, logger):
start_time = time();
arrangement = pymesh.Arrangement2();
arrangement.points = wires.vertices;
arrangement.segments = wires.edges;
arrangement.run();
mesh.add_attribute("face_centroid");
centroids = mesh.get_face_attribute("face_centroid");
r = arrangement.query(centroids);
finish_time = time();
t = finish_time - start_time;
logger.info("Arrangement running time: {}".format(t));
cell_type = | np.array([item[0] for item in r]) | numpy.array |
import pickle
from pathlib import Path
from typing import Tuple, Union
import click
import numpy
import rich
from molesp.cli._cli import compute_surface
from molesp.models import ESPMolecule, Surface
from nagl.utilities.toolkits import capture_toolkit_warnings
from openff.recharge.charges.bcc import BCCCollection, BCCGenerator
from openff.recharge.charges.library import (
LibraryChargeCollection,
LibraryChargeGenerator,
LibraryChargeParameter,
)
from openff.recharge.charges.qc import QCChargeGenerator, QCChargeSettings
from openff.recharge.charges.vsite import VirtualSiteCollection, VirtualSiteGenerator
from openff.recharge.conformers import ConformerGenerator, ConformerSettings
from openff.recharge.esp import ESPSettings
from openff.recharge.esp.psi4 import Psi4ESPGenerator
from openff.recharge.grids import MSKGridSettings
from openff.recharge.utilities.geometry import compute_inverse_distance_matrix
from openff.recharge.utilities.toolkits import VdWRadiiType, compute_vdw_radii
from openff.toolkit.topology import Molecule
from openff.units import unit
from openff.utilities import temporary_cd
from openmm import unit as openmm_unit
from pydantic import parse_file_as
_CACHED_CHARGES = {}
def compute_base_charge(
molecule: Molecule,
conformer_settings: ConformerSettings,
charge_settings: QCChargeSettings,
):
tagged_smiles = molecule.to_smiles(mapped=True)
if tagged_smiles in _CACHED_CHARGES:
return _CACHED_CHARGES[tagged_smiles]
conformers = ConformerGenerator.generate(molecule, conformer_settings)
charges = QCChargeGenerator.generate(molecule, conformers, charge_settings)
charge_collection = LibraryChargeCollection(
parameters=[
LibraryChargeParameter(
smiles=tagged_smiles,
value=[float(v) for v in charges.flatten().tolist()],
)
]
)
_CACHED_CHARGES[tagged_smiles] = charge_collection
return charge_collection
def compute_mm_esp(
molecule: Molecule,
conformer: unit.Quantity,
charge_collection: Union[
Tuple[ConformerSettings, QCChargeSettings], LibraryChargeCollection
],
bcc_collection: BCCCollection,
vsite_collection: VirtualSiteCollection,
grid: unit.Quantity,
):
console = rich.get_console()
console.print("applying MM charges")
if not isinstance(charge_collection, LibraryChargeCollection):
conformer_settings, charge_settings = charge_collection
charge_collection = compute_base_charge(
molecule, conformer_settings, charge_settings
)
atom_charges = LibraryChargeGenerator.generate(molecule, charge_collection)
if len(bcc_collection.parameters) > 0:
atom_charges += BCCGenerator.generate(molecule, bcc_collection)
if len(vsite_collection.parameters) > 0:
vsite_charges = VirtualSiteGenerator.generate_charge_increments(
molecule, vsite_collection
)
n_vsites = len(vsite_charges) - molecule.n_atoms
full_charges = (
numpy.vstack([atom_charges, numpy.zeros((n_vsites, 1))]) + vsite_charges
)
else:
full_charges = atom_charges
if len(vsite_collection.parameters) > 0:
vsite_coordinates = VirtualSiteGenerator.generate_positions(
molecule, vsite_collection, conformer
)
full_coordinates = | numpy.vstack([conformer, vsite_coordinates]) | numpy.vstack |
import pdb
import numpy as np
import scipy as sp
import scipy.optimize as op
import util
import matplotlib.pyplot as plt
import time
# Laplace Inference -----------------------------------------------------------
def negLogPosteriorUnNorm(xbar, ybar, C_big, d_big, K_bigInv, xdim, ydim):
xbar = np.ndarray.flatten(np.asarray(xbar))
ybar = np.ndarray.flatten(np.asarray(ybar))
T = int(len(d_big)/ydim)
C_big = np.asarray(C_big)
d_big = np.asarray(d_big)
K_bigInv = np.asarray(K_bigInv)
A = np.dot(C_big.T, xbar) + d_big
Aexp = np.exp(A)
L1 = np.dot(Aexp, np.ones(ydim*T))
L2 = - | np.dot(ybar, A.T) | numpy.dot |
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.image import imread
from mpl_toolkits.mplot3d import Axes3D
# 与门 权重偏置
AND_W = np.array([0.5, 0.5])
AND_B = -0.7
# 与非门 权重偏置
NAND_W = np.array([-0.5, -0.5])
NAND_B = 0.7
# 或门 权重偏置
OR_W = np.array([0.5, 0.5])
OR_B = -0.3
# 感知机
def Perceptron(x):
return np.array(x > 0, dtype=np.int)
# sigmoid
def Sigmoid(x):
return 1 / (1 + np.exp(-x))
# Relu
def Relu(x):
return np.maximum(0, x)
# 这个激活函数在"分类"中,比较常用
def Softmax(a):
c=np.max(a)
exp_a = np.exp(a-c)
y = exp_a / np.sum(exp_a)
return y
# 异或门
def XOR(x1, x2):
local_x1 = Perceptron(np.sum(np.array([x1, x2])*NAND_W)+NAND_B)
local_x2 = Perceptron(np.sum(np.array([x1, x2])*OR_W)+OR_B)
return Sigmoid(np.sum(np.array([local_x1, local_x2])*AND_W)+AND_B)
def test1():
print(XOR(0, 0))
print(XOR(1, 0))
print(XOR(0, 1))
print(XOR(1, 1))
def test2():
x = np.arange(-10, 10, 0.1)
y1 = Perceptron(x)
y2 = Sigmoid(x)
plt.plot(x, x,linestyle='--',label="x")
plt.plot(x, y1,label="Perceptron")
plt.plot(x, y2,label="Sigmoid")
plt.xlabel("X")
plt.ylabel("Y")
plt.ylim(-0.01, 1.01) # 指定y轴的范围
plt.legend()
plt.show()
#第三章
def identity_function(x):
return x
def test3():
# 输入层
X = np.array([1.0, 0.5])#输入层
W1 = np.array([[0.1, 0.3, 0.5], [0.2, 0.4, 0.6]])#输入层权重
B1 = np.array([0.1, 0.2, 0.3])#输入层偏置
A1 = np.dot(X, W1) + B1
Z1 = Sigmoid(A1)
#print(A1) # [0.3, 0.7, 1.1]
#print(Z1) # [0.57444252, 0.66818777, 0.75026011]
# 隐含层
W2 = np.array([[0.1, 0.4], [0.2, 0.5], [0.3, 0.6]])
B2 = np.array([0.1, 0.2])
A2 = np.dot(Z1, W2) + B2
Z2 = Sigmoid(A2)
# 输出层
W3 = np.array([[0.1, 0.3], [0.2, 0.4]])
B3 = np.array([0.1, 0.2])
A3 = np.dot(Z2, W3) + B3
Y = identity_function(A3) # 或者Y = A3
print(Y)
# 把test3规整下:
# 网络权重和偏置
def init_network():
network = {}
network['W1'] = np.array([[0.1, 0.3, 0.5], [0.2, 0.4, 0.6]])
network['b1'] = np.array([0.1, 0.2, 0.3])
network['W2'] = np.array([[0.1, 0.4], [0.2, 0.5], [0.3, 0.6]])
network['b2'] = np.array([0.1, 0.2])
network['W3'] = np.array([[0.1, 0.3], [0.2, 0.4]])
network['b3'] = np.array([0.1, 0.2])
return network
# 前向运算
def forward(network, x):
W1, W2, W3 = network['W1'], network['W2'], network['W3']
b1, b2, b3 = network['b1'], network['b2'], network['b3']
a1 = np.dot(x, W1) + b1
z1 = Sigmoid(a1)
a2 = np.dot(z1, W2) + b2
z2 = Sigmoid(a2)
a3 = np.dot(z2, W3) + b3
y = identity_function(a3)
return y
# 测试数据
def test4():
network = init_network()
x = np.array([1.0, 0.5])
y = forward(network, x)
print(y) # [ 0.31682708 0.69627909]
def test5():
a=np.array([0.3,2.9,4.0])
y=Softmax(a)
print(y)
def APerceptron(w,b,x):
y=np.sum(x*w)+b
# 激活函数
if(y>=0):
return 1
else:
return 0
# 第一层
XOR_W1_1 = np.array([0.5, 0.5])
XOR_B1_1 = -0.7
XOR_W1_2= np.array([-0.5, -0.5])
XOR_B1_2 = 0.3
# 第二层
XOR_W2 = | np.array([-0.5,-0.5]) | numpy.array |
import numpy as np
import modern_robotics as mr
from modern_robotics.core import Adjoint, FKinBody, JacobianBody, MatrixLog6, se3ToVec, TransInv
"""
Code to calculate the feedforward control for the youBot
"""
def FeedbackControl(X, Xd, Xd_next, Kp, Ki, dt, curr_config, Xerr_integral):
""" Calculates the kinematic task-space feedforward and feedback control law
Makes use of the equation: V(t) = [Adx^-1xd]Vd(t) + KpXerr(t) + Ki*integral(0:t)(Xerr(t))dt
Args:
X : Current actual end-effector configuration Tse
Xd : Current end-effector reference configuration Tse,d
Xd_next : End-effector reference configuration at the next timestep in
the reference trajectory Xd at Δt later
Kp : The feedback proportional gain
Ki : The feedback integral gain
dt : Timestep Δt between reference trajectory configurations
curr_config : The current configuration of the robot
Xerr_integral : Initial integral of the error (zeros)
Returns:
V : End-effector twist expressed in end-effector frame {e}
Controls : The commanded wheel and arm joint speeds (m/s)
Xerr : Error in X
"""
# initialize kinematics variables
l = 0.47/2 # forward-backward distance between the wheels (m)
w = 0.3/2 # side-to-side distance between wheels (m)
r = 0.0475 # radius of each wheel (m)
# the fixed offset from the chassis frame {b} to the base frame of the arm {0}
Tb0 = np.array([[1, 0, 0, 0.1662],
[0, 1, 0, 0],
[0, 0, 1, 0.0026],
[0, 0, 0, 1]])
# end-effector frame {e} relative to the arm base frame {0}
M0e = np.array([[1, 0, 0, 0.033],
[0, 1, 0, 0],
[0, 0, 1, 0.6546],
[0, 0, 0, 1]])
# the screw axes for the five joints in the end-effector frame {e}
Blist = np.array([[0, 0, 1, 0, 0.033, 0],
[0, -1, 0, -0.5076, 0, 0],
[0, -1, 0, -0.3526, 0, 0],
[0, -1, 0, -0.2176, 0, 0],
[0, 0, 1, 0, 0, 0]]).T
# find current joint angles
curr_joint_ang = curr_config[3:8]
# transformation from {0} to {e}
T0e = FKinBody(M0e, Blist, curr_joint_ang)
# transformation from {e} to {b}
Teb = TransInv(T0e)@TransInv(Tb0)
# compute the reference twist Vd
Log = MatrixLog6(TransInv(Xd)@Xd_next)
Vel = se3ToVec(Log)
Vd = 1/dt * Vel
# print(f"Vd: {Vd}")
# compute the Ad(x^-1xd) matrix
Adx_invxd = Adjoint(TransInv(X)@Xd)
Adx_invxdVd = Adx_invxd@Vd # 6x6 @ 6x1 = 6x1
# print(f"Adx_invxdVd: {Adx_invxdVd}")
# compute X error
Xerr = se3ToVec(MatrixLog6(TransInv(X)@Xd))
# print(f"Xerr: {Xerr}")
# compute the integral of the error
Xerr_integral += Xerr * dt
# print(f"Integral of error: {Xerr_integral}")
# compute V
V = Adx_invxdVd + Kp@Xerr + Ki@Xerr_integral
# print(f"V: {V}")
# F6 matrix
F6 = r/4 * np.array([[ 0, 0, 0, 0],
[ 0, 0, 0, 0],
[-1/(l+w), 1/(l+w), 1/(l+w), -1/(l+w)],
[ 1, 1, 1, 1],
[ -1, 1, -1, 1],
[ 0, 0, 0, 0]])
# arm jacobian
J = JacobianBody(Blist, curr_joint_ang)
# # joint limits
# J_limit = J.T
# if curr_joint_ang[0] < -2.95 or curr_joint_ang[0] > 2.95:
# J_limit[0] = J_limit[0]*0
# if curr_joint_ang[1] < -1 or curr_joint_ang[1] > 1:
# J_limit[1] = J_limit[1] * 0
# if curr_joint_ang[2] < -2 or curr_joint_ang[2] > 2:
# J_limit[2] = J_limit[2] * 0
# if curr_joint_ang[3] < -2 or curr_joint_ang[3] > 2:
# J_limit[3] = J_limit[3] * 0
# if curr_joint_ang[4] < -2.92 or curr_joint_ang[4] > 2.92:
# J_limit[4] = J_limit[4] * 0
# J = J_limit.T
# body jacobian
Jb = Adjoint(Teb) @ F6
Je = np.hstack((Jb, J)) ### make joint column zero depending on config to place joint limits
# print(f"Je: \n{np.around(Je, decimals=3)}")
# calculate the commanded wheel and arm joint speeds: u and thetadot
# using the Moore-Penrose pseudoinverse
# Je_pinv = [email protected]([email protected])
Je_pinv = np.linalg.pinv(Je, 1e-3)
# Je_pinv = np.linalg.pinv(Je)
controls = Je_pinv@V
# print(f"Controls: {np.around(controls, decimals=1)}")
return V, controls, Xerr
if __name__ == "__main__":
""" Main function to call FeedbackControl
"""
Xd = np.array([[ 0, 0, 1, 0.5],
[ 0, 1, 0, 0],
[-1, 0, 0, 0.5],
[ 0, 0, 0, 1]])
Xd_next = np.array([[ 0, 0, 1, 0.6],
[ 0, 1, 0, 0],
[-1, 0, 0, 0.3],
[ 0, 0, 0, 1]])
X = np.array([[ 0.170, 0, 0.985, 0.387],
[ 0, 1, 0, 0],
[-0.985, 0, 0.170, 0.570],
[ 0, 0, 0, 1]])
# Kp = np.zeros((6,6))
Kp = | np.identity(6) | numpy.identity |
import sys
import numpy as np
from astropy import units as u
from astropy.constants import G
from astropy.table import QTable
from scipy.integrate import solve_ivp
G = 6.7e-11 # Universal gravitational constant, SI
class Bodies:
def __init__(self):
self.posns = np.zeros((0,3))
self.vs = np.zeros((0,3))
self.ms = np.zeros((0))
self.rs = np.zeros((0))
self.sun = None
self.planets = []
self.nBodies = 0
self.time = 0
#----------------------------------------
# Some general utility methods
def is_iterable(self, x):
# a surprising omission from standard Python?
try:
iterator = iter(x)
except TypeError:
return False
else:
return True
def fix_units(self, val, unit):
"Convert to SI if necessary and return value as a Python scalar"
if isinstance(val, u.quantity.Quantity):
val = val.to(unit).value
return val
def veclen(self, vector):
# beware, units are lost and this just returns a number
return np.linalg.norm(vector)
def vecperp(self, vector):
"rotate 90 deg ccw, return normalised vector in x,y plane"
v = np.array([-vector[1], vector[0], 0])
return v/self.veclen(v)
def get_time(self):
"Cumulative integration time (s)"
return self.time*u.s
def CoM_velocity(self):
"Reruns velocity of center of mass"
return np.sum(self.vs * self.ms[:, np.newaxis], axis=0) / np.sum(self.ms)
def fix_CoM(self):
"Ensure CoM velocity is zero"
self.vs -= self.CoM_velocity()
#-----------------------------------------------------
# Several methods to add bodies to the collection
def add_sun(self, M, R=None):
"""
For 1-body problems, a large mass fixed at the origin
M = mass (kg or Quantity)
R = radius (m or Quantity); only for collision detection
"""
M = self.fix_units(M, u.kg)
R = self.fix_units(R, u.m)
self.sun = self.ms.size # index to this new body
self.posns = np.concatenate((self.posns, np.zeros((1,3))))
self.vs = np.concatenate((self.vs, np.zeros((1,3))))
self.ms = np.concatenate((self.ms, [M,]))
self.rs = np.concatenate((self.rs, [R,]))
self.nBodies = self.ms.size
def add_bodies(self, pos, v, m, R):
"""
Can be one body or many
single: need pos and v to be 3-item iterables
many: pos and p have shape (N,3), m and R are 1-D array-like
"""
if not self.is_iterable(m): # just have a single body
# make sure the 3-vectors are numpy arrays
# (this does nothing if they are already arrays)
pos = np.array(pos)
v = np.array(v)
# get everything to a suitable shape for concatenation
pos = pos[np.newaxis,:] # converts shape (3,) to (0,3)
v = v[np.newaxis,:]
m = [m,]
R = [R,]
self.posns = np.concatenate((self.posns, pos))
self.vs = np.concatenate((self.vs, v))
self.ms = np.concatenate((self.ms, [m,]))
self.rs = np.concatenate((self.rs, [R,]))
self.nBodies = self.ms.size
def add_planet_at_pericenter(self, a, e, i=0, phi=0, m=None, R=None):
"""
For setting up a 1-body Keplerian orbit.
a = semimajor axis (m or Quantity)
e = eccentricity
i = inclination (deg)
phi = orientation of perihelion (deg ccw from x-axis)
m = mass (kg or Quantity); only req if an N-body calc will be run
R = radius (m or Quantity); only for collision detection
"""
if self.sun is None:
display("Error: Please run add_sun() first")
return
else:
M_sun = self.ms[self.sun]
a = self.fix_units(a, u.m)
m = self.fix_units(m, u.kg)
R = self.fix_units(R, u.m)
P = np.sqrt(4 * np.pi**2 * a**3/(G * M_sun))
planet = {}
planet['P'] = P
planet['a'] = a
planet['e'] = e
planet['i'] = i
self.planets.append(planet)
# set starting position and velocity, at perihelion
r_dir = np.array([np.cos(phi), np.sin(phi), np.sin(i)])
rhat = r_dir/self.veclen(r_dir)
r_vec = a*(1-e) * rhat
vhat = self.vecperp(rhat)
v_vec = np.sqrt(G*M_sun/a*(1+e)/(1-e)) * vhat
self.posns = np.concatenate((self.posns, r_vec[np.newaxis,:]))
self.vs = np.concatenate((self.vs, v_vec[np.newaxis,:]))
self.ms = np.concatenate((self.ms, [m,]))
self.rs = np.concatenate((self.rs, [R,]))
self.nBodies = self.ms.size
def add_binary(self, masses, a, e, Rs=None):
"""
For setting up a 1-body Keplerian orbit.
masses = 2-tuple (kg or Quantity)
a = semimajor axis (m or Quantity)
e = eccentricity
m = mass (kg or Quantity); only req if an N-body calc will be run
Rs = radii (m or Quantity); only for collision detection
"""
raise NotImplementedError
def add_random(self, n, L=50*u.AU, power=1/3, masses=1*u.M_sun, vs=50*u.km/u.s, radii=5*u.R_earth):
"""
Add n bodies at random directions within a sphere of radius L (m)
Density will fall off as `power` from the origin
Masses (kg) and radii (m) can each be:
- a list/array which will be converted to length n as needed
- a number giving the mid-point of a distribution
"""
def random_direction():
ra = 2*np.pi*np.random.rand(n)
dec = np.arccos(2*np.random.rand(n) - 1) - np.pi/2
return ra, dec
def random_unit_vector():
theta, phi = random_direction()
x = np.cos(phi) * np.sin(theta)
y = np.cos(phi) * np.cos(theta)
z = np.sin(phi)
return np.vstack((x, y, z)).transpose()
def create_distribution(x, sd, shape=None):
if self.is_iterable(x): # list, may need to adjust length
if len(x) < n:
reps = n//len(x) + 1
x = np.tile(x, reps)
x = x[:n]
else: # x is a midpoint, create a Gaussian around it
# but don't let the tail go negative!
if shape:
x = np.abs(np.random.standard_normal(shape)*sd + 1) * x
else:
x = np.abs(np.random.randn(n)*sd + 1) * x
return x
L = self.fix_units(L, u.m)
masses = self.fix_units(masses, u.kg)
vs = self.fix_units(vs, u.m/u.s)
radii = self.fix_units(radii, u.m)
distances = L * np.random.rand(n)**power
posns = random_unit_vector() * distances[:,np.newaxis]
masses = create_distribution(masses, 0.2)
vs = create_distribution(vs, 0.3, shape=(n,3))
radii = create_distribution(radii, 0.1)
self.posns = np.concatenate((self.posns, posns))
self.vs = np.concatenate((self.vs, vs))
self.ms = np.concatenate((self.ms, masses))
self.rs = np.concatenate((self.rs, radii))
self.nBodies = self.ms.size
self.fix_CoM()
#-------------------------------------------------------------------
# Methods to integrate forward in time
def integrate_1body(self, t_end=None, nOrbits=1, dt=None,
points_per_orbit=200, inx=-1, resTbl=True):
"""
Run a 1-body (Keplerian) orbit.
nOrbits = number of full periods
dt = time step (s or Quantity)
points_per_orbit: used to calculate dt if necessary
inx = index into self.planets to get orbit data (defaults to last)
"""
if self.sun is None:
display("Error: Please run add_sun() first")
return
else:
M_sun = self.ms[self.sun]
# Quantities are accepted as parameters but the integrator needs dimensionless values
t_end = self.fix_units(t_end, u.s)
dt = self.fix_units(dt, u.s)
# get period and calculate (if necessary) time step
P = self.planets[inx]['P']
if dt is None:
dt = P/points_per_orbit # seconds
if t_end is None:
t_end = nOrbits*P # seconds
# set the total time range, and the intermediate time points
t_span = (0, t_end) # (start, end) 2-tuple
t_vals = | np.arange(0, t_end, dt) | numpy.arange |
# ***************************************************************
# Copyright (c) 2020 Jittor. All Rights Reserved.
# Authors:
# <NAME> <<EMAIL>>
# <NAME> <<EMAIL>>
# <NAME> <<EMAIL>>.
#
# This file is subject to the terms and conditions defined in
# file 'LICENSE.txt', which is part of this source code package.
# ***************************************************************
import jittor as jt
import numpy as np
import unittest
try:
import autograd.numpy as anp
from autograd import jacobian
has_autograd = True
except:
has_autograd = False
@unittest.skipIf(not has_autograd, "No autograd found.")
class TestCodeOp(unittest.TestCase):
def test_svd(self):
def check_svd(a):
u,s,v = anp.linalg.svd(a, full_matrices=0)
return u,s,v
def check_u(a):
u,s,v = anp.linalg.svd(a, full_matrices=0)
return u
def check_s(a):
u,s,v = anp.linalg.svd(a, full_matrices=0)
return s
def check_v(a):
u,s,v = anp.linalg.svd(a, full_matrices=0)
return v
for i in range(50):
#not for full-matrices!
a = jt.random((2,2,5,4))
c_a = anp.array(a.data)
u,s,v = jt.linalg.svd(a)
tu,ts,tv = check_svd(c_a)
assert np.allclose(tu,u.data)
assert np.allclose(ts,s.data)
assert np.allclose(tv,v.data)
ju = jt.grad(u,a)
js = jt.grad(s,a)
jv = jt.grad(v,a)
grad_u = jacobian(check_u)
gu = grad_u(c_a)
gu = np.sum(gu, 4)
gu = np.sum(gu, 4)
gu = np.sum(gu, 2)
gu = np.sum(gu, 2)
grad_s = jacobian(check_s)
gs = grad_s(c_a)
gs = np.sum(gs, 4)
gs = np.sum(gs, 2)
gs = np.sum(gs, 2)
grad_v = jacobian(check_v)
gv = grad_v(c_a)
gv = np.sum(gv, 4)
gv = np.sum(gv, 4)
gv = np.sum(gv, 2)
gv = np.sum(gv, 2)
try:
assert np.allclose(ju.data,gu,atol=1e-5)
except AssertionError:
print(ju.data)
print(gu)
try:
assert np.allclose(js.data,gs,atol=1e-5)
except AssertionError:
print(js.data)
print(gs)
try:
assert np.allclose(jv.data,gv,atol=1e-5)
except AssertionError:
print(jv.data)
print(gv)
def test_eigh(self):
def check_eigh(a,UPLO='L'):
w, v = anp.linalg.eigh(a,UPLO)
return w, v
def check_w(a,UPLO='L'):
w, v = anp.linalg.eigh(a,UPLO)
return w
def check_v(a,UPLO='L'):
w, v = anp.linalg.eigh(a,UPLO)
return v
for i in range(50):
a = jt.random((2,2,3,3))
c_a = a.data
w, v = jt.linalg.eigh(a)
tw, tv = check_eigh(c_a)
assert np.allclose(w.data,tw)
assert np.allclose(v.data,tv)
jw = jt.grad(w, a)
jv = jt.grad(v, a)
check_gw = jacobian(check_w)
check_gv = jacobian(check_v)
gw = check_gw(c_a)
gw = np.sum(gw,4)
gw = np.sum(gw,2)
gw = np.sum(gw,2)
assert np.allclose(gw,jw.data,rtol = 1,atol = 5e-8)
gv = check_gv(c_a)
gv = np.sum(gv,4)
gv = np.sum(gv,4)
gv = np.sum(gv,2)
gv = np.sum(gv,2)
assert np.allclose(gv,jv.data,rtol = 1,atol = 5e-8)
def test_pinv(self):
def check_pinv(a):
w = anp.linalg.pinv(a)
return w
for i in range(50):
x = jt.random((2,2,4,4))
c_a = x.data
mx = jt.linalg.pinv(x)
tx = check_pinv(c_a)
np.allclose(mx.data,tx)
jx = jt.grad(mx,x)
check_grad = jacobian(check_pinv)
gx = check_grad(c_a)
np.allclose(gx,jx.data)
def test_inv(self):
def check_inv(a):
w = anp.linalg.inv(a)
return w
for i in range(50):
tn = np.random.randn(4,4).astype('float32')*5
while np.allclose(np.linalg.det(tn),0):
tn = np.random.randn((4,4)).astype('float32')*5
x = jt.array(tn)
x = x.reindex([2,2,x.shape[0],x.shape[1]],["i2","i3"])
c_a = x.data
mx = jt.linalg.inv(x)
tx = check_inv(c_a)
np.allclose(mx.data,tx)
jx = jt.grad(mx,x)
check_grad = jacobian(check_inv)
gx = check_grad(c_a)
np.allclose(gx,jx.data)
def test_slogdet(self):
def check_ans(a):
s, w = anp.linalg.slogdet(a)
return s, w
def check_slogdet(a):
s, w = anp.linalg.slogdet(a)
return w
for i in range(50):
tn = np.random.randn(4,4).astype('float32')*10
while np.allclose(np.linalg.det(tn),0):
tn = np.random.randn((4,4)).astype('float32')*10
x = jt.array(tn)
x = x.reindex([2,2,x.shape[0],x.shape[1]],["i2","i3"])
s = list(x.shape)
det_s = s[:-2]
if len(det_s) == 0:
det_s.append(1)
sign, mx = jt.linalg.slogdet(x)
ts, ta = check_ans(x.data)
assert np.allclose(sign.data, ts)
assert np.allclose(mx.data, ta)
jx = jt.grad(mx,x)
check_sgrad = jacobian(check_slogdet)
gx = check_sgrad(x.data)
gx = np.sum(gx,2)
gx = np.sum(gx,2)
assert | np.allclose(gx,jx.data) | numpy.allclose |
import matplotlib.pyplot as plt
from pandas import read_csv
from sklearn.preprocessing import MinMaxScaler, StandardScaler
import numpy as np
from test_labels_loader import load_test_labels
def minmax_rescale(probability):
scaler = MinMaxScaler(feature_range=(0.000000001, 0.999999999))
return scaler.fit_transform(probability)
def softmax_rescale(probability):
norm_x = StandardScaler().fit_transform(probability)
return 1.0 / (1.0 + np.exp(-norm_x))
def plot(clips, probs, labels, scale=None):
x, y = [], []
for i, subject in enumerate(subjects):
subject_idx = []
for j, s in enumerate(clips):
if subject in s:
subject_idx.append(j)
subject_idx = np.array(subject_idx)
subj_prob = probs[subject_idx]
if scale == 'softmax':
y.extend(softmax_rescale(np.expand_dims(subj_prob, axis=1)))
elif scale == 'minmax':
y.extend(minmax_rescale(np.expand_dims(subj_prob, axis=1)))
else:
y.extend(subj_prob)
x.extend([i] * len(subject_idx))
x = np.array(x, dtype='float32')
y = | np.array(y) | numpy.array |
import numpy as np, copy, json, os
from numpy import sqrt, dot, cross
from numpy.linalg import norm
from itertools import combinations
from modules import functions as f
np.set_printoptions(suppress=True)
BQi = lambda x: [[x, 0, 0], [0, x, 0], [0, 0, x], [-x, 0, 0], [0, -x, 0], [0, 0, -x]]
sst_dict = {0: 'H', 1: 'E', 2: 'L'}
def st_or(xyz, bq, p):
res = None
xyz_tr = xyz - xyz[0]
norm = xyz_tr[1]/np.linalg.norm(xyz_tr[1])
ortha = np.cross(bq[1], norm)
a1 = f.dihedral(np.array([xyz_tr[1], bq[0], ortha, bq[1]]))
if a1 == a1:
xyz_r1 = f.rotate_dihedral(a1, ortha, bq[0], xyz_tr)
a2 = f.dihedral(np.array([xyz_r1[2], bq[0], xyz_r1[1], bq[2]]))
if a2 == a2:
xyz_r2 = f.rotate_dihedral(a2, xyz_r1[1], bq[0], xyz_r1)
q = trilaterate(xyz_r2, p)
if q is not None:
pts1 = np.vstack((xyz_r2, q[0]))
pts1 = f.rotate_dihedral(-a2, pts1[1], bq[0], pts1)
pts1 = f.rotate_dihedral(-a1, ortha, bq[0], pts1) + xyz[0]
pts2 = np.vstack((xyz_r2, q[1]))
pts2 = f.rotate_dihedral(-a2, pts2[1], bq[0], pts2)
pts2 = f.rotate_dihedral(-a1, ortha, bq[0], pts2) + xyz[0]
res = [pts1[-1], pts2[-1]]
return res
def trilaterate(pts, ds):
temp1 = pts[1]-pts[0]
e_x = temp1/norm(temp1)
temp2 = pts[2]-pts[0]
i = dot(e_x, temp2)
temp3 = temp2 - i*e_x
e_y = temp3/norm(temp3)
e_z = cross(e_x,e_y)
d = norm(pts[1]-pts[0])
j = dot(e_y,temp2)
x = (ds[0]**2 - ds[1]**2 + d*d) / (2*d)
y = (ds[0]**2 - ds[2]**2 - 2*i*x + i*i + j*j) / (2*j)
temp4 = ds[0]**2 - x*x - y*y
if temp4<0:
#raise Exception("The three spheres do not intersect!");
ds[:2] *=1.01
temp1 = pts[1]-pts[0]
e_x = temp1/norm(temp1)
temp2 = pts[2]-pts[0]
i = dot(e_x, temp2)
temp3 = temp2 - i*e_x
e_y = temp3/norm(temp3)
e_z = cross(e_x,e_y)
d = norm(pts[1]-pts[0])
j = dot(e_y,temp2)
x = (ds[0]**2 - ds[1]**2 + d*d) / (2*d)
y = (ds[0]**2 - ds[2]**2 - 2*i*x + i*i + j*j) / (2*j)
temp4 = ds[0]**2 - x*x - y*y
#if temp4<0:
# raise Exception("The three spheres do not intersect!");
if temp4 >= 0:
z = temp4**0.5
res = [[x, y, z], [x, y, -z]]
else:
res = None
return res
def check_side_of_plane(p, x):
v1 = p[1] - p[0]
v2 = p[2] - p[0]
va = x - p[0]
cp = np.cross(v1,v2)
d = np.dot(cp, va)
return d
def convert_dm2xyz_48o(dm, dm_ca, xx):
BQ = np.array([[0, 0, 0], [1, 0, 0], [1, 1, 0]])
dist = []
coords = []
for a in range(len(dm)):
ind = np.argsort([abs(x-a) for x in range(len(dm))])[:4]
ind_d = [i for i in list(range(len(dm))) if i not in ind]
init_pts = [dm_ca[ix] for ix in ind]
ypd = np.array([dm[a][ix] for ix in ind])
pos = []
for ip in range(len(init_pts)):
p1, yp1 = init_pts[ip], ypd[ip]
pr, ypr = np.delete(np.array(init_pts), ip, 0), np.delete(ypd, ip)
p = st_or(pr, BQ, ypr)
if p is not None:
#d = [np.abs(yp1 - f.distance(p1, i)) for i in p]
d = [np.abs(yp1 - f.distance(p1, i)) for i in p]
#if abs(d[0] - d[1]) > 0.7:
p = p[np.argsort(d)[0]].tolist()
pos.append(p)
if pos != []:
pos = np.mean(np.array(pos),axis=0)
coords.append(pos.tolist())
else:
print('None')
coords.append(None)
return coords
def convert_dm2xyz_48f(dm, x):
BQ = np.array([[0, 0, 0], [1, 0, 0], [1, 1, 0]])
dist = []
init_pts1 = BQi(x)
n = 0
for a in range(len(dm)-2):
if a==0:
ind = np.argsort(dm[a])[:4]
ind_d = | np.argsort(dm[a]) | numpy.argsort |
# -*- coding: utf-8 -*-
"""
Created on Tue Nov 2 10:45:24 2021
@author: wangy79
Data association class consists of
- data preprocess
- timestamp & frame # interpolation
- unit conversion
- get direction
- get lane info
- object stitching
- GNN: global nearest neighbor (online)
- BM: bipartite matching (online)
- JPDA: joint probablistic data association (online)
- TSM: Time-space matching (offline)
- data postprocess
- iteratively remove and save valid tracks
- output invalid (fragmented / wrong direction / overlapped) tracks
- outlier removal
- connect tracks
- visualization
- time-space diagrams for original data and DA'ed data
- # invalid tracks removed
- spacing distribution B&A
"""
import numpy as np
import utils
import pandas as pd
import utils_vis as vis
import matplotlib.pyplot as plt
import utils_evaluation as ev
import itertools
import multiprocessing
import torch
class Data_Association():
def __init__(self, data_path, params = None):
'''
params = {"method": "gnn",
"start": 0,
"end": 1000,
"lanes": []
"plot_start": 0, # for plotting tracks in online methods
"plot_end": 10,
"preprocess": True
}
'''
self.params = params
if params["preprocess"]:
self.df = utils.preprocess_MC(data_path)
else:
self.df = utils.read_data(data_path)
self.df = self.df[(self.df["Frame #"] >= params["start"]) & (self.df["Frame #"] <= params["end"])]
# if len(params["lanes"]) > 0:
# self.df = self.df[self.df["lane"].isin(params["lanes"])]
self.original = self.df.copy()
self.data = {}
def dist_score(self, B, B_data, DIST_MEAS='maha', DIRECTION=True):
'''
compute euclidean distance between two boxes B and B_data
B: predicted bbox location ['bbr_x','bbr_y', 'fbr_x','fbr_y','fbl_x','fbl_y','bbl_x', 'bbl_y']
B_data: measurement
'''
B = np.reshape(B,(-1,8))
B_data = np.reshape(B_data,(-1,8))
# check sign
if DIRECTION==True:
if (np.sign(B[0,[2]]-B[0,[0]])!=np.sign(B_data[0,[2]]-B_data[0,[0]])) : # if not the same x direction
return 99
diff = B-B_data
diff = diff[0]
if DIST_MEAS == 'xy':
# return np.linalg.norm(B-B_data,2) # RMSE
mae_x = np.mean(np.abs(diff[[0,2,4,6]]))
mae_y = np.mean(np.abs(diff[[1,3,5,7]]))
return (mae_x + mae_y)/2
# weighted x,y displacement, penalize y more heavily
elif DIST_MEAS == 'xyw':
alpha = 0.2
mae_x = np.mean(np.abs(diff[[0,2,4,6]]))
mae_y = np.mean(np.abs(diff[[1,3,5,7]]))
# return alpha*np.linalg.norm(B[[0,2,4,6]]-B_data[[0,2,4,6]],2) + (1-alpha)*np.linalg.norm(B[[1,3,5,7]]-B_data[[1,3,5,7]],2)
return alpha*mae_x + (1-alpha)*mae_y
# mahalanobis distance
elif DIST_MEAS == 'maha':
alpha = (1/1)**2
beta = (1/0.27)**2
d2 = 0
for i in range(4):
d2 += np.sqrt(alpha*diff[i]**2+beta*diff[2*i+1]**2)
return d2/4
# euclidean distance
elif DIST_MEAS == 'ed':
d2 = 0
for i in range(4):
d2 += np.sqrt(diff[i]**2+diff[2*i+1]**2)
return d2/4
else:
return
def iou(self,a,b,DIRECTION=True,AREA=False):
"""
Description
-----------
Calculates intersection over union for all sets of boxes in a and b
Parameters
----------
a : tensor of size [8,3]
bounding boxes in relative coords
b : array of size [8,3]
bounding boxes in relative coords
['bbr_x','bbr_y', 'fbr_x','fbr_y','fbl_x','fbl_y','bbl_x', 'bbl_y']
Returns
-------
iou - float between [0,1] if a, b are valid boxes, -1 otherwise
average iou for a and b
"""
a,b = np.reshape(a,(1,-1)), np.reshape(b,(1,-1))
# if has invalid measurements
if np.isnan(sum(sum(a))) or np.isnan(sum(sum(b))):
if AREA==True:
return 0,-1,-1
else: return 0
ax = np.sort(a[0,[0,2,4,6]])
ay = np.sort(a[0,[1,3,5,7]])
bx = np.sort(b[0,[0,2,4,6]])
by = np.sort(b[0,[1,3,5,7]])
area_a = (ax[3]-ax[0]) * (ay[3]-ay[0])
area_b = (bx[3]-bx[0]) * (by[3]-by[0])
if DIRECTION==True:
if (np.sign(a[0,[2]]-a[0,[0]])!=np.sign(b[0,[2]]-b[0,[0]])):# if not the same x / y direction
if AREA==True:
return -1,area_a,area_b
else:
return -1
minx = max(ax[0], bx[0]) # left
maxx = min(ax[2], bx[2])
miny = max(ay[1], by[1])
maxy = min(ay[3], by[3])
intersection = max(0, maxx-minx) * max(0,maxy-miny)
# union = area_a + area_b - intersection + 1e-06
union = min(area_a,area_b)
iou = intersection/union
if AREA==True:
return iou,area_a,area_b
else: return iou
def predict_tracks_df(self, tracks):
'''
tracks: [dictionary]. Key: car_id, value: df
if a track has only 1 frame, assume 25m/s
otherwise do constant-velocity one-step-forward prediction
Return:
x: last predicted position: array of n_car x 8
tracks: updated dictionary
'''
x = []
pts = ['bbr_x','bbr_y','fbr_x','fbr_y','fbl_x','fbl_y','bbl_x', 'bbl_y']
v = 30 #m/s
mpf = v/30
for car_id, track_df in tracks.items():
# # direction = track_df["direction"].iloc[0]
# direction = np.sign(track_df["fbr_x"].iloc[-1]-track_df["bbr_x"].iloc[-1])
track = np.array(track_df[pts])
direction = np.sign(track[-1][2]-track[-1][0])
# if len(track)>1: # average speed
# frames = np.arange(0,len(track))
# fit = np.polyfit(frames,track,1)
# est_speed = np.mean(fit[0,[0,2,4,6]])
# x_pred = np.polyval(fit, len(track))
# if abs(est_speed)<mpf/2 or (np.sign(est_speed)!=direction) or (abs(x_pred[0]-x_pred[2])<1): # too slow
# x_pred = track[-1,:] + direction* np.array([mpf,0,mpf,0,mpf,0,mpf,0])
# else:
x_pred = track[-1,:] + direction* np.array([mpf,0,mpf,0,mpf,0,mpf,0])
x_pred = np.reshape(x_pred,(1,-1))
x.append(x_pred) # prediction next frame, dim=nx8
new_row = pd.DataFrame(x_pred, columns=pts)
tracks[car_id] = pd.concat([tracks[car_id], new_row])
return x, tracks
def stitch_objects_gnn(self, THRESHOLD_1, THRESHOLD_2):
# define the x,y range to keep track of cars in FOV (meter)
xmin, xmax = min(self.df["x"].values)-10,max(self.df["x"].values)+10
ns = int(np.amin(np.array(self.df[['Frame #']]))) # start frame
nf = int(np.amax(np.array(self.df[['Frame #']]))) # end frame
tracks = dict() # a dictionary to store all current objects in view. key:ID, value:dataframe
pts = ['bbr_x','bbr_y','fbr_x','fbr_y','fbl_x','fbl_y','bbl_x', 'bbl_y']
# pts_img = ["fbrx","fbry","fblx","fbly", "bbrx", "bbry", "bblx", "bbly", "ftrx", "ftry", "ftlx", "ftly", "btrx", "btry", "btlx", "btly"]
newdf = pd.DataFrame()
for k in range(ns,nf):
print("\rFrame {}/{}".format(k,nf),end = "\r",flush = True)
frame = self.df.loc[(self.df['Frame #'] == k)] # TODO: use groupby frame to save time
y = np.array(frame[pts])
notnan = ~np.isnan(y).any(axis=1)
y = y[notnan] # remove rows with missing values (dim = mx8)
frame = frame.iloc[notnan,:]
frame = frame.reset_index(drop=True)
m_box = len(frame)
n_car = len(tracks)
# invalid_tracks = set()
if (n_car > 0): # delete track that are out of view
for car_id in list(tracks.keys()):
# delete track if total matched frames <
last_frame = tracks[car_id].iloc[-1]
last_frame_x = np.array(last_frame[pts])[[0,2,4,6]]
x1,x2 = min(last_frame_x),max(last_frame_x)
frames = tracks[car_id]["Frame #"].values
matched_bool = ~np.isnan(frames)
frames_matched = tracks[car_id].loc[matched_bool]
if (x1<xmin) or (x2>xmax):
if len(frames_matched) > 0: # TODO: this threshold could be a ratio
newid = frames_matched["ID"].iloc[0]
frames_matched["ID"] = newid #unify ID
newdf = pd.concat([newdf,frames_matched])
del tracks[car_id]
n_car -= 1
if (m_box == 0) and (n_car == 0): # simply advance to the next frame
continue
elif (m_box == 0) and (n_car > 0): # if no measurements in current frame, simply predict
x, tracks = self.predict_tracks_df(tracks)
elif (m_box > 0) and (n_car == 0): # create new tracks (initialize)
for i, row in frame.iterrows():
row = frame.loc[i:i,:]
tracks[row['ID'].iloc[0]] = row
else:
x, tracks = self.predict_tracks_df(tracks)
n_car = len(tracks)
curr_id = list(tracks.keys()) # should be n id's
# score = np.ones([m_box,n_car])*(99)
score_dist = np.zeros([m_box,n_car])
score_iou =np.zeros([m_box,n_car])
invalid_meas = set()
# invalid_tracks = set()
for m in range(m_box):
for n in range(n_car):
score_dist[m,n] = self.dist_score(x[n],y[m],'maha')
score_iou[m,n], areaa, areab = self.iou(x[n],y[m],DIRECTION=False,AREA=True)
# if areaa < 0.5:
# invalid_tracks.add(n)
if areab < 1:
invalid_meas.add(m)
# if (1120<k<1130):
# vis.plot_track(np.array(np.vstack(x), dtype=float), np.array(y,dtype=float), curr_id, frame["ID"].values, xmin,xmax, k)
# if 333 in curr_id:
# print("")
gate = np.logical_or(score_dist<THRESHOLD_1, score_iou>0)
matched_length = []
for carid in curr_id:
track = tracks[carid]
matched_length.append(track["Frame #"].count())
pq = np.argsort(matched_length)[::-1] # priority queue
matched_m = set()
for n in pq:
if not any(gate[:,n]): # no matched meas for this track
continue
# find the best match meas for this track
tracks[curr_id[n]] = tracks[curr_id[n]].reset_index(drop=True)
idx_in_gate = np.where(gate[:,n])[0]
best_idx = np.argmin(score_dist[idx_in_gate,n])
m = idx_in_gate[best_idx]
avg_meas = frame.loc[m:m]
tracks[curr_id[n]].drop(tracks[curr_id[n]].tail(1).index,inplace=True) # drop the last row (prediction)
tracks[curr_id[n]] = pd.concat([tracks[curr_id[n]], avg_meas],ignore_index=True)
gate[m,:] = False # elimite m from future selection
matched_m.add(m)
m_unassociated = set(np.arange(m_box))-matched_m
for m in m_unassociated:
# !TODO: make sure that y[m] at not in the gate of each other
if (m not in invalid_meas):
new_id = frame['ID'].iloc[m]
new_meas = frame.loc[m:m]
tracks[new_id] = new_meas
self.df = newdf
return newdf
def stitch_objects_bm(self, THRESHOLD_1, THRESHOLD_2):
'''
bipartite matching based on Maha distance cost
'''
xmin, xmax = min(self.df["x"].values)-10,max(self.df["x"].values)+10
ns = int(np.amin(np.array(self.df[['Frame #']]))) # start frame
nf = int(np.amax(np.array(self.df[['Frame #']]))) # end frame
tracks = dict() # a dictionary to store all current objects in view. key:ID, value:dataframe
pts = ['bbr_x','bbr_y','fbr_x','fbr_y','fbl_x','fbl_y','bbl_x', 'bbl_y']
# pts_img = ["fbrx","fbry","fblx","fbly", "bbrx", "bbry", "bblx", "bbly", "ftrx", "ftry", "ftlx", "ftly", "btrx", "btry", "btlx", "btly"]
newdf = pd.DataFrame()
for k in range(ns,nf):
print("\rFrame {}/{}".format(k,nf),end = "\r",flush = True)
frame = self.df.loc[(self.df['Frame #'] == k)] # TODO: use groupby frame to save time
y = np.array(frame[pts])
notnan = ~np.isnan(y).any(axis=1)
y = y[notnan] # remove rows with missing values (dim = mx8)
frame = frame.iloc[notnan,:]
frame = frame.reset_index(drop=True)
m_box = len(frame)
n_car = len(tracks)
invalid_tracks = set()
if (n_car > 0): # delete track that are out of view
for car_id in list(tracks.keys()):
# delete track if total matched frames <
last_frame = tracks[car_id].iloc[-1]
last_frame_x = np.array(last_frame[pts])[[0,2,4,6]]
x1,x2 = min(last_frame_x),max(last_frame_x)
frames = tracks[car_id]["Frame #"].values
matched_bool = ~np.isnan(frames)
frames_matched = tracks[car_id].loc[matched_bool]
if (x1<xmin) or (x2>xmax) or (car_id in invalid_tracks):
if len(frames_matched) > 0: # TODO: this threshold could be a ratio
newid = frames_matched["ID"].iloc[0]
frames_matched["ID"] = newid #unify ID
newdf = pd.concat([newdf,frames_matched])
del tracks[car_id]
n_car -= 1
if (m_box == 0) and (n_car == 0): # simply advance to the next frame
continue
elif (m_box == 0) and (n_car > 0): # if no measurements in current frame, simply predict
x, tracks = self.predict_tracks_df(tracks)
elif (m_box > 0) and (n_car == 0): # create new tracks (initialize)
for i, row in frame.iterrows():
row = frame.loc[i:i,:]
tracks[row['ID'].iloc[0]] = row
else:
x, tracks = self.predict_tracks_df(tracks)
n_car = len(tracks)
curr_id = list(tracks.keys()) # should be n id's
# score = np.ones([m_box,n_car])*(99)
score_dist = np.zeros([m_box,n_car])
score_iou =np.zeros([m_box,n_car])
invalid_meas = set()
invalid_tracks = set()
for m in range(m_box):
for n in range(n_car):
score_dist[m,n] = self.dist_score(x[n],y[m],'maha')
score_iou[m,n], areaa, areab = self.iou(x[n],y[m],DIRECTION=False,AREA=True)
if areaa < 0.5:
invalid_tracks.add(n)
if areab < 1:
invalid_meas.add(m)
# if (1715<k<1760):
# vis.plot_track(np.array(np.vstack(x), dtype=float), np.array(y,dtype=float), curr_id, frame["ID"].values, xmin,xmax, k)
# bipartite matching
# score_dist[score_dist>THRESHOLD_1]=np.inf
a,b = scipy.optimize.linear_sum_assignment(score_dist)
gate = np.logical_or(score_dist<THRESHOLD_1, score_iou>0)
matched_m = set()
for i in range(len(a)):
if gate[a[i]][b[i]]:
n,m = b[i], a[i]
tracks[curr_id[n]] = tracks[curr_id[n]].reset_index(drop=True)
avg_meas = frame.loc[m:m]
tracks[curr_id[n]].drop(tracks[curr_id[n]].tail(1).index,inplace=True) # drop the last row (prediction)
tracks[curr_id[n]] = pd.concat([tracks[curr_id[n]], avg_meas],ignore_index=True)
matched_m.add(m)
# m_unassociated = np.where(np.sum(gate, axis=1)==0)[0]
m_unassociated = set(np.arange(m_box))-matched_m
for m in m_unassociated:
# !TODO: make sure that y[m] at not in the gate of each other
if (m not in invalid_meas) and (all(gate[m,:])==False) :
new_id = frame['ID'].iloc[m]
new_meas = frame.loc[m:m]
tracks[new_id] = new_meas
print("\n")
print("Before DA: {} unique IDs".format(self.df.groupby("ID").ngroups))
print("After DA: {} unique IDs".format(newdf.groupby("ID").ngroups))
self.df = newdf
return
def stitch_objects_jpda(self, THRESHOLD_1, THRESHOLD_2):
'''
10/20/2021
use JPDA, weighted average of all meas that fall into a gate (defined by IOU and mahalanobis distance)
create new ID for meas out side of the gate
'''
# define the x,y range to keep track of cars in FOV (meter)
xmin, xmax = min(self.df["x"].values)-10,max(self.df["x"].values)+10
ns = int(np.amin(np.array(self.df[['Frame #']]))) # start frame
nf = int(np.amax(np.array(self.df[['Frame #']]))) # end frame
tracks = dict() # a dictionary to store all current objects in view. key:ID, value:dataframe
pts = ['bbr_x','bbr_y','fbr_x','fbr_y','fbl_x','fbl_y','bbl_x', 'bbl_y']
pts_img = ["fbrx","fbry","fblx","fbly", "bbrx", "bbry", "bblx", "bbly", "ftrx", "ftry", "ftlx", "ftly", "btrx", "btry", "btlx", "btly"]
newdf = pd.DataFrame()
for k in range(ns,nf):
print("\rFrame {}/{}".format(k,nf),end = "\r",flush = True)
frame = self.df.loc[(self.df['Frame #'] == k)] # TODO: use groupby frame to save time
y = np.array(frame[pts])
notnan = ~np.isnan(y).any(axis=1)
y = y[notnan] # remove rows with missing values (dim = mx8)
frame = frame.iloc[notnan,:]
frame = frame.reset_index(drop=True)
m_box = len(frame)
n_car = len(tracks)
if (n_car > 0): # delete track that are out of view
for car_id in list(tracks.keys()):
# delete track if total matched frames <
last_frame = tracks[car_id].iloc[-1]
last_frame_x = np.array(last_frame[pts])[[0,2,4,6]]
x1,x2 = min(last_frame_x),max(last_frame_x)
frames = tracks[car_id]["Frame #"].values
matched_bool = ~np.isnan(frames)
frames_matched = tracks[car_id].loc[matched_bool]
if (x1<xmin) or (x2>xmax):
if len(frames_matched) > 0: # TODO: this threshold could be a ratio
newid = frames_matched["ID"].iloc[0]
frames_matched["ID"] = newid #unify ID
newdf = pd.concat([newdf,frames_matched])
del tracks[car_id]
n_car -= 1
if (m_box == 0) and (n_car == 0): # simply advance to the next frame
continue
elif (m_box == 0) and (n_car > 0): # if no measurements in current frame, simply predict
x, tracks = self.predict_tracks_df(tracks)
elif (m_box > 0) and (n_car == 0): # create new tracks (initialize)
for i, row in frame.iterrows():
row = frame.loc[i:i,:]
tracks[row['ID'].iloc[0]] = row
else:
x, tracks = self.predict_tracks_df(tracks)
n_car = len(tracks)
curr_id = list(tracks.keys()) # should be n id's
# score = np.ones([m_box,n_car])*(99)
score_dist = np.zeros([m_box,n_car])
score_iou =np.zeros([m_box,n_car])
invalid_meas = []
for m in range(m_box):
for n in range(n_car):
score_dist[m,n] = self.dist_score(x[n],y[m],'maha')
score_iou[m,n], areaa, areab = self.iou(x[n],y[m],DIRECTION=False,AREA=True)
if areab < 2: # invalid measurement
score_dist[m,:] = 99
score_iou[m,:] = -1
invalid_meas.append(m)
if (1260<k<1300):
vis.plot_track(np.array(np.vstack(x), dtype=float), np.array(y,dtype=float), curr_id, frame["ID"].values, xmin,xmax, k)
# if k == 409:
# print("")
# matching
gate = np.logical_or(score_dist<THRESHOLD_1, score_iou>0)
for n in range(n_car):
if any(gate[:,n]):
# calculate weighted average
tracks[curr_id[n]] = tracks[curr_id[n]].reset_index(drop=True)
frames_in_gate = frame.iloc[gate[:,n]]
if len(frames_in_gate) == 1:
avg_meas = frames_in_gate
else:
w = 1/score_dist[gate[:,n],n]
w = w / w.sum(axis=0)
frame_vals = np.array(frames_in_gate[pts_img+pts])
avg_meas_vals = np.reshape(np.dot(w,frame_vals),(1,-1))
avg_meas = pd.DataFrame(data=avg_meas_vals, columns=pts_img + pts)
avg_meas["Frame #"] = k
tracks[curr_id[n]].drop(tracks[curr_id[n]].tail(1).index,inplace=True) # drop the last row (prediction)
tracks[curr_id[n]] = pd.concat([tracks[curr_id[n]], avg_meas],ignore_index=True)
m_unassociated = np.where( | np.sum(gate, axis=1) | numpy.sum |
from __future__ import print_function, absolute_import, division
import numpy as np
from numba import unittest_support as unittest
from numba import hsa, intp
@hsa.jit(device=True)
def device_scan_generic(tid, data):
"""Inclusive prefix sum within a single block
Requires tid should have range [0, data.size) and data.size must be
power of 2.
"""
n = data.size
# Upsweep
offset = 1
d = n // 2
while d > 0:
hsa.barrier(hsa.CLK_GLOBAL_MEM_FENCE)
if tid < d:
ai = offset * (2 * tid + 1) - 1
bi = offset * (2 * tid + 2) - 1
data[bi] += data[ai]
offset *= 2
d //= 2
hsa.barrier(hsa.CLK_GLOBAL_MEM_FENCE)
prefixsum = data[n - 1]
hsa.barrier(hsa.CLK_GLOBAL_MEM_FENCE)
if tid == 0:
data[n - 1] = 0
# Downsweep
d = 1
offset = n
while d < n:
offset //= 2
hsa.barrier(hsa.CLK_GLOBAL_MEM_FENCE)
if tid < d:
ai = offset * (2 * tid + 1) - 1
bi = offset * (2 * tid + 2) - 1
tmp = data[ai]
data[ai] = data[bi]
data[bi] += tmp
d *= 2
hsa.barrier(hsa.CLK_GLOBAL_MEM_FENCE)
return prefixsum
_WARPSIZE = 64
@hsa.jit(device=True)
def warp_scan(tid, temp, inclusive):
"""Intra-warp scan
Note
----
Assume all threads are in lockstep
"""
hsa.wavebarrier()
lane = tid & (_WARPSIZE - 1)
if lane >= 1:
temp[tid] += temp[tid - 1]
hsa.wavebarrier()
if lane >= 2:
temp[tid] += temp[tid - 2]
hsa.wavebarrier()
if lane >= 4:
temp[tid] += temp[tid - 4]
hsa.wavebarrier()
if lane >= 8:
temp[tid] += temp[tid - 8]
hsa.wavebarrier()
if lane >= 16:
temp[tid] += temp[tid - 16]
hsa.wavebarrier()
if lane >= 32:
temp[tid] += temp[tid - 32]
hsa.wavebarrier()
if inclusive:
return temp[tid]
else:
return temp[tid - 1] if lane > 0 else 0
@hsa.jit(device=True)
def device_scan(tid, data, temp, inclusive):
"""
Args
----
tid:
thread id
data: scalar
input for tid
temp: shared memory for temporary work
"""
lane = tid & (_WARPSIZE - 1)
warpid = tid >> 6
# Preload
temp[tid] = data
hsa.barrier(hsa.CLK_GLOBAL_MEM_FENCE)
# Scan warps in parallel
warp_scan_res = warp_scan(tid, temp, inclusive)
hsa.barrier(hsa.CLK_GLOBAL_MEM_FENCE)
# Get parital result
if lane == (_WARPSIZE - 1):
temp[warpid] = temp[tid]
hsa.barrier(hsa.CLK_GLOBAL_MEM_FENCE)
# Scan the partial results
if warpid == 0:
warp_scan(tid, temp, True)
hsa.barrier(hsa.CLK_GLOBAL_MEM_FENCE)
# Accumlate scanned partial results
if warpid > 0:
warp_scan_res += temp[warpid - 1]
hsa.barrier(hsa.CLK_GLOBAL_MEM_FENCE)
# Output
if tid == temp.size - 1:
# Last thread computes prefix sum
if inclusive:
temp[0] = warp_scan_res
else:
temp[0] = warp_scan_res + data
hsa.barrier(hsa.CLK_GLOBAL_MEM_FENCE)
# Load prefixsum
prefixsum = temp[0]
hsa.barrier(hsa.CLK_GLOBAL_MEM_FENCE)
return warp_scan_res, prefixsum
@hsa.jit(device=True)
def shuffle_up(val, width):
tid = hsa.get_local_id(0)
hsa.wavebarrier()
res = hsa.activelanepermute_wavewidth(val, tid - width, 0, False)
return res
@hsa.jit(device=True)
def shuf_wave_inclusive_scan(val):
tid = hsa.get_local_id(0)
lane = tid & (_WARPSIZE - 1)
hsa.wavebarrier()
shuf = shuffle_up(val, 1)
if lane >= 1:
val += shuf
hsa.wavebarrier()
shuf = shuffle_up(val, 2)
if lane >= 2:
val += shuf
hsa.wavebarrier()
shuf = shuffle_up(val, 4)
if lane >= 4:
val += shuf
hsa.wavebarrier()
shuf = shuffle_up(val, 8)
if lane >= 8:
val += shuf
hsa.wavebarrier()
shuf = shuffle_up(val, 16)
if lane >= 16:
val += shuf
hsa.wavebarrier()
shuf = shuffle_up(val, 32)
if lane >= 32:
val += shuf
hsa.wavebarrier()
return val
@hsa.jit(device=True)
def shuf_device_inclusive_scan(data, temp):
"""
Args
----
data: scalar
input for tid
temp: shared memory for temporary work, requires at least
threadcount/wavesize storage
"""
tid = hsa.get_local_id(0)
lane = tid & (_WARPSIZE - 1)
warpid = tid >> 6
# Scan warps in parallel
warp_scan_res = shuf_wave_inclusive_scan(data)
hsa.barrier()
# Store partial sum into shared memory
if lane == (_WARPSIZE - 1):
temp[warpid] = warp_scan_res
hsa.barrier()
# Scan the partial sum by first wave
if warpid == 0:
shuf_wave_inclusive_scan(temp[lane])
hsa.barrier()
# Get block sum for each wave
blocksum = 0 # first wave is 0
if warpid > 0:
blocksum = temp[warpid - 1]
return warp_scan_res + blocksum
class TestScan(unittest.TestCase):
def test_single_block(self):
@hsa.jit
def scan_block(data, sums):
sm_data = hsa.shared.array(64, dtype=intp)
tid = hsa.get_local_id(0)
gid = hsa.get_global_id(0)
blkid = hsa.get_group_id(0)
sm_data[tid] = data[gid]
prefixsum = device_scan_generic(tid, sm_data)
data[gid] = sm_data[tid]
if tid == 0:
sums[blkid] = prefixsum
data = | np.random.randint(0, 4, size=64) | numpy.random.randint |
import numpy as np
import datetime
from time import time
from .binning import Binning
from .binning import Binning_Types
from .helper import objectview
from .preprocessors import DataSource
class BundleGenerator():
def __init__(self, model, binning):
self.__model = model
self.__binning = binning.copy()
self.__last_seed = None
self.__compute_probability_matrix()
pass
def recommended_amount(self, real_histogram):
"""real_histogram: the histogram of the model's source data
binned with the new binning."""
min_prob = self.probabilities[
(self.probabilities[:, -1] > 0) *
(real_histogram.values.flatten() > 0),
-1].min()
if min_prob > 0:
return int(np.ceil(1/min_prob))
else:
return 0
def expected_best_quality(self, amount, real_histogram):
"""real_histogram: the histogram of the model's source data
binned with the new binning."""
index = np.array([p * amount >= 1 or
real_histogram.values.flatten()[i] == 0
for i, p in enumerate(self.probabilities[:, -1])])
return self.binning.volumes.flatten()[index].sum() / \
self.binning.total_volume
def __compute_probability_matrix(self):
all_edges = [
np.unique(np.concatenate((gbe, mbe)))
for gbe, mbe in zip(self.binning.edges,
self.model.binning.edges)
]
# Create sub_edges for each bin and along each dimension.
sub_edges = []
for edges, coarse in zip(all_edges, self.binning.edges):
sub_edges.append(
[edges[(edges >= left) * (edges <= right)]
for left, right in zip(coarse[:-1], coarse[1:])]
)
# sub_edges is an n-dim list of lists of arrays:
# sub_edges[dim][bin_index] contains the sub edges along dimension
# dim for bin with index bin_index along that dimension.
# Create a 1d list of all bin indices (along all dimensions)
bin_indices = [range(0, i) for i in self.binning.counts]
bin_indices = np.meshgrid(*bin_indices, indexing='ij')
bin_indices = list(zip(*[mg.flatten() for mg in bin_indices]))
# here bin_indices equals [ (x0, y0, z0), (x0, y0, z1), (x0, y1, z0) ... ]
# Probabilities is a matrix with one row per bin with the format:
# c_x, c_y, c_z, ... , probability
# for each bin/row, where c_i indicates the center of the bin.
probabilities = np.zeros((len(bin_indices),
self.binning.dimensions + 1))
for i, bin_index in enumerate(bin_indices):
# Find center of current bin
probabilities[i, :-1] = [cpd[idx] for idx, cpd in
zip(bin_index, self.binning.centers)]
# Create sub-binning to calculate probability of bin
sub_binning = Binning(Binning_Types.SUBBINNING,
[sub_edges[dim][idx] for dim, idx in enumerate(bin_index)])
factors = sub_binning.volumes / sub_binning.total_volume
alltF = self.model.F(*sub_binning.meshgrids).flatten()
alltF = [x if x > 0.0 else 0.0 for x in alltF]
alltF = alltF * factors.flatten()
probabilities[i, -1] = sum(alltF)
probabilities[:, -1] /= | np.linalg.norm(probabilities[:, -1], ord=1) | numpy.linalg.norm |
import warnings
import ctypes as _ctypes
# Load mkl_spblas through the libmkl_rt common interface
# Check each of these library types
_MKL_SO_LINUX = "libmkl_rt.so"
_MKL_SO_OSX = "libmkl_rt.dylib"
_MKL_SO_WINDOWS = "mkl_rt.dll"
# There's probably a better way to do this
_libmkl, _libmkl_loading_errors = None, []
for so_file in [_MKL_SO_LINUX, _MKL_SO_OSX, _MKL_SO_WINDOWS]:
try:
_libmkl = _ctypes.cdll.LoadLibrary(so_file)
break
except (OSError, ImportError) as err:
_libmkl_loading_errors.append(err)
if _libmkl is None:
ierr_msg = "Unable to load the MKL libraries through libmkl_rt. Try setting $LD_LIBRARY_PATH."
ierr_msg += "\n\t" + "\n\t".join(map(lambda x: str(x), _libmkl_loading_errors))
raise ImportError(ierr_msg)
# Use mkl-service to check version if it's installed
# Since it's not on PyPi I don't want to make this an actual package dependency
# So without it just create mock functions and don't do version checking
try:
from mkl import get_version, get_version_string
except ImportError:
def get_version():
return None
def get_version_string():
return None
if get_version() is not None and get_version()["MajorVersion"] < 2020:
msg = "Loaded version of MKL is out of date: {v}".format(v=get_version_string())
warnings.warn(msg)
import numpy as np
import scipy.sparse as _spsparse
from numpy.ctypeslib import ndpointer, as_array
NUMPY_FLOAT_DTYPES = [np.float32, np.float64]
class MKL:
""" This class holds shared object references to C functions with arg and returntypes that can be adjusted"""
MKL_INT = None
MKL_INT_NUMPY = None
# Import function for creating a MKL CSR object
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-create-csr
_mkl_sparse_d_create_csr = _libmkl.mkl_sparse_d_create_csr
# Import function for creating a MKL CSR object
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-create-csr
_mkl_sparse_s_create_csr = _libmkl.mkl_sparse_s_create_csr
# Import function for creating a MKL CSC object
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-create-csc
_mkl_sparse_d_create_csc = _libmkl.mkl_sparse_d_create_csc
# Import function for creating a MKL CSC object
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-create-csc
_mkl_sparse_s_create_csc = _libmkl.mkl_sparse_s_create_csc
# Export function for exporting a MKL CSR object
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-export-csr
_mkl_sparse_d_export_csr = _libmkl.mkl_sparse_d_export_csr
# Export function for exporting a MKL CSR object
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-export-csr
_mkl_sparse_s_export_csr = _libmkl.mkl_sparse_s_export_csr
# Export function for exporting a MKL CSC object
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-export-csc
_mkl_sparse_d_export_csc = _libmkl.mkl_sparse_d_export_csc
# Export function for exporting a MKL CSC object
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-export-csc
_mkl_sparse_s_export_csc = _libmkl.mkl_sparse_s_export_csc
# Import function for matmul
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-spmm
_mkl_sparse_spmm = _libmkl.mkl_sparse_spmm
# Import function for product of sparse matrix with its transpose
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-syrk
_mkl_sparse_syrk = _libmkl.mkl_sparse_syrk
# Import function for cleaning up MKL objects
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-destroy
_mkl_sparse_destroy = _libmkl.mkl_sparse_destroy
# Import function for ordering MKL objects
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-order
_mkl_sparse_order = _libmkl.mkl_sparse_order
# Import function for coverting to CSR
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-convert-csr
_mkl_sparse_convert_csr = _libmkl.mkl_sparse_convert_csr
# Import function for matmul single dense
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-spmm
_mkl_sparse_s_spmmd = _libmkl.mkl_sparse_s_spmmd
# Import function for matmul double dense
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-spmm
_mkl_sparse_d_spmmd = _libmkl.mkl_sparse_d_spmmd
# Import function for matmul single sparse*dense
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-mm
_mkl_sparse_s_mm = _libmkl.mkl_sparse_s_mm
# Import function for matmul double sparse*dense
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-mm
_mkl_sparse_d_mm = _libmkl.mkl_sparse_d_mm
# Import function for matmul single dense*dense
# https://software.intel.com/en-us/mkl-developer-reference-c-cblas-gemm
_cblas_sgemm = _libmkl.cblas_sgemm
# Import function for matmul double dense*dense
# https://software.intel.com/en-us/mkl-developer-reference-c-cblas-gemm
_cblas_dgemm = _libmkl.cblas_dgemm
# Import function for matrix * vector
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-mv
_mkl_sparse_s_mv = _libmkl.mkl_sparse_s_mv
# Import function for matrix * vector
# https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-mv
_mkl_sparse_d_mv = _libmkl.mkl_sparse_d_mv
@classmethod
def _set_int_type(cls, c_type, np_type):
cls.MKL_INT = c_type
cls.MKL_INT_NUMPY = np_type
cls._mkl_sparse_d_create_csr.argtypes = cls._mkl_sparse_create_argtypes(_ctypes.c_double)
cls._mkl_sparse_d_create_csr.restypes = _ctypes.c_int
cls._mkl_sparse_s_create_csr.argtypes = cls._mkl_sparse_create_argtypes(_ctypes.c_float)
cls._mkl_sparse_s_create_csr.restypes = _ctypes.c_int
cls._mkl_sparse_d_create_csc.argtypes = cls._mkl_sparse_create_argtypes(_ctypes.c_double)
cls._mkl_sparse_d_create_csc.restypes = _ctypes.c_int
cls._mkl_sparse_s_create_csc.argtypes = cls._mkl_sparse_create_argtypes(_ctypes.c_float)
cls._mkl_sparse_s_create_csc.restypes = _ctypes.c_int
cls._mkl_sparse_d_export_csr.argtypes = cls._mkl_export_create_argtypes(_ctypes.c_double)
cls._mkl_sparse_d_export_csr.restypes = _ctypes.c_int
cls._mkl_sparse_s_export_csr.argtypes = cls._mkl_export_create_argtypes(_ctypes.c_float)
cls._mkl_sparse_s_export_csr.restypes = _ctypes.c_int
cls._mkl_sparse_d_export_csc.argtypes = cls._mkl_export_create_argtypes(_ctypes.c_double)
cls._mkl_sparse_d_export_csc.restypes = _ctypes.c_int
cls._mkl_sparse_s_export_csr.argtypes = cls._mkl_export_create_argtypes(_ctypes.c_float)
cls._mkl_sparse_s_export_csr.restypes = _ctypes.c_int
cls._mkl_sparse_spmm.argtypes = [_ctypes.c_int,
sparse_matrix_t,
sparse_matrix_t,
_ctypes.POINTER(sparse_matrix_t)]
cls._mkl_sparse_spmm.restypes = _ctypes.c_int
cls._mkl_sparse_s_spmmd.argtypes = cls._mkl_sparse_spmmd_argtypes(_ctypes.c_float)
cls._mkl_sparse_s_spmmd.restypes = _ctypes.c_int
cls._mkl_sparse_d_spmmd.argtypes = cls._mkl_sparse_spmmd_argtypes(_ctypes.c_double)
cls._mkl_sparse_d_spmmd.restypes = _ctypes.c_int
cls._mkl_sparse_s_mm.argtypes = cls._mkl_sparse_mm_argtypes(_ctypes.c_float)
cls._mkl_sparse_s_mm.restypes = _ctypes.c_int
cls._mkl_sparse_d_mm.argtypes = cls._mkl_sparse_mm_argtypes(_ctypes.c_double)
cls._mkl_sparse_d_mm.restypes = _ctypes.c_int
cls._cblas_sgemm.argtypes = cls._cblas_gemm_argtypes(_ctypes.c_float)
cls._cblas_sgemm.restypes = None
cls._cblas_dgemm.argtypes = cls._cblas_gemm_argtypes(_ctypes.c_double)
cls._cblas_dgemm.restypes = None
cls._mkl_sparse_destroy.argtypes = [sparse_matrix_t]
cls._mkl_sparse_destroy.restypes = _ctypes.c_int
cls._mkl_sparse_order.argtypes = [sparse_matrix_t]
cls._mkl_sparse_order.restypes = _ctypes.c_int
cls._mkl_sparse_s_mv.argtypes = cls._mkl_sparse_mv_argtypes(_ctypes.c_float)
cls._mkl_sparse_s_mv.restypes = _ctypes.c_int
cls._mkl_sparse_d_mv.argtypes = cls._mkl_sparse_mv_argtypes(_ctypes.c_double)
cls._mkl_sparse_d_mv.restypes = _ctypes.c_int
def __init__(self):
raise NotImplementedError("This class is not intended to be instanced")
""" The following methods return the argtype lists for each MKL function that has s and d variants"""
@staticmethod
def _mkl_sparse_create_argtypes(prec_type):
return [_ctypes.POINTER(sparse_matrix_t),
_ctypes.c_int,
MKL.MKL_INT,
MKL.MKL_INT,
ndpointer(dtype=MKL.MKL_INT, ndim=1, flags='C_CONTIGUOUS'),
ndpointer(dtype=MKL.MKL_INT, ndim=1, flags='C_CONTIGUOUS'),
ndpointer(dtype=MKL.MKL_INT, ndim=1, flags='C_CONTIGUOUS'),
ndpointer(dtype=prec_type, ndim=1, flags='C_CONTIGUOUS')]
@staticmethod
def _mkl_export_create_argtypes(prec_type):
return [sparse_matrix_t,
_ctypes.POINTER(_ctypes.c_int),
_ctypes.POINTER(MKL.MKL_INT),
_ctypes.POINTER(MKL.MKL_INT),
_ctypes.POINTER(_ctypes.POINTER(MKL.MKL_INT)),
_ctypes.POINTER(_ctypes.POINTER(MKL.MKL_INT)),
_ctypes.POINTER(_ctypes.POINTER(MKL.MKL_INT)),
_ctypes.POINTER(_ctypes.POINTER(prec_type))]
@staticmethod
def _cblas_gemm_argtypes(prec_type):
return [_ctypes.c_int,
_ctypes.c_int,
_ctypes.c_int,
MKL.MKL_INT,
MKL.MKL_INT,
MKL.MKL_INT,
prec_type,
ndpointer(dtype=prec_type, ndim=2),
MKL.MKL_INT,
ndpointer(dtype=prec_type, ndim=2),
MKL.MKL_INT,
prec_type,
_ctypes.POINTER(prec_type),
MKL.MKL_INT]
@staticmethod
def _mkl_sparse_spmmd_argtypes(prec_type):
return [_ctypes.c_int,
sparse_matrix_t,
sparse_matrix_t,
_ctypes.c_int,
_ctypes.POINTER(prec_type), MKL.MKL_INT]
@staticmethod
def _mkl_sparse_mm_argtypes(prec_type):
return [_ctypes.c_int,
prec_type,
sparse_matrix_t,
matrix_descr,
_ctypes.c_int,
ndpointer(dtype=prec_type, ndim=2),
MKL.MKL_INT,
MKL.MKL_INT,
prec_type,
_ctypes.POINTER(prec_type),
MKL.MKL_INT]
@staticmethod
def _mkl_sparse_mv_argtypes(prec_type):
return [_ctypes.c_int,
prec_type,
sparse_matrix_t,
matrix_descr,
ndpointer(dtype=prec_type, ndim=1),
prec_type,
_ctypes.POINTER(prec_type)]
# Construct opaque struct & type
class _sparse_matrix(_ctypes.Structure):
pass
sparse_matrix_t = _ctypes.POINTER(_sparse_matrix)
# Matrix description struct
class matrix_descr(_ctypes.Structure):
_fields_ = [("sparse_matrix_type_t", _ctypes.c_int),
("sparse_fill_mode_t", _ctypes.c_int),
("sparse_diag_type_t", _ctypes.c_int)]
def __init__(self, sparse_matrix_type_t=20, sparse_fill_mode_t=0, sparse_diag_type_t=0):
super(matrix_descr, self).__init__(sparse_matrix_type_t, sparse_fill_mode_t, sparse_diag_type_t)
# Define standard return codes
RETURN_CODES = {0: "SPARSE_STATUS_SUCCESS",
1: "SPARSE_STATUS_NOT_INITIALIZED",
2: "SPARSE_STATUS_ALLOC_FAILED",
3: "SPARSE_STATUS_INVALID_VALUE",
4: "SPARSE_STATUS_EXECUTION_FAILED",
5: "SPARSE_STATUS_INTERNAL_ERROR",
6: "SPARSE_STATUS_NOT_SUPPORTED"}
# Define order codes
LAYOUT_CODE_C = 101
LAYOUT_CODE_F = 102
def _check_scipy_index_typing(sparse_matrix):
"""
Ensure that the sparse matrix indicies are in the correct integer type
:param sparse_matrix: Scipy matrix in CSC or CSR format
:type sparse_matrix: scipy.sparse.spmatrix
"""
int_max = np.iinfo(MKL.MKL_INT_NUMPY).max
if (sparse_matrix.nnz > int_max) or (max(sparse_matrix.shape) > int_max):
msg = "MKL interface is {t} and cannot hold matrix {m}".format(m=repr(sparse_matrix), t=MKL.MKL_INT_NUMPY)
raise ValueError(msg)
# Cast indexes to MKL_INT type
if sparse_matrix.indptr.dtype != MKL.MKL_INT_NUMPY:
sparse_matrix.indptr = sparse_matrix.indptr.astype(MKL.MKL_INT_NUMPY)
if sparse_matrix.indices.dtype != MKL.MKL_INT_NUMPY:
sparse_matrix.indices = sparse_matrix.indices.astype(MKL.MKL_INT_NUMPY)
def _get_numpy_layout(numpy_arr):
"""
Get the array layout code for a dense array in C or F order.
Raises a ValueError if the array is not contiguous.
:param numpy_arr: Numpy dense array
:type numpy_arr: np.ndarray
:return: The layout code for MKL and the leading dimension
:rtype: int, int
"""
if numpy_arr.flags.c_contiguous:
return LAYOUT_CODE_C, numpy_arr.shape[1]
elif numpy_arr.flags.f_contiguous:
return LAYOUT_CODE_F, numpy_arr.shape[0]
elif not numpy_arr.flags.contiguous:
raise ValueError("Array is not contiguous")
else:
raise ValueError("Array layout check has failed for unknown reason")
def _create_mkl_sparse(matrix):
"""
Create MKL internal representation
:param matrix: Sparse data in CSR or CSC format
:type matrix: scipy.sparse.spmatrix
:return ref, double_precision: Handle for the MKL internal representation and boolean for double precision
:rtype: sparse_matrix_t, float
"""
# Figure out which dtype for data
if matrix.dtype == np.float32:
double_precision = False
elif matrix.dtype == np.float64:
double_precision = True
else:
raise ValueError("Only float32 or float64 dtypes are supported")
# Figure out which matrix creation function to use
if _spsparse.isspmatrix_csr(matrix):
assert matrix.indptr.shape[0] == matrix.shape[0] + 1
handle_func = MKL._mkl_sparse_d_create_csr if double_precision else MKL._mkl_sparse_s_create_csr
elif _spsparse.isspmatrix_csc(matrix):
assert matrix.indptr.shape[0] == matrix.shape[1] + 1
handle_func = MKL._mkl_sparse_d_create_csc if double_precision else MKL._mkl_sparse_s_create_csc
else:
raise ValueError("Matrix is not CSC or CSR")
# Make sure indices are of the correct integer type
_check_scipy_index_typing(matrix)
assert matrix.data.shape[0] == matrix.indices.shape[0]
return _pass_mkl_handle(matrix, handle_func), double_precision
def _pass_mkl_handle(data, handle_func):
"""
Create MKL internal representation
:param data: Sparse data
:type data: scipy.sparse.spmatrix
:return ref: Handle for the MKL internal representation
:rtype: sparse_matrix_t
"""
# Create a pointer for the output matrix
ref = sparse_matrix_t()
# Load into a MKL data structure and check return
ret_val = handle_func(_ctypes.byref(ref),
_ctypes.c_int(0),
MKL.MKL_INT(data.shape[0]),
MKL.MKL_INT(data.shape[1]),
data.indptr[0:-1],
data.indptr[1:],
data.indices,
data.data)
# Check return
if ret_val != 0:
err_msg = "{fn} returned {v} ({e})".format(fn=handle_func.__name__, v=ret_val, e=RETURN_CODES[ret_val])
raise ValueError(err_msg)
return ref
def _export_mkl(csr_mkl_handle, double_precision, output_type="csr"):
"""
Export a MKL sparse handle
:param csr_mkl_handle: Handle for the MKL internal representation
:type csr_mkl_handle: sparse_matrix_t
:param double_precision: Use float64 if True, float32 if False. This MUST match the underlying float type - this
defines a memory view, it does not cast.
:type double_precision: bool
:param output_type: The structure of the MKL handle (and therefore the type of scipy sparse to create)
:type output_type: str
:return: Sparse matrix in scipy format
:rtype: scipy.spmatrix
"""
# Create the pointers for the output data
indptrb = _ctypes.POINTER(MKL.MKL_INT)()
indptren = _ctypes.POINTER(MKL.MKL_INT)()
indices = _ctypes.POINTER(MKL.MKL_INT)()
ordering = _ctypes.c_int()
nrows = MKL.MKL_INT()
ncols = MKL.MKL_INT()
output_type = output_type.lower()
if output_type == "csr":
out_func = MKL._mkl_sparse_d_export_csr if double_precision else MKL._mkl_sparse_s_export_csr
sp_matrix_constructor = _spsparse.csr_matrix
elif output_type == "csc":
out_func = MKL._mkl_sparse_d_export_csc if double_precision else MKL._mkl_sparse_s_export_csc
sp_matrix_constructor = _spsparse.csc_matrix
else:
raise ValueError("Only CSR and CSC output types are supported")
if double_precision:
data = _ctypes.POINTER(_ctypes.c_double)()
final_dtype = np.float64
else:
data = _ctypes.POINTER(_ctypes.c_float)()
final_dtype = np.float32
ret_val = out_func(csr_mkl_handle,
_ctypes.byref(ordering),
_ctypes.byref(nrows),
_ctypes.byref(ncols),
_ctypes.byref(indptrb),
_ctypes.byref(indptren),
_ctypes.byref(indices),
_ctypes.byref(data))
# Check return
if ret_val != 0:
err_msg = "{fn} returned {v} ({e})".format(fn=out_func.__name__, v=ret_val, e=RETURN_CODES[ret_val])
raise ValueError(err_msg)
# Check ordering
if ordering.value != 0:
raise ValueError("1-indexing (F-style) is not supported")
# Get matrix dims
ncols = ncols.value
nrows = nrows.value
# If any axis is 0 return an empty matrix
if nrows == 0 or ncols == 0:
return sp_matrix_constructor((nrows, ncols), dtype=final_dtype)
# Get the index dimension
index_dim = nrows if output_type == "csr" else ncols
# Construct a numpy array and add 0 to first position for scipy.sparse's 3-array indexing
indptrb = as_array(indptrb, shape=(index_dim,))
indptren = as_array(indptren, shape=(index_dim,))
indptren = np.insert(indptren, 0, indptrb[0])
nnz = indptren[-1] - indptrb[0]
# If there are no non-zeros, return an empty matrix
# If the number of non-zeros is insane, raise a ValueError
if nnz == 0:
return sp_matrix_constructor((nrows, ncols), dtype=final_dtype)
elif nnz < 0 or nnz > ncols * nrows:
raise ValueError("Matrix ({m} x {n}) is attempting to index {z} elements".format(m=nrows, n=ncols, z=nnz))
# Construct numpy arrays from data pointer and from indicies pointer
data = np.array(as_array(data, shape=(nnz,)), copy=True)
indices = np.array(as_array(indices, shape=(nnz,)), copy=True)
# Pack and return the matrix
return sp_matrix_constructor((data, indices, indptren), shape=(nrows, ncols))
def _destroy_mkl_handle(ref_handle):
"""
Deallocate a MKL sparse handle
:param ref_handle:
:type ref_handle: sparse_matrix_t
"""
ret_val = MKL._mkl_sparse_destroy(ref_handle)
if ret_val != 0:
raise ValueError("mkl_sparse_destroy returned {v} ({e})".format(v=ret_val, e=RETURN_CODES[ret_val]))
def _order_mkl_handle(ref_handle):
"""
Reorder indexes in a MKL sparse handle
:param ref_handle:
:type ref_handle: sparse_matrix_t
"""
ret_val = MKL._mkl_sparse_order(ref_handle)
if ret_val != 0:
raise ValueError("mkl_sparse_order returned {v} ({e})".format(v=ret_val, e=RETURN_CODES[ret_val]))
def _convert_to_csr(ref_handle, destroy_original=False):
"""
Convert a MKL sparse handle to CSR format
:param ref_handle:
:type ref_handle: sparse_matrix_t
:return:
"""
csr_ref = sparse_matrix_t()
ret_val = MKL._mkl_sparse_convert_csr(ref_handle, _ctypes.c_int(10), _ctypes.byref(csr_ref))
if ret_val != 0:
try:
_destroy_mkl_handle(csr_ref)
except ValueError:
pass
raise ValueError("mkl_sparse_convert_csr returned {v} ({e})".format(v=ret_val, e=RETURN_CODES[ret_val]))
if destroy_original:
_destroy_mkl_handle(ref_handle)
return csr_ref
def _sanity_check(matrix_a, matrix_b, allow_vector=False):
"""
Check matrix dimensions
:param matrix_a: sp.sparse or numpy array
:param matrix_b: sp.sparse or numpy array
"""
a_2d, b_2d = matrix_a.ndim == 2, matrix_b.ndim == 2
a_vec, b_vec = _is_dense_vector(matrix_a), _is_dense_vector(matrix_b)
# Check to make sure that both matrices are 2-d
if not allow_vector and (not a_2d or not b_2d):
err_msg = "Matrices must be 2d: {m1} * {m2} is not valid".format(m1=matrix_a.shape, m2=matrix_b.shape)
raise ValueError(err_msg)
invalid_ndims = not (a_2d or a_vec) or not (b_2d, b_vec)
invalid_align = (matrix_a.shape[1] if not matrix_a.ndim == 1 else matrix_a.shape[0]) != matrix_b.shape[0]
# Check to make sure that this multiplication can work
if invalid_align or invalid_ndims:
err_msg = "Matrix alignment error: {m1} * {m2} is not valid".format(m1=matrix_a.shape, m2=matrix_b.shape)
raise ValueError(err_msg)
def _cast_to_float64(matrix):
""" Make a copy of the array as double precision floats or return the reference if it already is"""
return matrix.astype(np.float64) if matrix.dtype != np.float64 else matrix
def _type_check(matrix_a, matrix_b, cast=False, dprint=print):
"""
Make sure that both matrices are single precision floats or both are double precision floats
If not, convert to double precision floats if cast is True, or raise an error if cast is False
"""
# Check dtypes
if matrix_a.dtype == np.float32 and matrix_b.dtype == np.float32:
return matrix_a, matrix_b
elif matrix_a.dtype == np.float64 and matrix_b.dtype == np.float64:
return matrix_a, matrix_b
elif (matrix_a.dtype != np.float64 or matrix_b.dtype != np.float64) and cast:
dprint("Recasting matrix data types {a} and {b} to np.float64".format(a=matrix_a.dtype,
b=matrix_b.dtype))
return _cast_to_float64(matrix_a), _cast_to_float64(matrix_b)
elif matrix_a.dtype != np.float64 or matrix_b.dtype != np.float64:
err_msg = "Matrix data types must be in concordance; {a} and {b} provided".format(a=matrix_a.dtype,
b=matrix_b.dtype)
raise ValueError(err_msg)
def _is_dense_vector(m_or_v):
return not _spsparse.issparse(m_or_v) and ((m_or_v.ndim == 1) or ((m_or_v.ndim == 2) and min(m_or_v.shape) == 1))
def _empty_output_check(matrix_a, matrix_b):
"""Check for trivial cases where an empty array should be produced"""
# One dimension is zero
if min([*matrix_a.shape, *matrix_b.shape]) == 0:
return True
# The sparse array is empty
elif _spsparse.issparse(matrix_a) and min(matrix_a.data.shape[0], matrix_a.indices.shape[0]) == 0:
return True
elif _spsparse.issparse(matrix_b) and min(matrix_b.data.shape[0], matrix_b.indices.shape[0]) == 0:
return True
# Neither trivial condition
else:
return False
def _validate_dtype():
"""
Test to make sure that this library works by creating a random sparse array in CSC format,
then converting it to CSR format and making sure is has not raised an exception.
"""
test_array = _spsparse.random(5, 5, density=0.5, format="csc", dtype=np.float32, random_state=50)
test_comparison = test_array.A
csc_ref, precision_flag = _create_mkl_sparse(test_array)
try:
csr_ref = _convert_to_csr(csc_ref)
final_array = _export_mkl(csr_ref, precision_flag)
if not | np.allclose(test_comparison, final_array.A) | numpy.allclose |
# coding: utf-8
# Copyright (c) 2021 AkaiKKRteam.
# Distributed under the terms of the Apache License, Version 2.0.
#!/bin/env python
from .Error import *
from .Unit import *
import sys
import numpy as np
from pymatgen.io.cif import CifParser
from pymatgen.core import Structure, PeriodicSite
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
from pymatgen.core.periodic_table import Element
import pandas as pd
from .ElementKkr import ElementKKR
_kkr_bohr = Unit().length_au2ang
if False:
try:
from pymatgen.symmetry import kpath
_use_kpath = False
except ImportError:
print("Warning: no kpath in pymatgen. kpath will be omitted.")
_use_kpath = False
class _BravaisKKR:
dict = {
1: "trc", # triclinic
2: "trc", # triclinic
3: "sm", # simple monoclinic
4: "sm", # simple monoclinic
5: "bsm", # base centered monoclinic
6: "sm", # simple monoclinic
7: "sm", # simple monoclinic
8: "bsm", # base centered monoclinic
9: "bsm", # base centered monoclinic
10: "sm", # simple monoclinic
11: "sm", # simple monoclinic
12: "bsm", # base centered monoclinic
13: "sm", # simple monoclinic
14: "sm", # simple monoclinic
15: "bsm", # base centered monoclinic
16: "so", # simple orthorhombic
17: "so", # simple orthorhombic
18: "so", # simple orthorhombic
19: "so", # simple orthorhombic
20: "bso", # base centered orthorhombic
21: "bso", # base centered orthorhombic
22: "fco", # face centered orthorhombic
23: "bco", # body centered orthorhombic
24: "bco", # body centered orthorhombic
25: "so", # simple orthorhombic
26: "so", # simple orthorhombic
27: "so", # simple orthorhombic
28: "so", # simple orthorhombic
29: "so", # simple orthorhombic
30: "so", # simple orthorhombic
31: "so", # simple orthorhombic
32: "so", # simple orthorhombic
33: "so", # simple orthorhombic
34: "so", # simple orthorhombic
35: "bso", # base centered orthorhombic
36: "bso", # base centered orthorhombic
37: "bso", # base centered orthorhombic
38: "bso", # base centered orthorhombic
39: "bso", # base centered orthorhombic
40: "bso", # base centered orthorhombic
41: "bso", # base centered orthorhombic
42: "fco", # face centered orthorhombic
43: "fco", # face centered orthorhombic
44: "bco", # body centered orthorhombic
45: "bco", # body centered orthorhombic
46: "bco", # body centered orthorhombic
47: "so", # simple orthorhombic
48: "so", # simple orthorhombic
49: "so", # simple orthorhombic
50: "so", # simple orthorhombic
51: "so", # simple orthorhombic
52: "so", # simple orthorhombic
53: "so", # simple orthorhombic
54: "so", # simple orthorhombic
55: "so", # simple orthorhombic
56: "so", # simple orthorhombic
57: "so", # simple orthorhombic
58: "so", # simple orthorhombic
59: "so", # simple orthorhombic
60: "so", # simple orthorhombic
61: "so", # simple orthorhombic
62: "so", # simple orthorhombic
63: "bso", # base centered orthorhombic
64: "bso", # base centered orthorhombic
65: "bso", # base centered orthorhombic
66: "bso", # base centered orthorhombic
67: "bso", # base centered orthorhombic
68: "bso", # base centered orthorhombic
69: "fco", # face centered orthorhombic
70: "fco", # face centered orthorhombic
71: "bco", # body centered orthorhombic
72: "bco", # body centered orthorhombic
73: "bco", # body centered orthorhombic
74: "bco", # body centered orthorhombic
75: "st", # simple tetragonal
76: "st", # simple tetragonal
77: "st", # simple tetragonal
78: "st", # simple tetragonal
79: "bct", # body centered tetragonal
80: "bct", # body centered tetragonal
81: "st", # simple tetragonal
82: "bct", # body centered tetragonal
83: "st", # simple tetragonal
84: "st", # simple tetragonal
85: "st", # simple tetragonal
86: "st", # simple tetragonal
87: "bct", # body centered tetragonal
88: "bct", # body centered tetragonal
89: "st", # simple tetragonal
90: "st", # simple tetragonal
91: "st", # simple tetragonal
92: "st", # simple tetragonal
93: "st", # simple tetragonal
94: "st", # simple tetragonal
95: "st", # simple tetragonal
96: "st", # simple tetragonal
97: "bct", # body centered tetragonal
98: "bct", # body centered tetragonal
99: "st", # simple tetragonal
100: "st", # simple tetragonal
101: "st", # simple tetragonal
102: "st", # simple tetragonal
103: "st", # simple tetragonal
104: "st", # simple tetragonal
105: "st", # simple tetragonal
106: "st", # simple tetragonal
107: "bct", # body centered tetragonal
108: "bct", # body centered tetragonal
109: "bct", # body centered tetragonal
110: "bct", # body centered tetragonal
111: "st", # simple tetragonal
112: "st", # simple tetragonal
113: "st", # simple tetragonal
114: "st", # simple tetragonal
115: "st", # simple tetragonal
116: "st", # simple tetragonal
117: "st", # simple tetragonal
118: "st", # simple tetragonal
119: "bct", # body centered tetragonal
120: "bct", # body centered tetragonal
121: "bct", # body centered tetragonal
122: "bct", # body centered tetragonal
123: "st", # simple tetragonal
124: "st", # simple tetragonal
125: "st", # simple tetragonal
126: "st", # simple tetragonal
127: "st", # simple tetragonal
128: "st", # simple tetragonal
129: "st", # simple tetragonal
130: "st", # simple tetragonal
131: "st", # simple tetragonal
132: "st", # simple tetragonal
133: "st", # simple tetragonal
134: "st", # simple tetragonal
135: "st", # simple tetragonal
136: "st", # simple tetragonal
137: "st", # simple tetragonal
138: "st", # simple tetragonal
139: "bct", # body centered tetragonal
140: "bct", # body centered tetragonal
141: "bct", # body centered tetragonal
142: "bct", # body centered tetragonal
143: "hcp", # hexagonal close packed
144: "hcp", # hexagonal close packed
145: "hcp", # hexagonal close packed
146: "rhb", # rhombohedral(trigonal)
147: "hcp", # hexagonal close packed
148: "rhb", # rhombohedral(trigonal)
149: "hcp", # hexagonal close packed
150: "hcp", # hexagonal close packed
151: "hcp", # hexagonal close packed
152: "hcp", # hexagonal close packed
153: "hcp", # hexagonal close packed
154: "hcp", # hexagonal close packed
155: "rhb", # rhombohedral(trigonal)
156: "hcp", # hexagonal close packed
157: "hcp", # hexagonal close packed
158: "hcp", # hexagonal close packed
159: "hcp", # hexagonal close packed
160: "rhb", # rhombohedral(trigonal)
161: "rhb", # rhombohedral(trigonal)
162: "hcp", # hexagonal close packed
163: "hcp", # hexagonal close packed
164: "hcp", # hexagonal close packed
165: "hcp", # hexagonal close packed
166: "rhb", # rhombohedral(trigonal)
167: "rhb", # rhombohedral(trigonal)
168: "hcp", # hexagonal close packed
169: "hcp", # hexagonal close packed
170: "hcp", # hexagonal close packed
171: "hcp", # hexagonal close packed
172: "hcp", # hexagonal close packed
173: "hcp", # hexagonal close packed
174: "hcp", # hexagonal close packed
175: "hcp", # hexagonal close packed
176: "hcp", # hexagonal close packed
177: "hcp", # hexagonal close packed
178: "hcp", # hexagonal close packed
179: "hcp", # hexagonal close packed
180: "hcp", # hexagonal close packed
181: "hcp", # hexagonal close packed
182: "hcp", # hexagonal close packed
183: "hcp", # hexagonal close packed
184: "hcp", # hexagonal close packed
185: "hcp", # hexagonal close packed
186: "hcp", # hexagonal close packed
187: "hcp", # hexagonal close packed
188: "hcp", # hexagonal close packed
189: "hcp", # hexagonal close packed
190: "hcp", # hexagonal close packed
191: "hcp", # hexagonal close packed
192: "hcp", # hexagonal close packed
193: "hcp", # hexagonal close packed
194: "hcp", # hexagonal close packed
195: "sc", # simple cubic
196: "fcc", # face centered cubic
197: "bcc", # body centered cubic
198: "sc", # simple cubic
199: "bcc", # body centered cubic
200: "sc", # simple cubic
201: "sc", # simple cubic
202: "fcc", # face centered cubic
203: "fcc", # face centered cubic
204: "bcc", # body centered cubic
205: "sc", # simple cubic
206: "bcc", # body centered cubic
207: "sc", # simple cubic
208: "sc", # simple cubic
209: "fcc", # face centered cubic
210: "fcc", # face centered cubic
211: "bcc", # body centered cubic
212: "sc", # simple cubic
213: "sc", # simple cubic
214: "bcc", # body centered cubic
215: "sc", # simple cubic
216: "fcc", # face centered cubic
217: "bcc", # body centered cubic
218: "sc", # simple cubic
219: "fcc", # face centered cubic
220: "bcc", # body centered cubic
221: "sc", # simple cubic
222: "sc", # simple cubic
223: "sc", # simple cubic
224: "sc", # simple cubic
225: "fcc", # face centered cubic
226: "fcc", # face centered cubic
227: "fcc", # face centered cubic
228: "fcc", # face centered cubic
229: "bcc", # body centered cubic
230: "bcc", # body centered cubic
}
@staticmethod
def getType(group):
if group in _BravaisKKR.dict:
return _BravaisKKR.dict[group]
else:
return "aux"
class _TranslationKKR:
matrix = {
"sc": np.array([[+1.0, 0.0, 0.0], [0.0, +1.0, 0.0], [0.0, 0.0, +1.0]]),
"fcc": np.array([[0.0, 0.5, 0.5], [0.5, 0.0, 0.5], [0.5, 0.5, 0.0]]),
"bcc": np.array([[-0.5, 0.5, 0.5], [0.5, -0.5, 0.5], [0.5, 0.5, -0.5]]),
"hcp": np.array([[+1.0, 0.0, 0.0], [0.0, +1.0, 0.0], [0.0, 0.0, +1.0]]),
"rhb": np.array([[2.0, 1.0, 1.0], [-1.0, 1.0, 1.0], [-1.0, -2.0, 1.0]])/3.0,
"st": np.array([[+1.0, 0.0, 0.0], [0.0, +1.0, 0.0], [0.0, 0.0, +1.0]]),
"bct": np.array([[-0.5, 0.5, 0.5], [0.5, -0.5, 0.5], [0.5, 0.5, -0.5]]),
"so": np.array([[+1.0, 0.0, 0.0], [0.0, +1.0, 0.0], [0.0, 0.0, +1.0]]),
"fco": np.array([[0.0, 0.5, 0.5], [0.5, 0.0, 0.5], [0.5, 0.5, 0.0]]),
"bco": | np.array([[-0.5, 0.5, 0.5], [0.5, -0.5, 0.5], [0.5, 0.5, -0.5]]) | numpy.array |
import numpy as np
import scipy.stats
import copy
from astropy.tests.helper import pytest
from astropy.modeling import models
from scipy.special import gammaln as scipy_gammaln
from stingray import Lightcurve, Powerspectrum
from stingray.modeling import Posterior, PSDPosterior, \
PoissonPosterior, GaussianPosterior, LaplacePosterior
from stingray.modeling import set_logprior
from stingray.modeling.posterior import logmin
from stingray.modeling.posterior import IncorrectParameterError
from stingray.modeling.posterior import LogLikelihood
np.random.seed(20150907)
class TestMeta(object):
def test_use_loglikelihood_class_directly(self):
with pytest.raises(TypeError):
a = LogLikelihood(1, 2, models.Lorentz1D)
def test_inherit_loglikelihood_improperly(self):
class a(LogLikelihood):
def __init__(self, *args, **kwargs):
LogLikelihood.__init__(self, *args, **kwargs)
with pytest.raises(TypeError):
a(1, 2, models.Lorentz1D)
def test_inherit_loglikelihood_properly(self):
class a(LogLikelihood):
def __init__(self, *args, **kwargs):
LogLikelihood.__init__(self, *args, **kwargs)
def evaluate(self, parameters):
pass
a(1, 2, models.Lorentz1D)
class TestSetPrior(object):
@classmethod
def setup_class(cls):
photon_arrivals = np.sort(np.random.uniform(0,1000, size=10000))
cls.lc = Lightcurve.make_lightcurve(photon_arrivals, dt=1.0)
cls.ps = Powerspectrum(cls.lc, norm="frac")
pl = models.PowerLaw1D()
pl.x_0.fixed = True
cls.lpost = PSDPosterior(cls.ps.freq, cls.ps.power, pl, m=cls.ps.m)
def test_set_prior_runs(self):
p_alpha = lambda alpha: ((-1. <= alpha) & (alpha <= 5.))/6.0
p_amplitude = lambda amplitude: ((-10 <= np.log(amplitude)) &
(( | np.log(amplitude) | numpy.log |
"""
"""
import csv
import datetime
import gzip
import os
import time
import numpy as np
import tensorflow as tf
import qdraw.dataset as dataset
import qdraw.dataset_iterator as dataset_iterator
def build_model(data):
"""
"""
FLAGS = tf.app.flags.FLAGS
# NOTE: choose model
if FLAGS.model == 'mobilenets':
import qdraw.model_mobilenets as chosen_model
elif FLAGS.model == 'mobilenets_v2':
import qdraw.model_mobilenets_v2 as chosen_model
elif FLAGS.model == 'resnet':
import qdraw.model_resnet as chosen_model
elif FLAGS.model == 'blind':
import qdraw.model_blind as chosen_model
elif FLAGS.model == 'null':
import qdraw.model_null as chosen_model
# NOTE:
step = tf.train.get_or_create_global_step()
# NOTE:
training = tf.placeholder(shape=[], dtype=tf.bool)
# NOTE:
learning_rate = tf.placeholder(shape=[], dtype=tf.float32)
# NOTE:
if FLAGS.optimizer == 'adam':
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)
elif FLAGS.optimizer == 'nesterov':
optimizer = tf.train.MomentumOptimizer(
learning_rate=learning_rate,
momentum=0.9,
use_nesterov=True)
#
keyids, images, strokes, lengths, recognized, labels = \
data['iterator'].get_next()
model = chosen_model.build_model(
images, strokes, lengths, labels, training)
update_ops = tf.get_collection(tf.GraphKeys.UPDATE_OPS)
new_model = {
'keyids': keyids,
'images': images,
'strokes': strokes,
'lengths': lengths,
'recognized': recognized,
'labels': labels,
'step': step,
'training': training,
'learning_rate': learning_rate,
'dataset_handle': data['dataset_handle'],
'loss': model['loss'],
'logits': model['logits'],
'swa': [],
}
# NOTE: helper function to create a placeholder for a variable
def placeholder(g):
return tf.placeholder(shape=g.shape, dtype=g.dtype)
with tf.control_dependencies(update_ops):
gradients_and_vars = optimizer.compute_gradients(model['loss'])
# NOTE: if cyclic_batch_size_multiplier_max is great than 1, we will do
# gradients aggregation later
# NOTE: an operator to collect computed gradients
new_model['gradients_result'] = [g for g, v in gradients_and_vars]
gradients_and_vars = [(placeholder(g), v) for g, v in gradients_and_vars]
# NOTE: an operator to feed manipulated gradients
new_model['gradients_source'] = [g for g, v in gradients_and_vars]
new_model['optimizer'] = \
optimizer.apply_gradients(gradients_and_vars, global_step=step)
# NOTE: Averaging Weights Leads to Wider Optima and Better
# Generalization, 3.2 batch normalization
# for updating training variables' running averaging
if FLAGS.swa_enable:
for variable in tf.trainable_variables():
ph = placeholder(variable)
new_model['swa'].append({
'variable': variable,
'placeholder': ph,
'var_op': tf.assign(variable, ph),
'amount': 0.0,
'swa_weights': 0.0,
'tmp_weights': 0.0})
return new_model
def train(session, experiment):
"""
"""
FLAGS = tf.app.flags.FLAGS
model = experiment['model']
step = session.run(model['step'])
# NOTE: learning rate interpolation for cyclic training
lr_min = FLAGS.cyclic_learning_rate_min
lr_max = FLAGS.cyclic_learning_rate_max
alpha = (step % FLAGS.cyclic_num_steps) / (FLAGS.cyclic_num_steps - 1)
learning_rate = lr_max + (lr_min - lr_max) * alpha
# NOTE: feeds for training
feeds = {
model['dataset_handle']: experiment['data']['train_handle'],
model['learning_rate']: learning_rate,
model['training']: True,
}
# NOTE: if cyclic_batch_size_multiplier_max is great than 1, we want to do
# gradients aggregation
# NOTE: batch multiplier interpolation for cyclic training
scale_min = FLAGS.cyclic_batch_size_multiplier_min
scale_max = FLAGS.cyclic_batch_size_multiplier_max
# NOTE: assume FLAGS.cyclic_num_steps being far freater then scale
beta = FLAGS.cyclic_num_steps // (scale_max - scale_min + 1)
batch_multiplier = scale_min + (step % FLAGS.cyclic_num_steps) // beta
all_gradients = []
losses = 0.0
# NOTE: compute gradients on nano batches
for i in range(batch_multiplier):
loss, gradients = session.run(
[model['loss'], model['gradients_result']], feed_dict=feeds)
losses += loss
all_gradients.append(gradients)
# NOTE: aggregate & apply gradients
feeds = {
model['learning_rate']: learning_rate,
}
for i, gradients_source in enumerate(model['gradients_source']):
gradients = | np.stack([g[i] for g in all_gradients], axis=0) | numpy.stack |
"""
Some handy utility functions used by the other modules.
"""
from copy import deepcopy
import numpy as np
def centres_to_edges(centres):
"Assuming centres is regularly spaced, return bin edges"
dx = centres[1] - centres[0]
return np.linspace(centres[0] - dx / 2, centres[-1] + dx / 2, len(centres) + 1)
def numerical_jac(func, args, dx=1e-5):
if np.isscalar(dx):
dx = np.repeat(dx, len(args))
y0 = func(args)
out = [0] * len(args)
args = list(args)
for i in range(len(args)):
args[i] += dx[i]
yy = func(args)
out[i] = (yy - y0) / dx[i]
args[i] -= dx[i]
return | np.array(out) | numpy.array |
# flake8: noqa
from pkg_resources import resource_filename
from functools import lru_cache
import warnings
import numpy as np
from ...matlab_funcs import besselh, besselj, gammaln, lscov, quadl
from ...sci_funcs import legendrePlm
from ...core import stress2legendre
def boundary(costheta, a=1, epsilon=.1, nu=0):
"""Projected boundary of a prolate spheroid
Compute the boundary according to equation (4) in
:cite:`Boyde2009` with the addition of the
Poisson's ratio of the object.
.. math::
B(\\theta) = a (1+\\epsilon)
\\left[ (1+\\epsilon)^2 - \\epsilon (1+\\nu)
(2+\\epsilon (1-\\nu)) \\cos^2 \\theta \\right]^{-1/2}
This boundary function was derived for a prolate spheroid under
the assumption that the semi-major axis :math:`a` and the
semi-minor axes :math:`b=c` are defined as
.. math::
a = b \\cdot \\frac{1+ \\epsilon}{1- \\nu \\epsilon}
The boundary function :math:`B(\\theta)` can be derived with
the above relation using the equation for a prolate spheroid.
Parameters
----------
costheta: float or np.ndarray
Cosine of polar coordinates :math:`\\theta`
at which to compute the boundary.
a: float
Equatorial radii of prolate spheroid (semi-minor axis).
epsilon: float
Stretch ratio; defines size of semi-major axis:
:math:`a = (1+\\epsilon) b`. Note that this is not
the eccentricity of the prolate spheroid.
nu: float
Poisson's ratio :math:`\\nu` of the material.
Returns
-------
B: 1d ndarray
Radial object boundary in dependence of theta
:math:`B(\\theta)`.
Notes
-----
For :math:`\\nu=0`, the above equation becomes
equation (4) in :cite:`Boyde2009`.
"""
x = costheta
B = a * (1 + epsilon) \
/ ((1 + epsilon)**2
- epsilon * (1 + nu) * (2 + epsilon * (1 - nu)) * x**2)**.5
return B
@lru_cache(maxsize=32)
def get_hgc():
"""Load hypergeometric coefficients from *hypergeomdata2.dat*.
These coefficients were computed by <NAME>
using Wolfram Mathematica.
"""
hpath = resource_filename("ggf.stress.boyde2009", "hypergeomdata2.dat")
hgc = np.loadtxt(hpath)
return hgc
def stress(object_index=1.41, medium_index=1.3465, poisson_ratio=0.45,
semi_minor=2.8466e-6, stretch_ratio=0.1, wavelength=780e-9,
beam_waist=3, power_left=.6, power_right=.6, dist=100e-6,
n_points=100, theta_max=np.pi, field_approx="davis",
ret_legendre_decomp=False, verbose=False):
"""Compute the stress acting on a prolate spheroid
The prolate spheroid has semi-major axis :math:`a` and
semi-minor axis :math:`b=c`.
Parameters
----------
object_index: float
Refractive index of the spheroid
medium_index: float
Refractive index of the surrounding medium
poisson_ratio: float
Poisson's ratio of the spheroid material
semi_minor: float
Semi-minor axis (inner) radius of the stretched object
:math:`b=c`.
stretch_ratio: float
Measure of the deformation, defined as :math:`(a - b) / b`
wavelength: float
Wavelenth of the gaussian beam [m]
beam_waist: float
Beam waist radius of the gaussian beam [wavelengths]
power_left: float
Laser power of the left beam [W]
power_right: float
Laser power of the right beam [W]
dist: float
Distance between beam waist and object center [m]
n_points: int
Number of points to compute stresses for
theta_max: float
Maximum angle to compute stressed for
field_approx: str
TODO
ret_legendre_decomp: bool
If True, return coefficients of decomposition of stress
into Legendre polynomials
verbose: int
Increase verbosity
Returns
-------
theta: 1d ndarray
Angles for which stresses are computed
sigma_rr: 1d ndarray
Radial stress corresponding to angles
coeff: 1d ndarray
If `ret_legendre_decomp` is True, return compositions
of decomposition of stress into Legendre polynomials.
Notes
-----
- The angles `theta` are computed on a grid that does not
include zero and `theta_max`.
- This implementation was first presented in :cite:`Boyde2009`.
"""
if field_approx not in ["davis", "barton"]:
raise ValueError("`field_approx` must be 'davis' or 'barton'")
object_index = complex(object_index)
medium_index = complex(medium_index)
W0 = beam_waist * wavelength
epsilon = stretch_ratio
nu = poisson_ratio
# ZRL = 0.5*medium_index*2*np.pi/wavelength*W0**2 # Rayleigh range [m]
# WZ = W0*(1+(beam_pos+d)**2/ZRL**2)**0.5 # beam waist at specified
# position [m]
K0 = 2 * np.pi / wavelength # wave vector [m]
Alpha = semi_minor * K0 # size parameter
C = 3e8 # speed of light [m/s]
# maximum number of orders
lmax = np.int(np.round(2 + Alpha + 4 * (Alpha)**(1 / 3) + 10))
if lmax > 120:
msg = 'Required number of orders for accurate expansion exceeds allowed maximum!' \
+ 'Reduce size of trapped particle!'
raise ValueError(msg)
if epsilon == 0:
# spherical object, no point-matching needed (mmax = 0)
mmax = 3
else:
if (epsilon > 0.15):
warnings.warn('Stretching ratio is high: {}'.format(epsilon))
# spheroidal object, point-matching required (mmax has to be divisible
# by 3)
mmax = 6 * lmax
# permittivity in surrounding medium [1]
EpsilonI = medium_index**2
EpsilonII = object_index**2 # permittivity in within cell [1]
MuI = 1.000 # permeability in surrounding medium [1]
MuII = 1.000 # permeability within cell [1]
# wave constant in Maxwell's equations (surrounding medium) [1/m]
K1I = 1j * K0 * EpsilonI
# wave constant in Maxwell's equations (within cell) [1/m]
K1II = 1j * K0 * EpsilonII
# wave constant in Maxwell's equations (surrounding medium) [1/m]
K2I = 1j * K0
# wave constant in Maxwell's equations (within cell) [1/m]
K2II = 1j * K0
KI = (-K1I * K2I)**0.5 # wave vector (surrounding medium) [1/m]
KII = (-K1II * K2II)**0.5 # wave vector (within cell) [1/m]
# dimensionless parameters
k0 = 1 # wave vector
a = semi_minor * K0 # internal radius of stretched cell
d = dist * K0 # distance from cell centre to optical stretcher
# ap = a*(1+stretch_ratio) # semi-major axis (after stretching)
# bp = a*(1-poisson_ratio*stretch_ratio) # semi-minor axis (after
# stretching)
w0 = W0 * K0 # Gaussian width
# wave constant in Maxwell's equations (surrounding medium)
k1I = K1I / K0
# wave constant in Maxwell's equations (within cell)
k1II = K1II / K0
# wave constant in Maxwell's equations (surrounding medium)
k2I = K2I / K0
# wave constant in Maxwell's equations (within cell)
k2II = K2II / K0
kI = KI / K0 # wave vector (surrounding medium)
kII = KII / K0 # wave vector (within cell)
beta = kI # wave vector of Gaussian beam
# other definitions
# amplitude of electric field of left laser [kg m/(s**2 C)]
EL = np.sqrt(power_left / (medium_index * C * W0**2))
# amplitude of electric field of right laser [kg m/(s**2 C)]
ER = np.sqrt(power_right / (medium_index * C * W0**2))
HL = beta / k0 * EL # left laser amplitude of magnetic field
HR = beta / k0 * ER # right laser amplitude of magnetic field
zR = beta * w0**2 / 2 # definition of Rayleigh range
S = (1 + 1j * d / zR)**(-1) # complex amplitude for Taylor expansion
s = 1 / (beta * w0) # expansion parameter for Gaussian (Barton)
# Functions
# object boundary function: r(th) = a*B1(x) x= cos(th)
def B1(x): return boundary(costheta=x, a=1, epsilon=epsilon, nu=nu)
# Riccati Bessel functions and their derivatives
# Riccati Bessel function (psi)
def psi(l, z): return (np.pi / 2 * z)**(1 / 2) * besselj(l + 1 / 2, z)
def psi1(l, z): return (np.pi / (2. * z))**(1 / 2) * \
(z * besselj(l - 1 / 2, z) - l *
besselj(l + 1 / 2, z)) # first derivative (psi')
def psi2(l, z): return (np.pi / 2)**(1 / 2) * (l + l**2 - z**2) * \
besselj(l + 1 / 2, z) * z**(-3 / 2) # second derivative (psi'')
# First order Taylor expansion of psi is too inaccurate for larger values of k*a*Eps.
# Hence, to match 1-st and higher order terms in Eps, subtract the 0-th order terms (no angular dependence)
# from the exact function psi (including angular dependence)
# Riccati Bessel function excluding angular dependence in 0-th order
# (psiex)
def psiex(l, z, x): return psi(l, z * B1(x)) - psi(l, z)
def psi1ex(l, z, x): return psi1(l, z * B1(x)) - \
psi1(l, z) # first derivative of psiex
def psi2ex(l, z, x): return psi2(l, z * B1(x)) - \
psi2(l, z) # second derivative of psi
# defined for abbreviation
def psixx(l, z, x): return psi(l, z * B1(x))
def psi1xx(l, z, x): return psi1(l, z * B1(x))
def psi2xx(l, z, x): return psi2(l, z * B1(x))
# Hankel function and its derivative
def xi(l, z): return (np.pi / 2 * z)**(1 / 2) * besselh(l + 1 / 2, z)
def xi1(l, z): return (np.pi / (2 * z))**(1 / 2) * \
((l + 1) * besselh(l + 1 / 2, z) - z * besselh(l + 3 / 2, z))
def xi2(l, z): return (np.pi / 2)**(1 / 2) / \
z**(3 / 2) * (l + l**2 - z**2) * besselh(l + 1 / 2, z)
# Comments: see above for psiex
def xiex(l, z, x): return xi(l, z * B1(x)) - xi(l, z)
def xi1ex(l, z, x): return xi1(l, z * B1(x)) - xi1(l, z)
def xi2ex(l, z, x): return xi2(l, z * B1(x)) - xi2(l, z)
def xixx(l, z, x): return xi(l, z * B1(x))
def xi1xx(l, z, x): return xi1(l, z * B1(x))
def xi2xx(l, z, x): return xi2(l, z * B1(x))
#% Associated Legendre functions P(m)_l(x) and their derivatives
#% select mth component of vector 'legendre' [P**(m)_l(x)]
# [zeros(m,1);1;zeros(l-m,1)].'*legendre(l,x)
#% legendre polynomial [P**(m)_l(x)]
def legendrePl(l, x): return legendrePlm(1, l, x)
#% legendre polynomial [P**(1)_l(x)]
def legendrePlm1(m, l, x): return (
(l - m + 1.) * legendrePlm(m, l + 1, x) - (l + 1.) * x * legendrePlm(m, l, x)) / (x**2 - 1)
#% derivative d/dx[P**(m)_l(x)]
def legendrePl1(l, x): return legendrePlm1(1, l, x)
# defined to avoid division by zero (which can occur for x=1 in
# legendrePl1...
def legendrePlmex1(m, l, x): return -((l - m + 1) *
legendrePlm(m, l + 1, x) - (l + 1) * x * legendrePlm(m, l, x))
def legendrePlex1(l, x): return legendrePlmex1(1, l, x)
# Hypergeometric and Gamma functions
hypergeomcoeff = get_hgc()
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
# Gaussian beam (incident fields) - in Cartesian basis (either Davis first order or Barton fifth order fields)
# electric and magnetic fields according to Davis (first order)
if field_approx == "davis":
# left
def eExiL(r, th, phi): return EL * (1 + 1j * (r * np.cos(th) + d) / zR)**(-1) * np.exp(-r**2 *
np.sin(th)**2 / (w0**2 * (1 + 1j * (r * np.cos(th) + d) / zR))) * np.exp(1j * beta * (r * np.cos(th) + d))
def eEyiL(r, th, phi): return 0
def eEziL(r, th, phi): return -1j * (1 + 1j * (r * np.cos(th) + d) /
zR)**(-1) * r * np.sin(th) * np.cos(phi) / zR * eExiL(r, th, phi)
def eHxiL(r, th, phi): return 0
def eHyiL(r, th, phi): return HL * (1 + 1j * (r * np.cos(th) + d) / zR)**(-1) * np.exp(-r**2 *
np.sin(th)**2 / (w0**2 * (1 + 1j * (r * np.cos(th) + d) / zR))) * np.exp(1j * beta * (r * np.cos(th) + d))
def eHziL(r, th, phi): return -1j * (1 + 1j * (r * np.cos(th) + d) /
zR)**(-1) * r * np.sin(th) * np.sin(phi) / zR * eHyiL(r, th, phi)
# right
def eExiR(r, th, phi): return ER * (1 - 1j * (r * np.cos(th) - d) / zR)**(-1) * np.exp(-r**2 *
np.sin(th)**2 / (w0**2 * (1 - 1j * (r * np.cos(th) - d) / zR))) * np.exp(-1j * beta * (r * np.cos(th) - d))
def eEyiR(r, th, phi): return 0
def eEziR(r, th, phi): return +1j * (1 - 1j * (r * np.cos(th) - d) /
zR)**(-1) * r * np.sin(th) * np.cos(phi) / zR * eExiR(r, th, phi)
def eHxiR(r, th, phi): return 0
def eHyiR(r, th, phi): return -HR * (1 - 1j * (r * np.cos(th) - d) / zR)**(-1) * np.exp(-r**2 *
np.sin(th)**2 / (w0**2 * (1 - 1j * (r * | np.cos(th) | numpy.cos |
"""
MesoNet
Authors: <NAME> and <NAME>, <NAME>
https://github.com/bf777/MesoNet
Licensed under the Creative Commons Attribution 4.0 International License (see LICENSE for details)
This file has been adapted from data.py in https://github.com/zhixuhao/unet
"""
from __future__ import print_function
from tensorflow.keras.preprocessing.image import ImageDataGenerator
import numpy as np
import os
import skimage.io as io
import skimage.transform as trans
def adjustData(img, mask, flag_multi_class, num_class):
if flag_multi_class:
img = img / 255
mask = mask[:, :, :, 0] if (len(mask.shape) == 4) else mask[:, :, 0]
new_mask = | np.zeros(mask.shape + (num_class,)) | numpy.zeros |
from .COAsT import COAsT # ???
import numpy as np
import xarray as xr
from .logging_util import get_slug, debug, error, info
import sklearn.metrics as metrics
from . import general_utils, plot_util, crps_util
class ALTIMETRY(COAsT):
'''
An object for reading, storing and manipulating altimetry data.
Currently the object contains functionality for reading altimetry netCDF
data from the CMEMS database. This is the default for initialisation.
Data should be stored in an xarray.Dataset, in the form:
* Date Format Overview *
1. A single dimension (time).
2. Three coordinates: time, latitude, longitude. All lie on the 't_dim'
dimension.
3. Observed variable DataArrays on the t_dim dimension.
There are currently no naming conventions for the variables however
examples from the CMEMS database include sla_filtered, sla_unfiltered and
mdt (mean dynamic topography).
* Methods Overview *
*Initialisation and File Reading*
-> __init__(): Initialises an ALTIMETRY object.
-> read_cmems(): Reads data from a CMEMS netCDF file.
*Plotting*
-> quick_plot(): Makes a quick along-track plot of specified data.
*Model Comparison*
-> obs_operator(): For interpolating model data to this object.
-> cprs(): Calculates the CRPS between a model and obs variable.
-> difference(): Differences two specified variables
-> absolute_error(): Absolute difference, two variables
-> mean_absolute_error(): MAE between two variables
-> root_mean_square_error(): RMSE between two variables
-> time_mean(): Mean of a variable in time
-> time_std(): St. Dev of a variable in time
-> time_correlation(): Correlation between two variables
-> time_covariance(): Covariance between two variables
-> basic_stats(): Calculates multiple of the above metrics.
'''
##############################################################################
### ~ Initialisation and File Reading ~ ###
##############################################################################
def __init__(self, file=None, chunks: dict=None, multiple=False):
debug(f"Creating a new {get_slug(self)}")
if file is not None:
self.read_cmems(file, chunks, multiple)
else:
self.dataset = None
debug(f"{get_slug(self)} initialised")
return
def read_cmems(self, file, chunks, multiple):
''' Reads altimetry data from a CMEMS netcdf file. Calls COAsT.init()
to make use of its load methods'''
super().__init__(file, chunks, multiple)
self.dataset = self.dataset.rename_dims(self.dim_mapping)
#self.dataset.attrs = {}
def set_dimension_mapping(self):
self.dim_mapping = {'time': 't_dim'}
debug(f"{get_slug(self)} dim_mapping set to {self.dim_mapping}")
def set_variable_mapping(self):
self.var_mapping = None
debug(f"{get_slug(self)} var_mapping set to {self.var_mapping}")
def subset_indices_lonlat_box(self, lonbounds, latbounds):
"""Generates array indices for data which lies in a given lon/lat box.
Keyword arguments:
lon -- Longitudes, 1D or 2D.
lat -- Latitudes, 1D or 2D
lonbounds -- Array of form [min_longitude=-180, max_longitude=180]
latbounds -- Array of form [min_latitude, max_latitude]
return: Indices corresponding to datapoints inside specified box
"""
debug(f"Subsetting {get_slug(self)} indices in {lonbounds}, {latbounds}")
lon = self.dataset.longitude.copy()
lat = self.dataset.latitude
lon[lon>180] = lon[lon>180] - 360
lon[lon<-180] = lon[lon<-180] + 360
ff1 = ( lon > lonbounds[0] ).astype(int) # FIXME This should fail? We can just treat bools as ints here...
ff2 = ( lon < lonbounds[1] ).astype(int)
ff3 = ( lat > latbounds[0] ).astype(int)
ff4 = ( lat < latbounds[1] ).astype(int)
indices = np.where( ff1 * ff2 * ff3 * ff4 )
return indices[0]
##############################################################################
### ~ Plotting ~ ###
##############################################################################
def quick_plot(self, color_var_str: str=None):
'''
'''
if color_var_str is not None:
color_var = self.dataset[color_var_str]
title = color_var_str
else:
color_var = None
title = 'Altimetry observation locations'
info("Drawing a quick plot...")
fig, ax = plot_util.geo_scatter(self.dataset.longitude,
self.dataset.latitude,
c=color_var, title=title )
info("Plot ready, displaying!")
return fig, ax
##############################################################################
### ~ Model Comparison ~ ###
##############################################################################
def obs_operator(self, model, mod_var_name:str,
time_interp = 'nearest', model_mask=None):
'''
For interpolating a model dataarray onto altimetry locations and times.
For ALTIMETRY, the interpolation is done independently in two steps:
1. Horizontal space
2. Time
Model data is taken at the surface if necessary (0 index).
Example usage:
--------------
altimetry.obs_operator(nemo_obj, 'sossheig')
Parameters
----------
model : model object (e.g. NEMO)
mod_var: variable name string to use from model object
time_interp: time interpolation method (optional, default: 'nearest')
This can take any string scipy.interpolate would take. e.g.
'nearest', 'linear' or 'cubic'
model_mask : Mask to apply to model data in geographical interpolation
of model. For example, use to ignore land points.
If None, no mask is applied. If 'bathy', model variable
(bathymetry==0) is used. Custom 2D mask arrays can be
supplied.
Returns
-------
Adds a DataArray to self.dataset, containing interpolated values.
'''
debug(f"Interpolating {get_slug(model)} \"{mod_var_name}\" with time_interp \"{time_interp}\"")
# Determine mask
if model_mask=='bathy':
model_mask = model.dataset.bathymetry.values==0
# Get data arrays
mod_var_array = model.dataset[mod_var_name]
# Get data arrays
mod_var = model.dataset[mod_var_name]
# Depth interpolation -> for now just take 0 index
if 'z_dim' in mod_var.dims:
mod_var = mod_var.isel(z_dim=0).squeeze()
# Cast lat/lon to numpy arrays
obs_lon = np.array(self.dataset.longitude).flatten()
obs_lat = np.array(self.dataset.latitude).flatten()
interpolated = model.interpolate_in_space(mod_var, obs_lon,
obs_lat)
# Interpolate in time if t_dim exists in model array
if 't_dim' in mod_var.dims:
interpolated = model.interpolate_in_time(interpolated,
self.dataset.time,
interp_method=time_interp)
# Take diagonal from interpolated array (which contains too many points)
diag_len = interpolated.shape[0]
diag_ind = xr.DataArray(np.arange(0, diag_len))
interpolated = interpolated.isel(interp_dim=diag_ind, t_dim=diag_ind)
interpolated = interpolated.swap_dims({'dim_0':'t_dim'})
# Store interpolated array in dataset
new_var_name = 'interp_' + mod_var_name
self.dataset[new_var_name] = interpolated
def crps(self, model_object, model_var_name, obs_var_name,
nh_radius: float = 20, time_interp:str='linear',
create_new_object = True):
'''
Comparison of observed variable to modelled using the Continuous
Ranked Probability Score. This is done using this ALTIMETRY object.
This method specifically performs a single-observation neighbourhood-
forecast method.
Parameters
----------
model_object (model) : Model object (NEMO) containing model data
model_var_name (str) : Name of model variable to compare.
obs_var_name (str) : Name of observed variable to compare.
nh_radius (float) : Neighbourhood radius (km)
time_interp (str) : Type of time interpolation to use (s)
create_new_obj (bool): If True, save output to new ALTIMETRY obj.
Otherwise, save to this obj.
Returns
-------
xarray.Dataset containing times, sealevel and quality control flags
Example Useage
-------
# Compare modelled 'sossheig' with 'sla_filtered' using CRPS
crps = altimetry.crps(nemo, 'sossheig', 'sla_filtered')
'''
mod_var = model_object.dataset[model_var_name]
obs_var = self.dataset[obs_var_name]
crps_list, n_model_pts, contains_land = crps_util.crps_sonf_moving(
mod_var,
obs_var.longitude.values,
obs_var.latitude.values,
obs_var.values,
obs_var.time.values,
nh_radius, time_interp )
if create_new_object:
new_object = ALTIMETRY()
new_dataset = self.dataset[['longitude','latitude','time']]
new_dataset['crps'] = (('t_dim'),crps_list)
new_dataset['crps_n_model_pts'] = (('t_dim'), n_model_pts)
new_dataset['crps_contains_land'] = (('t_dim'), contains_land)
new_object.dataset = new_dataset
return new_object
else:
self.dataset['crps'] = (('t_dim'),crps_list)
self.dataset['crps_n_model_pts'] = (('t_dim'), n_model_pts)
self.dataset['crps_contains_land'] = (('t_dim'), contains_land)
def difference(self, var_str0:str, var_str1:str, date0=None, date1=None):
''' Difference two variables defined by var_str0 and var_str1 between
two dates date0 and date1. Returns xr.DataArray '''
var0 = self.dataset[var_str0]
var1 = self.dataset[var_str1]
var0 = general_utils.dataarray_time_slice(var0, date0, date1).values
var1 = general_utils.dataarray_time_slice(var1, date0, date1).values
diff = var0 - var1
return xr.DataArray(diff, dims='t_dim', name='error',
coords={'time':self.dataset.time})
def absolute_error(self, var_str0, var_str1, date0=None, date1=None):
''' Absolute difference two variables defined by var_str0 and var_str1
between two dates date0 and date1. Return xr.DataArray '''
var0 = self.dataset[var_str0]
var1 = self.dataset[var_str1]
var0 = general_utils.dataarray_time_slice(var0, date0, date1).values
var1 = general_utils.dataarray_time_slice(var1, date0, date1).values
adiff = np.abs(var0 - var1)
return xr.DataArray(adiff, dims='t_dim', name='absolute_error',
coords={'time':self.dataset.time})
def mean_absolute_error(self, var_str0, var_str1, date0=None, date1=None):
''' Mean absolute difference two variables defined by var_str0 and
var_str1 between two dates date0 and date1. Return xr.DataArray '''
var0 = self.dataset[var_str0]
var1 = self.dataset[var_str1]
var0 = general_utils.dataarray_time_slice(var0, date0, date1).values
var1 = general_utils.dataarray_time_slice(var1, date0, date1).values
mae = metrics.mean_absolute_error(var0, var1)
return mae
def root_mean_square_error(self, var_str0, var_str1, date0=None, date1=None):
''' Root mean square difference two variables defined by var_str0 and
var_str1 between two dates date0 and date1. Return xr.DataArray '''
var0 = self.dataset[var_str0]
var1 = self.dataset[var_str1]
var0 = general_utils.dataarray_time_slice(var0, date0, date1).values
var1 = general_utils.dataarray_time_slice(var1, date0, date1).values
rmse = metrics.mean_squared_error(var0, var1)
return np.sqrt(rmse)
def time_mean(self, var_str, date0=None, date1=None):
''' Time mean of variable var_str between dates date0, date1'''
var = self.dataset[var_str]
var = general_utils.dataarray_time_slice(var, date0, date1)
return | np.nanmean(var) | numpy.nanmean |
import numpy as np
import scipy.spatial.distance as spatial
from numpy import linalg as LA
def get_dim(edgelist):
"""Given an adjacency list for a graph, returns the number of nodes in
the graph.
"""
node_dict = {}
node_count = 0
for edge in edgelist:
p, q = edge[ :2]
if p not in node_dict:
node_dict[p] = True
node_count += 1
if q not in node_dict:
node_dict[q] = True
node_count += 1
return node_count
def densify(edgelist, dim = None, directed = False):
"""Given an adjacency list for the graph, computes the adjacency
matrix.
"""
if dim is None:
dim = get_dim(edgelist)
A = np.zeros((dim, dim), dtype = np.double)
for edge in edgelist:
p, q, wt = edge
A[p, q] = wt
if not directed:
A[q, p] = wt
return A
def compute_pinverse_diagonal(D):
D_i = D.copy()
for i in range(D_i.shape[0]):
D_i[i, i] = 1 / D[i, i] if D[i, i] != 0 else 0
return D_i
def compute_X_normalized(A, D, t = -1, lm = 1, is_normalized = True):
D_i = compute_pinverse_diagonal(D)
P = np.matmul(D_i, A)
Identity = np.identity(A.shape[0])
e = np.ones((A.shape[0], 1))
# Compute W
scale = np.matmul(e.T, np.matmul(D, e))[0, 0]
W = np.multiply(1 / scale, np.matmul(e, np.matmul(e.T, D)))
up_P = | np.multiply(lm, P - W) | numpy.multiply |
# An implementation of Experience Replay (ER) with reservoir sampling and without using tasks from Algorithm 4 of https://openreview.net/pdf?id=B1gTShAct7
# Copyright 2019-present, IBM Research
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
import torch
import torch.nn as nn
import torch.optim as optim
from torch.autograd import Variable
import numpy as np
from .common import MLP, ResNet18
import random
from torch.nn.modules.loss import CrossEntropyLoss
from random import shuffle
import sys
import warnings
warnings.filterwarnings("ignore")
class Net(nn.Module):
def __init__(self,
n_inputs,
n_outputs,
n_tasks,
args):
super(Net, self).__init__()
self.args = args
nl, nh = args.n_layers, args.n_hiddens
self.net_o = MLP([n_inputs] + [nh] * nl + [n_outputs])
self.net_n = MLP([n_inputs] + [nh] * nl + [n_outputs])
self.bce = CrossEntropyLoss()
self.mse = nn.MSELoss()
self.l1 = nn.L1Loss()
self.n_outputs = n_outputs
self.opt = optim.SGD(self.net_n.parameters(), args.lr)
self.batchSize = int(args.replay_batch_size)
self.memories = args.memories
# allocate buffer
self.M = []
self.age = 0
# handle gpus if specified
self.cuda = args.cuda
if self.cuda:
self.net_n = self.net_n.cuda()
self.net_o = self.net_o.cuda()
def forward(self, x, t):
output = self.net_n(x)
return output, None
def getBatch(self,x,y,t):
mxi = np.array(x)
myi = np.array(y)
bxs = []
bys = []
bxs1 = []
bys1 = []
if len(self.M) > 0:
order = [i for i in range(0,len(self.M))]
osize = min(self.batchSize,len(self.M))
for j in range(0,osize):
shuffle(order)
k = order[j]
x,y,t = self.M[k]
xi = np.array(x)
yi = np.array(y)
bxs.append(xi)
bys.append(yi)
bxs1.append(xi)
bys1.append(yi)
bxs.append(mxi)
bys.append(myi)
bxs = Variable(torch.from_numpy(np.array(bxs))).float().view(-1,784)
bys = Variable(torch.from_numpy(np.array(bys))).long().view(-1)
bxs1 = Variable(torch.from_numpy( | np.array(bxs1) | numpy.array |
# Author: <NAME> <<EMAIL>>
from copy import deepcopy
from itertools import chain, product
from math import log
from operator import (
add, iadd, sub, isub, mul, imul, pow, ipow, truediv, itruediv, floordiv, ifloordiv, mod, imod)
import os
import pickle
import shutil
from string import ascii_lowercase
import tempfile
import warnings
import mne
import numpy as np
from numpy.testing import (
assert_equal, assert_array_equal, assert_allclose,
assert_array_almost_equal)
import pytest
from scipy import signal
from eelbrain import (
datasets, load, Var, Factor, NDVar, Datalist, Dataset, Celltable,
Case, Categorial, Scalar, Sensor, UTS, set_tmin,
align, align1, choose, combine,
cwt_morlet, shuffled_index)
from eelbrain._data_obj import (
all_equal, asvar, assub, FULL_AXIS_SLICE, longname, SourceSpace,
assert_has_no_empty_cells)
from eelbrain._exceptions import DimensionMismatchError
from eelbrain._stats.stats import rms
from eelbrain._utils.numpy_utils import newaxis
from eelbrain.testing import (
assert_dataobj_equal, assert_dataset_equal, assert_source_space_equal,
requires_mne_sample_data, skip_on_windows)
OPERATORS = ((add, iadd, '+'),
(sub, isub, '-'),
(mul, imul, '*'),
(mul, imul, '*'),
(pow, ipow, '**'),
(truediv, itruediv, '/'),
(floordiv, ifloordiv, '//'),
(mod, imod, '%'))
def test_aggregate():
"Test aggregation methods"
ds = datasets.get_uts()
drop = ('rm', 'ind', 'YBin', 'YCat')
# don't handle inconsistencies silently
with pytest.raises(ValueError):
ds.aggregate('A%B')
dsa = ds.aggregate('A%B', drop=drop)
assert_array_equal(dsa['n'], [15, 15, 15, 15])
idx1 = ds.eval("logical_and(A=='a0', B=='b0')")
assert dsa['Y', 0] == ds['Y', idx1].mean()
# unequal cell counts
ds = ds[:-3]
dsa = ds.aggregate('A%B', drop=drop)
assert_array_equal(dsa['n'], [15, 15, 15, 12])
idx1 = ds.eval("logical_and(A=='a0', B=='b0')")
assert dsa['Y', 0] == ds['Y', idx1].mean()
# equalize count
dsa = ds.aggregate('A%B', drop=drop, equal_count=True)
assert_array_equal(dsa['n'], [12, 12, 12, 12])
idx1_12 = np.logical_and(idx1, idx1.cumsum() <= 12)
assert dsa['Y', 0] == ds['Y', idx1_12].mean()
# equalize count with empty cell
sds = ds.sub("logical_or(A == 'a1', B == 'b1')")
dsa = sds.aggregate('A%B', drop=drop, equal_count=True)
assert_array_equal(dsa['n'], [12, 12, 12])
def test_align():
"Testing align() and align1() functions"
ds = datasets.get_uv()
# index the dataset
ds.index()
ds['aindex'] = ds.eval("A.enumerate_cells()")
# subset
idx4 = np.arange(0, ds.n_cases, 4)
idx4i = idx4[::-1]
ds2 = ds.sub(np.arange(0, ds.n_cases, 2))
# shuffle the whole dataset
shuffle_index = np.arange(ds.n_cases)
np.random.shuffle(shuffle_index)
ds_shuffled = ds[shuffle_index]
# align1: align Dataset to index
dsa = align1(ds2, idx4)
assert_array_equal(dsa['index'], idx4, "align1() failure")
dsa = align1(ds2, idx4i)
assert_array_equal(dsa['index'], idx4i, "align1() failure")
# d_idx as Var
dsa = align1(ds2[::2], idx4, idx4i)
assert_array_equal(dsa['index'], idx4i, "align1() failure")
with pytest.raises(ValueError):
align1(ds2, idx4, idx4i)
# Factor index
with pytest.raises(ValueError):
align1(ds, ds['rm', ::-1], 'rm')
fds = ds[:20]
dsa = align1(fds, fds['rm', ::-1], 'rm')
assert_array_equal(dsa['index'], np.arange(19, -1, -1), "align1 Factor")
# align two datasets
dsa1, dsa2 = align(ds, ds2)
assert_array_equal(dsa1['index'], dsa2['index'], "align() failure")
dsa1, dsa2 = align(ds, ds2[::-1])
assert_array_equal(dsa1['index'], dsa2['index'], "align() failure")
dsa1, dsa2 = align(ds, ds_shuffled)
assert_dataset_equal(dsa1, dsa2)
# align using categorial
dsa1, dsa2 = align(ds, ds_shuffled, 'A % aindex')
assert_dataset_equal(dsa1, dsa2)
dsa1, dsa2 = align(ds, ds_shuffled, 'aindex % A')
assert_dataset_equal(dsa1, dsa2)
def test_celltable():
"Test the Celltable class."
ds = datasets.get_uts()
ds['cat'] = Factor('abcd', repeat=15)
ct = Celltable('Y', 'A', ds=ds)
assert ct.n_cases == 60
assert ct.n_cells == 2
assert repr(ct) == "Celltable(Y, A)"
assert repr(Celltable(ds['Y'].x, 'A', ds=ds)) == "Celltable(<ndarray>, A)"
assert repr(Celltable(ds['Y'].x, ds['A'].x, ds=ds)) == "Celltable(<ndarray>, <Factor>)"
ct = Celltable('Y', 'A', match='rm', ds=ds)
assert ct.n_cases == 30
assert ct.n_cells == 2
# cat argument
ct = Celltable('Y', 'cat', cat=('c', 'b'), ds=ds)
assert ct.n_cases == 30
assert ct.x[0] == 'c'
assert ct.x[-1] == 'b'
with pytest.raises(ValueError):
Celltable('Y', 'cat', cat=('c', 'e'), ds=ds)
ct = Celltable('Y', 'A', match='rm', ds=ds)
assert ct.n_cases == 30
assert np.all(ct.groups['a0'] == ct.groups['a1'])
ct = Celltable('Y', 'cat', match='rm', cat=('c', 'b'), ds=ds)
assert ct.n_cases == 30
assert ct.x[0] == 'c'
assert ct.x[-1] == 'b'
# catch unequal length
with pytest.raises(ValueError):
Celltable(ds['Y', :-1], 'cat', ds=ds)
with pytest.raises(ValueError):
Celltable(ds['Y', :-1], 'cat', match='rm', ds=ds)
# coercion of numerical X
X = ds.eval("A == 'a0'")
ct = Celltable('Y', X, cat=(None, None), ds=ds)
assert ct.cat == ('False', 'True')
assert_array_equal(ct.data['True'], ds['Y', X])
ct = Celltable('Y', X, cat=('True', 'False'), ds=ds)
assert ('True', 'False') == ct.cat
assert_array_equal(ct.data['True'], ds['Y', X])
# test coercion of Y
ct = Celltable(ds['Y'].x, 'A', ds=ds)
assert isinstance(ct.y, np.ndarray)
ct = Celltable(ds['Y'].x, 'A', ds=ds, coercion=asvar)
assert isinstance(ct.y, Var)
# test sub
ds_sub = ds.sub("A == 'a0'")
ct_sub = Celltable('Y', 'B', ds=ds_sub)
ct = Celltable('Y', 'B', sub="A == 'a0'", ds=ds)
assert_dataobj_equal(ct_sub.y, ct.y)
ct_sub = Celltable('Y', 'B', sub="Var(A == 'a0')", cat=('b0', 'b1'), ds=ds)
assert_dataobj_equal(ct_sub.y, ct.y)
# test sub with rm
ct_sub = Celltable('Y', 'B', match='rm', ds=ds_sub)
ct = Celltable('Y', 'B', match='rm', sub="A == 'a0'", ds=ds)
assert_dataobj_equal(ct_sub.y, ct.y)
# Interaction match
ct = Celltable('Y', 'A', match='B % rm', ds=ds)
assert ct.all_within
assert_dataobj_equal(combine((ct.data['a0'], ct.data['a1'])), ds['Y'])
# test rm sorting
ds = Dataset()
ds['rm'] = Factor('abc', repeat=4)
ds['Y'] = Var(np.arange(3.).repeat(4))
ds['X'] = Factor('ab', repeat=2, tile=3)
idx = np.arange(12)
np.random.shuffle(idx)
ds = ds[idx]
ct = Celltable('Y', 'X', 'rm', ds=ds)
assert_array_equal(ct.match, Factor('abc', tile=2))
assert_array_equal(ct.y, np.tile(np.arange(3.), 2))
assert_array_equal(ct.x, Factor('ab', repeat=3))
def test_coercion():
"Test data class coercion"
ds = datasets.get_uts()
ds['avar'] = Var.from_dict(ds['A'], {'a0': 0, 'a1': 1})
assert_array_equal(assub("A == 'a0'", ds), ds['A'] == 'a0')
assert_array_equal(assub("avar == 0", ds), ds['avar'] == 0)
with warnings.catch_warnings(): # element-wise comparison
warnings.simplefilter("ignore")
with pytest.raises(TypeError):
assub("avar == '0'", ds)
def test_choose():
"Test choose()"
ds = datasets.get_uts(True)[::4]
utsnd = ds['utsnd']
utsnd2 = utsnd + 1.
idx = ds['B'] == 'b0'
idxi = np.invert(idx)
y = choose(idx, (utsnd, utsnd2))
assert_array_equal(y.x[idx], utsnd2.x[idx])
assert_array_equal(y.x[idxi], utsnd.x[idxi])
with pytest.raises(DimensionMismatchError):
choose(idx, (utsnd, utsnd.sub(sensor='1')))
def test_combine():
"Test combine()"
ds1 = datasets.get_uts()
ds2 = datasets.get_uts()
n = ds1.n_cases
ds = combine((ds1, ds2))
assert_array_equal(ds2['Y'].x, ds['Y'].x[n:])
# list of numbers
assert_dataobj_equal(combine((1., 2., 1.)), Var((1., 2., 1.)))
assert_dataobj_equal(combine(('a', 'b', 'a')), Factor('aba'))
# combine Datasets with unequal keys
del ds1['Y']
# raise
with pytest.raises(KeyError):
combine((ds1, ds2))
with pytest.raises(KeyError):
combine((ds2, ds1))
# drop
del ds2['YCat']
ds = combine((ds1, ds2), incomplete='drop')
assert 'Y' not in ds
assert 'YCat' not in ds
# fill in
ds = combine((ds1, ds2), incomplete='fill in')
assert_array_equal(ds['Y'].x[n:], ds2['Y'].x)
assert_array_equal(np.isnan(ds['Y'].x[:n]), True)
assert_array_equal(ds['YCat'][:n], ds1['YCat'])
assert_array_equal(ds['YCat'][n:], '')
# invalid input
with pytest.raises(ValueError):
combine(())
with pytest.raises(TypeError):
combine((ds2['A'], ds2['Y']))
# combine NDVar with unequel dimensions
ds = datasets.get_uts(utsnd=True)
y = ds['utsnd']
y1 = y.sub(sensor=['0', '1', '2', '3'])
y2 = y.sub(sensor=['1', '2', '3', '4'])
ds1 = Dataset((y1,), info={'a': np.arange(2), 'b': [np.arange(2)]})
ds2 = Dataset((y2,), info={'a': np.arange(2), 'b': [np.arange(2)]})
dsc = combine((ds1, ds2))
y = dsc['utsnd']
assert list(y.sensor.names) == ['1', '2', '3']
dims = ('case', 'sensor', 'time')
ref = np.concatenate((y1.get_data(dims)[:, 1:], y2.get_data(dims)[:, :3]))
assert_array_equal(y.get_data(dims), ref, "combine utsnd")
# info
assert_array_equal(dsc.info['a'], np.arange(2))
assert len(dsc.info['b']) == 1
assert_array_equal(dsc.info['b'][0], np.arange(2))
def test_datalist():
"Test Datalist class"
dl = Datalist(range(10))
# indexing
assert dl[3] == 3
x = dl[:3]
assert isinstance(x, Datalist)
assert_array_equal(x, list(range(3)))
assert_array_equal(dl[8:], list(range(8, 10)))
x = dl[np.arange(10) < 3]
assert isinstance(x, Datalist)
assert_array_equal(x, list(range(3)))
assert_array_equal(dl[np.arange(3)], list(range(3)))
# __add__
x = dl + list(range(10, 12))
assert isinstance(x, Datalist)
assert_array_equal(x, list(range(12)))
# aggregate
x = dl.aggregate(Factor('ab', repeat=5))
assert isinstance(x, Datalist)
assert_array_equal(x, [2.0, 7.0])
# repr
dl = Datalist([['a', 'b'], [], ['a']])
assert str(dl) == "[['a', 'b'], [], ['a']]"
dl = Datalist([['a', 'b'], [], ['a']], fmt='strlist')
assert str(dl) == '[[a, b], [], [a]]'
assert str(dl[:2]) == '[[a, b], []]'
# eq
a = Datalist([[], [1], [], [1]])
b = Datalist([[], [], [2], [1]])
assert_array_equal(a == b, [True, False, False, True])
assert_array_equal(a != b, [False, True, True, False])
# deepcopy
ac = deepcopy(a)
assert ac is not a
assert_array_equal(ac, a)
ac[0].append(1)
assert_array_equal(ac == a, [False, True, True, True])
# __setitem__
ac[:2] = (1, 2)
assert_array_equal(ac == [1, 2, [], [1]], True)
ac[np.arange(2, 4)] = [3, 4]
assert_array_equal(ac == list(range(1, 5)), True)
with pytest.raises(ValueError):
ac[np.arange(2)] = np.arange(3)
# update
a._update_listlist(b)
assert_array_equal(a, [[], [1], [2], [1]])
def test_dataset():
"Basic dataset operations"
ds = Dataset()
# naming
ds['f'] = Factor('abab')
assert ds['f'].name == 'f'
# ds.add()
with pytest.raises(ValueError):
ds.add(Factor('aabb')) # no name
ds.add(Factor('aabb', name='g'))
assert ds['g'].name == 'g'
# ds.update()
ds = Dataset()
ds.update({'f': Factor('abab')})
assert ds['f'].name == 'f'
# checks on assignemnt
ds = Dataset()
ds['a'] = Factor('abab')
# key check
with pytest.raises(ValueError):
ds[:, '1'] = 'value'
# value check
with pytest.raises(ValueError):
ds['b'] = Factor('abcde') # length mismatch
with pytest.raises(TypeError):
ds['b'] = {i: i for i in range(4)}
def test_dataset_combining():
"Test Dataset combination methods"
ds = datasets.get_uv()
del ds['fltvar'], ds['intvar'], ds['A']
ds2 = datasets.get_uv()
del ds2['fltvar'], ds2['intvar']
ds.update(ds2)
assert_array_equal(ds['A'], ds2['A'])
ds2 = datasets.get_uv()
del ds2['fltvar'], ds2['intvar']
ds2['B'][5] = 'something_else'
del ds['A']
with pytest.raises(ValueError):
ds.update(ds2)
def test_dataset_indexing():
"""Test Dataset indexing"""
ds = datasets.get_uv()
ds.index('case')
# indexing values
assert ds['A', 1] == ds['A'][1]
assert ds[1, 'A'] == ds['A'][1]
# indexing variables
assert_dataobj_equal(ds[:, 'A'], ds['A'])
assert_dataobj_equal(ds['A', :], ds['A'])
assert_dataobj_equal(ds[:10, 'A'], ds['A'][:10])
assert_dataobj_equal(ds['A', :10], ds['A'][:10])
assert_dataobj_equal(ds.sub("case < 10", 'A'), ds['A'][:10])
# new Dataset through indexing
ds2 = Dataset()
ds2['A'] = ds['A']
assert_dataset_equal(ds[('A',)], ds2)
ds2['B'] = ds['B']
assert_dataset_equal(ds['A', 'B'], ds2)
assert_dataset_equal(ds[('A', 'B'), :10], ds2[:10])
assert_dataset_equal(ds[:10, ('A', 'B')], ds2[:10])
# empty index
assert_dataobj_equal(ds2[[]], Dataset([Factor([], 'A'), Factor([], 'B')]))
# assigning value
ds[2, 'A'] = 'hello'
assert ds[2, 'A'] == 'hello'
ds['A', 2] = 'not_hello'
assert ds[2, 'A'] == 'not_hello'
# assigning new factor
ds['C', :] = 'c'
assert np.all(ds.eval("C == 'c'"))
# assigning new Var
ds['D1', :] = 5.
ds[:, 'D2'] = 5.
assert_array_equal(ds['D1'], 5)
assert_array_equal(ds['D2'], 5)
# test illegal names
f = Factor('aaabbb')
with pytest.raises(ValueError):
ds['%dsa'] = f
with pytest.raises(ValueError):
ds['432'] = f
with pytest.raises(ValueError):
ds['%dsa', :] = 'value'
with pytest.raises(ValueError):
ds[:, '%dsa'] = 'value'
with pytest.raises(ValueError):
ds['432', :] = 4.
with pytest.raises(ValueError):
ds[:, '432'] = 4.
# deleting items
del ds['A']
assert 'A' not in ds
with pytest.raises(KeyError):
_ = ds['A']
del ds['B', 'rm']
assert 'B' not in ds and 'rm' not in ds
def test_dataset_repr():
"Test Dataset string representation methods"
ds = datasets.get_uts()
assert repr(ds) == "<Dataset n_cases=60 {'A':F, 'B':F, 'rm':F, 'ind':F, 'Y':V, 'YBin':F, 'YCat':F, 'uts':Vnd}>"
assert str(ds.head()) == str(ds[:10])
assert str(ds.tail()) == str(ds[-10:])
assert str(ds.summary(50)) == """Key Type Values
--------------------------------------------------
A Factor a0:30, a1:30
B Factor b0:30, b1:30
rm Factor R00:4, R01:4... (15 cells, random)
ind Factor R00, R01... (60 cells, random)
Y Var -3.53027 - 3.04498
YBin Factor c1:34, c2:26
YCat Factor c1:17, c2:24, c3:19
uts NDVar 100 time; -2.67343 - 4.56283
--------------------------------------------------
Dataset: 60 cases"""
assert str(ds[:5].summary()) == """Key Type Values
-----------------------------------------------------------
A Factor a0:5
B Factor b0:5
rm Factor R00, R01, R02, R03, R04 (random)
ind Factor R00, R01, R02, R03, R04 (random)
Y Var 0.77358, 1.01346, 1.89424, 2.09773, 2.55396
YBin Factor c1:4, c2
YCat Factor c1:2, c2:2, c3
uts NDVar 100 time; -0.634835 - 4.56283
-----------------------------------------------------------
Dataset: 5 cases"""
def test_dataset_sorting():
"Test Dataset sorting methods"
test_array = np.arange(10)
ds = Dataset()
ds['v'] = Var(test_array)
ds['f'] = Factor(test_array)
# shuffle the Dataset
rand_idx = test_array.copy()
np.random.shuffle(rand_idx)
ds_shuffled = ds[rand_idx]
# ascending, Var, copy
dsa = ds_shuffled.sorted('v')
assert_dataset_equal(dsa, ds)
# descending, Factor, in-place
ds_shuffled.sort('f', descending=True)
assert_dataset_equal(ds_shuffled, ds[::-1])
def test_dim_categorial():
"Test Categorial Dimension"
values = ['a', 'b', 'c', 'abc']
name = 'cat'
dim = Categorial(name, values)
# basic properties
print(dim)
assert len(dim) == len(values)
# persistence
s = pickle.dumps(dim, pickle.HIGHEST_PROTOCOL)
dim_ = pickle.loads(s)
assert dim_ == dim
# indexing
sub_values = values[:2]
idx = dim._array_index(sub_values)
assert dim[idx] == Categorial(name, sub_values)
assert dim._array_index('a') == values.index('a')
assert dim._array_index('abc') == values.index('abc')
with pytest.raises(TypeError):
dim._array_index(('a', 'b', 'c'))
# intersection
dim2 = Categorial(name, ['c', 'b', 'e'])
dim_i = dim.intersect(dim2)
assert dim_i == Categorial(name, ['b', 'c'])
# connectivity
dim = Categorial(name, ['c', 'b', 'e'], [('b', 'c'), ('b', 'e')])
assert_array_equal(dim.connectivity(), [[0, 1], [1, 2]])
def test_dim_scalar():
"Test Scalar Dimension"
d = Scalar('scalar', [20, 30, 40, 50, 60, 70])
assert repr(d) == "Scalar('scalar', [20, ..., 70] (6))"
assert d._array_index(20) == 0
assert d._array_index(30) == 1
assert d._array_index(21) == 0
with pytest.raises(IndexError):
d._array_index(25)
# binning
edges, dim = d._bin(step=20)
assert edges == [20, 40, 60, 80]
assert dim == Scalar('scalar', [30, 50, 70])
edges, dim = d._bin(start=30, stop=70, step=20)
assert edges == [30, 50, 70]
assert dim == Scalar('scalar', [40, 60])
# range not divisible by step
with pytest.raises(ValueError):
d._bin(start=30, step=20)
with pytest.raises(ValueError):
d._bin(stop=70, step=20)
# nbins
edges, dim = d._bin(nbins=3)
assert edges == [20, 40, 60, None]
assert dim == Scalar('scalar', [30, 50, 70])
edges, dim = d._bin(nbins=2)
assert edges == [20, 50, None]
assert dim == Scalar('scalar', [35, 65])
# uneven bin size
with pytest.raises(ValueError):
d._bin(nbins=4)
# approximate start/stop
edges, dim = d._bin(25, 65, nbins=2)
assert edges == [30, 50, 70]
edges, dim = d._bin(25, 65, 20)
assert edges == [30, 50, 70]
def test_dim_uts():
"Test UTS Dimension"
uts = UTS(-0.1, 0.005, 301)
# basic indexing
with pytest.raises(ValueError):
uts._array_index(1.5)
with pytest.raises(ValueError):
uts._array_index(-.15)
# make sure indexing rounds correctly for floats
for i, s in enumerate(np.arange(0, 1.4, 0.05)):
idx = uts._array_index((-0.1 + s, s))
assert idx.start == 10 * i
assert idx.stop == 20 + 10 * i
# intersection
uts1 = UTS(-0.1, 0.01, 50)
uts2 = UTS(0, 0.01, 20)
intersection = uts1.intersect(uts2)
assert intersection == uts2
idx = uts1._array_index((0, 0.2))
assert uts1[idx] == uts2
def test_effect():
"Test _Effect class"
# .enumerate_cells()
f1 = Factor('aabbccaabbcc')
f2 = Factor('abababababab')
i = f1 % f2
n1 = np.concatenate((np.tile([0, 1], 3), np.tile([2, 3], 3)))
assert_array_equal(f1.enumerate_cells(), n1)
assert_array_equal(f2.enumerate_cells(), np.arange(6).repeat(2))
assert_array_equal(i.enumerate_cells(), np.arange(2).repeat(6))
def test_equality():
u = Var(np.arange(5.))
v = Var(np.arange(5.))
assert all_equal(u, v)
u[-1] = np.nan
assert not all_equal(u, v)
v[-1] = np.nan
assert not all_equal(u, v)
assert all_equal(u, v, True)
def test_factor():
"Test basic Factor functionality"
# initializing
assert_array_equal(Factor('ab'), ['a', 'b'])
assert_array_equal(Factor('ab', repeat=2), ['a', 'a', 'b', 'b'])
assert_array_equal(Factor('ab', repeat=np.array([2, 1])), ['a', 'a', 'b'])
empty_factor = Factor([])
assert len(empty_factor) == 0
assert_dataobj_equal(Factor(np.empty(0)), empty_factor)
# from Factor
f = Factor('aabbcc')
assert_array_equal(Factor(f), f)
assert_array_equal(Factor(f, labels={'a': 'b'}), Factor('bbbbcc'))
# removing a cell
f = Factor('aabbcc')
assert f.cells == ('a', 'b', 'c')
assert f.n_cells == 3
f[f == 'c'] = 'a'
assert f.cells == ('a', 'b')
assert f.n_cells == 2
# cell order
a = np.tile(np.arange(3), 3)
f = Factor(a, labels={2: 'a', 1: 'b', 0: 'c'})
assert f.cells == ('a', 'b', 'c')
assert f[:2].cells == ('b', 'c')
# not alphabetical
f = Factor(a, labels={0: 'c', 1: 'b', 2: 'a'})
assert f.cells == ('c', 'b', 'a')
assert f[:2].cells == ('c', 'b')
f[f == 'b'] = 'c'
assert f.cells == ('c', 'a')
# initialize from factor
f = Factor(a, labels={0: 'c', 1: 'b', 2: 'a'})
f2 = Factor(f, labels={'c': 'c', 'b': 'c', 'a': 'a'})
assert f2.cells == ('c', 'a')
# superfluous label
f2 = Factor(f, labels={'c': 'a', 'x': 'c', 'b': 'b', 'a': 'c'})
assert f2.cells == ('a', 'b', 'c')
# sort
f = Factor(a, labels={0: 'c', 1: 'b', 2: 'a'})
f.sort_cells(('a', 'c', 'b'))
assert f.cells == ('a', 'c', 'b')
# label length
lens = [2, 5, 32, 2, 32, 524]
f = Factor(['a' * l for l in lens], 'f')
fl = f.label_length()
assert_array_equal(fl, lens)
assert fl.info['longname'] == 'f.label_length()'
lens2 = [3, 5, 32, 2, 32, 523]
f2 = Factor(['b' * l for l in lens2], 'f2')
assert_array_equal(fl - f2.label_length(), [a - b for a, b in zip(lens, lens2)])
# equality
f = Factor('aabbcc')
assert_equal(f == Factor('aabbcc'), True)
assert_equal(f == Factor('bbccaa'), False)
assert_equal(f == Factor('aabxxx'), (True, True, True, False, False, False))
assert_equal(f == Var(np.ones(6)), False)
# Factor.as_var()
assert_array_equal(f.as_var(dict(zip('abc', range(3)))), [0, 0, 1, 1, 2, 2])
assert_array_equal(f.as_var({'a': 1}, 2), [1, 1, 2, 2, 2, 2])
with pytest.raises(KeyError):
f.as_var({'a': 1})
# Factor.floodfill()
f = Factor([' ', ' ', '1', '2', ' ', ' ', '3', ' ', ' ', '2', ' ', ' ', '1'])
regions = [ 1, 1, 1, 2, 2, 2, 3, 3, 3, 2, 2, 1, 1]
regions2 = [ 1, 1, 1, 2, 2, 3, 3, 2, 2, 2, 2, 1, 1]
regions3 = [ 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2]
target3 = ['1', '1', '1', '2', '2', '2', '3', '3', '2', '2', '2', '2', '1']
target_p = [' ', ' ', '1', '2', '2', '2', '3', '3', '3', '2', '2', '2', '1']
assert_array_equal(f.floodfill(regions, ' '), Var(regions).as_factor())
assert_array_equal(f.floodfill(regions2, ' '), Var(regions2).as_factor())
assert_array_equal(f.floodfill(regions3, ' '), target3)
assert_array_equal(f.floodfill('previous', ' '), target_p)
f = Factor(['', '', 'a', '', 'e', 'r', ''])
assert_array_equal(f.floodfill([1, 1, 1, 11, 11, 11, 11]), Factor('aaaeerr'))
def test_factor_relabel():
"Test Factor.relabel() method"
f = Factor('aaabbbccc')
f.update_labels({'a': 'd'})
assert_array_equal(f, Factor('dddbbbccc'))
f.update_labels({'d': 'c', 'c': 'd'})
assert_array_equal(f, Factor('cccbbbddd'))
f.update_labels({'d': 'c'})
assert_array_equal(f, Factor('cccbbbccc'))
with pytest.raises(KeyError):
f.update_labels({'a': 'c'})
def test_interaction():
"Test Interaction"
ds = datasets.get_uv()
A = ds['A']
B = ds['B']
i = A % B
# eq for sequence
assert_array_equal(i == A % B, True)
assert_array_equal(i == B % A, False)
assert_array_equal(i == A, False)
assert_array_equal(i == ds['fltvar'], False)
assert_array_equal(ds.eval("A%B") == Factor(ds['A']) % B, True)
# eq for element
for a, b in product(A.cells, B.cells):
assert_array_equal(i == (a, b), np.logical_and(A == a, B == b))
# Interaction.as_factor()
a = Factor('aabb')
i = a % Factor('cdcd')
assert_dataobj_equal(i.as_factor(), Factor(['a c', 'a d', 'b c', 'b d']))
i = a % Factor(['c', '', 'c', ''])
assert_dataobj_equal(i.as_factor(), Factor(['a c', 'a', 'b c', 'b']))
# pickling
ip = pickle.loads(pickle.dumps(i))
assert_dataobj_equal(ip, i)
def test_isin():
"Test .isin() methods"
values = np.array([ 6, -6, 6, -2, -1, 0, -10, -5, -10, -6])
v = values[0]
v2 = values[:2]
labels = {i: c for i, c in enumerate(ascii_lowercase, -10)}
vl = labels[v]
v2l = [labels[v_] for v_ in v2]
target = np.logical_or(values == v2[0], values == v2[1])
inv_target = np.invert(target)
index_target = np.flatnonzero(values == v)
empty = np.array([])
var = Var(values)
assert_array_equal(var.index(v), index_target)
assert_array_equal(var.isin(v2), target)
assert_array_equal(var.isany(*v2), target)
assert_array_equal(var.isnot(*v2), inv_target)
assert_array_equal(var.isnotin(v2), inv_target)
var0 = Var([])
assert_array_equal(var0.isin(v2), empty)
assert_array_equal(var0.isany(*v2), empty)
assert_array_equal(var0.isnot(*v2), empty)
assert_array_equal(var0.isnotin(v2), empty)
f = Factor(values, labels=labels)
assert_array_equal(f.index(vl), index_target)
assert_array_equal(f.isin(v2l), target)
assert_array_equal(f.isany(*v2l), target)
assert_array_equal(f.isnot(*v2l), inv_target)
assert_array_equal(f.isnotin(v2l), inv_target)
f0 = Factor([])
assert_array_equal(f0.isin(v2l), empty)
assert_array_equal(f0.isany(*v2l), empty)
assert_array_equal(f0.isnot(*v2l), empty)
assert_array_equal(f0.isnotin(v2l), empty)
def test_longname():
"Test info['longname'] entry"
ds = Dataset()
u = Var([2], 'u')
v = Var([1], 'v')
# simple operations, also tested in test_var()
assert longname(v.abs()) == 'abs(v)'
assert longname(u * v) == "u * v"
assert longname(u * v.abs()) == "u * abs(v)"
# Dataset assigning
ds['abs_v'] = v.abs()
assert longname(ds['abs_v']) == 'abs(v)'
def test_model():
"Test Model class"
a = Factor('ab', repeat=3, name='a')
b = Factor('ab', tile=3, name='b')
u = Var([1, 1, 1, -1, -1, -1], 'u')
v = Var([1., 2., 3., 4., 5., 6.], 'v')
w = Var([1., 0., 0., 1., 1., 0.], 'w')
# model repr
m = a * b + v
assert repr(m) == "a + b + a % b + v"
lines = ("intercept a b a x b v",
"-----------------------------",
"1 1 1 1 1",
"1 1 0 0 2",
"1 1 1 1 3",
"1 0 0 0 4",
"1 0 1 0 5",
"1 0 0 0 6")
assert str(m) == '\n'.join(lines)
assert str(m.head(2)) == '\n'.join(lines[:4])
assert str(m.tail(2)) == '\n'.join(lines[:2] + lines[-2:])
str(m.info())
# model without explicit names
x1 = Factor('ab', repeat=2)
x2 = Factor('ab', tile=2)
m = x1 * x2
assert repr(m) == "<?> + <?> + <?> % <?>"
# catch explicit intercept
intercept = Factor('i', repeat=4, name='intercept')
with pytest.raises(ValueError):
_ = a * intercept
# different var/factor combinations
assert a * b == a + b + a % b
assert a * v == a + v + a % v
assert a * (v + w) == a + v + w + a % v + a % w
# parametrization
m = v + w + v * w
p = m._parametrize('dummy')
assert p.column_names == ['intercept', 'v', 'w', 'v * w']
assert_array_equal(p.x[:, p.terms['intercept']], 1)
assert_array_equal(p.x[:, p.terms['v']], v.x[:, None])
assert_array_equal(p.x[:, p.terms['w']], w.x[:, None])
assert_array_equal(p.x[:, p.terms['v * w']], (v * w).x[:, None])
# persistence
mp = pickle.loads(pickle.dumps(m, pickle.HIGHEST_PROTOCOL))
mpp = mp._parametrize('dummy')
assert_array_equal(mpp.x, p.x)
# nested Vars
m = (v + w) * u
assert_dataobj_equal(m.effects[2], u)
assert_dataobj_equal(m.effects[3], v * u)
assert_dataobj_equal(m.effects[4], w * u)
m = u * (v + w)
assert_dataobj_equal(m.effects[0], u)
assert_dataobj_equal(m.effects[3], u * v)
assert_dataobj_equal(m.effects[4], u * w)
m = (v + w) % u
assert_dataobj_equal(m.effects[0], v * u)
assert_dataobj_equal(m.effects[1], w * u)
m = u % (v + w)
assert_dataobj_equal(m.effects[0], u * v)
assert_dataobj_equal(m.effects[1], u * w)
def test_ndvar():
"Test the NDVar class"
ds = datasets.get_uts(utsnd=True)
x = ds['utsnd']
# meaningful slicing
with pytest.raises(KeyError):
x.sub(sensor='5')
assert_equal(x.sub(sensor='4'), x.x[:, 4])
assert_equal(x.sub(sensor=['4', '3', '2']), x.x[:, [4, 3, 2]])
assert_equal(x.sub(sensor=['4']), x.x[:, [4]])
assert_equal(x.sub(case=1, sensor='4'), x.x[1, 4])
# setup indices
s_case = slice(10, 13)
s_sensor = slice('2', '4')
s_time = slice(0.1, 0.2)
b_case = np.bincount([10, 11, 12], minlength=len(x)).astype(bool)
b_sensor = np.array([False, False, True, True, False])
b_time = np.bincount(range(30, 40), minlength=len(x.time)).astype(bool)
a_case = np.arange(10, 13)
a_sensor = ['2', '3']
a_time = np.arange(0.1, 0.2, 0.01)
# slicing with different index kinds
tgt = x.x[s_case, 2:4, 30:40]
assert tgt.shape == (3, 2, 10)
# single
assert_equal(x.sub(case=s_case, sensor=s_sensor, time=s_time), tgt)
assert_equal(x.sub(case=a_case, sensor=a_sensor, time=a_time), tgt)
assert_equal(x.sub(case=b_case, sensor=b_sensor, time=b_time), tgt)
# bool & slice
assert_equal(x.sub(case=b_case, sensor=s_sensor, time=s_time), tgt)
assert_equal(x.sub(case=s_case, sensor=b_sensor, time=s_time), tgt)
assert_equal(x.sub(case=s_case, sensor=s_sensor, time=b_time), tgt)
assert_equal(x.sub(case=b_case, sensor=b_sensor, time=s_time), tgt)
assert_equal(x.sub(case=s_case, sensor=b_sensor, time=b_time), tgt)
assert_equal(x.sub(case=b_case, sensor=s_sensor, time=b_time), tgt)
# bool & array
assert_equal(x.sub(case=b_case, sensor=a_sensor, time=a_time), tgt)
assert_equal(x.sub(case=a_case, sensor=b_sensor, time=a_time), tgt)
assert_equal(x.sub(case=a_case, sensor=a_sensor, time=b_time), tgt)
assert_equal(x.sub(case=b_case, sensor=b_sensor, time=a_time), tgt)
assert_equal(x.sub(case=a_case, sensor=b_sensor, time=b_time), tgt)
assert_equal(x.sub(case=b_case, sensor=a_sensor, time=b_time), tgt)
# slice & array
assert_equal(x.sub(case=s_case, sensor=a_sensor, time=a_time), tgt)
assert_equal(x.sub(case=a_case, sensor=s_sensor, time=a_time), tgt)
assert_equal(x.sub(case=a_case, sensor=a_sensor, time=s_time), tgt)
assert_equal(x.sub(case=s_case, sensor=s_sensor, time=a_time), tgt)
assert_equal(x.sub(case=a_case, sensor=s_sensor, time=s_time), tgt)
assert_equal(x.sub(case=s_case, sensor=a_sensor, time=s_time), tgt)
# all three
assert_equal(x.sub(case=a_case, sensor=b_sensor, time=s_time), tgt)
assert_equal(x.sub(case=a_case, sensor=s_sensor, time=b_time), tgt)
assert_equal(x.sub(case=b_case, sensor=a_sensor, time=s_time), tgt)
assert_equal(x.sub(case=b_case, sensor=s_sensor, time=a_time), tgt)
assert_equal(x.sub(case=s_case, sensor=a_sensor, time=b_time), tgt)
assert_equal(x.sub(case=s_case, sensor=b_sensor, time=a_time), tgt)
# norm
y = x / x.norm('sensor')
assert_allclose(y.norm('sensor'), 1.)
y = ds['uts'].mean('case').norm('time')
assert isinstance(y, float)
# dot
m = NDVar([1, 0, -1, 0, 0], x.sensor)
# -> time
y = m.dot(x[0])
assert_array_equal(y.x, x.x[0, 0] - x.x[0, 2])
# -> case x time
y_all = m.dot(x)
assert len(y_all) == len(x)
assert_dataobj_equal(y_all[0], y)
# -> scalar
y = m.dot(x[0, :, 0.200])
assert y == x.x[0, 0, 40] - x.x[0, 2, 40]
# Var
v_case = Var(b_case)
assert_equal(x.sub(case=v_case, sensor=b_sensor, time=a_time), tgt)
# univariate result
assert_dataobj_equal(x.sub(sensor='2', time=0.1),
Var(x.x[:, 2, 30], x.name))
assert x.sub(case=0, sensor='2', time=0.1) == x.x[0, 2, 30]
# baseline correction
x_bl = x - x.summary(time=(None, 0))
# assert that the baseline is 0
bl = x_bl.summary('case', 'sensor', time=(None, 0))
assert abs(bl) < 1e-10
# iteration
for i, xi in enumerate(x):
assert_dataobj_equal(xi, x[i])
if i > 4:
break
def test_ndvar_binning():
"Test NDVar.bin()"
x = np.arange(10)
time = UTS(-0.1, 0.1, 10)
x_dst = x.reshape((5, 2)).mean(1)
time_dst = np.arange(0., 0.9, 0.2)
# 1-d
ndvar = NDVar(x, (time,))
b = ndvar.bin(0.2)
assert_array_equal(b.x, x_dst, "Binned data")
assert_array_equal(b.time, time_dst, "Bin times")
b = ndvar.sub(time=(0, 0.8)).bin(0.4)
assert b.shape == (2,)
# 2-d
ndvar = NDVar(np.vstack((x, x, x)), ('case', time))
b = ndvar.bin(0.2)
assert_array_equal(b.x, np.vstack((x_dst, x_dst, x_dst)), "Binned data")
assert_array_equal(b.time, time_dst, "Bin times")
# time:
x = np.ones((5, 70))
ndvar = NDVar(x, ('case', UTS(0.45000000000000007, 0.005, 70)))
binned_ndvar = ndvar.bin(0.05)
assert_array_equal(binned_ndvar.x, 1.)
assert binned_ndvar.shape == (5, 7)
# n_bins
x = np.ones((2, 601))
ndvar = NDVar(x, ('case', UTS(-0.1, 0.001, 601)))
binned_ndvar = ndvar.bin(0.1, 0.1, 0.4)
assert binned_ndvar.shape == (2, 3)
def test_ndvar_connectivity():
"Test NDVar dimensions with conectvity graph"
ds = datasets.get_uts(utsnd=True)
x = ds['utsnd']
# non-monotonic index
sub_mono = x.sub(sensor=['2', '3', '4'])
sub_nonmono = x.sub(sensor=['4', '3', '2'])
argsort = np.array([2,1,0])
conn = argsort[sub_mono.sensor.connectivity().ravel()].reshape((-1, 2))
assert_equal(sub_nonmono.sensor.connectivity(), conn)
# date for labeling
x1 = ds.eval("utsnd[logical_and(A=='a0', B=='b0')].mean('case')")
x2 = ds.eval("utsnd[A=='a1'].mean('case')")
x = x1 + x2
# insert point that is connected by sensors but not by grid
x.x[0, 50:55] = 4
# custom connectivity on first axis
l = x.label_clusters(3)
assert len(l.info['cids']) == 5
assert_array_equal(np.unique(l.x), np.append([0], l.info['cids']))
# custom connectivity second
sensor, time = x.dims
x = NDVar(x.x.T, (time, sensor))
l = x.label_clusters(3)
assert len(l.info['cids']) == 5
# disconnected
cat = Categorial('categorial', ('a', 'b', 'c', 'd', 'e'))
x = NDVar(x.x, (time, cat))
l = x.label_clusters(3)
assert len(l.info['cids']) == 13
# ordered
scalar = Scalar('ordered', range(5))
x = NDVar(x.x, (time, scalar))
l = x.label_clusters(3)
assert len(l.info['cids']) == 6
def ndvar_index(x, dimname, index, a_index, index_repr=True):
"Helper function for test_ndvar_indexing"
ax = x.get_axis(dimname)
index_prefix = FULL_AXIS_SLICE * ax
if dimname != 'case':
dim = x.get_dim(dimname)
assert_equal(dim._array_index(index), a_index)
if index_repr is not False:
if index_repr is True:
index_repr = index
assert dim._dim_index(a_index) == index_repr
x_array = x.x[index_prefix + (a_index,)]
x1 = x.sub(**{dimname: index})
x2 = x[index_prefix + (index,)]
assert_array_equal(x1.x, x_array)
assert_dataobj_equal(x2, x1)
def test_ndvar_indexing():
ds = datasets.get_uts(utsnd=True)
x = ds['utsnd']
# case
ndvar_index(x, 'case', 1, 1)
ndvar_index(x, 'case', [0, 3], [0, 3])
ndvar_index(x, 'case', slice(0, 10, 2), slice(0, 10, 2))
# Sensor
ndvar_index(x, 'sensor', '0', 0)
ndvar_index(x, 'sensor', ['0', '2'], [0, 2])
ndvar_index(x, 'sensor', slice('0', '2'), slice(0, 2))
ndvar_index(x, 'sensor', 0, 0, False)
ndvar_index(x, 'sensor', [0, 2], [0, 2], False)
ndvar_index(x, 'sensor', slice(0, 2), slice(0, 2), False)
# UTS
ndvar_index(x, 'time', 0, 20)
ndvar_index(x, 'time', 0.1, 30)
ndvar_index(x, 'time', 0.102, 30, False)
ndvar_index(x, 'time', [0, 0.1, 0.2], [20, 30, 40])
ndvar_index(x, 'time', slice(0.1, None), slice(30, None))
ndvar_index(x, 'time', slice(0.2), slice(40))
ndvar_index(x, 'time', slice(0.202), slice(41), False)
ndvar_index(x, 'time', slice(0.1, 0.2), slice(30, 40))
ndvar_index(x, 'time', slice(0.102, 0.2), slice(31, 40), False)
ndvar_index(x, 'time', slice(0.1, None, 0.1), slice(30, None, 10))
ndvar_index(x, 'time', slice(0.1, None, 1), slice(30, None, 100))
# NDVar as index
sens_mean = x.mean(('case', 'time'))
idx = sens_mean > 0
pos = sens_mean[idx]
assert_array_equal(pos.x > 0, True)
# NDVar as index along one dimension
x_tc = x.sub(sensor='1')
x_time = NDVar(x_tc.time.times >= 0.3, dims=(x_tc.time,))
assert_dataobj_equal(x_tc[x_time], x_tc.sub(time=(0.3, None)))
# NDVar whose dimension is smaller
x_time_sub = x_time.sub(time=(0.2, None))
assert_dataobj_equal(x_tc[x_time_sub], x_tc.sub(time=(0.3, None)))
# out of range index
with pytest.raises(ValueError):
x.sub(time=(0.1, 0.81))
with pytest.raises(IndexError):
x.sub(time=(-0.25, 0.1))
# newaxis
with pytest.raises(IndexError):
_ = x[newaxis]
x0 = x[0]
assert not x0.has_case
assert x0[newaxis].has_case
# Scalar
x = cwt_morlet(ds['uts'], [8, 10, 13, 17])
with pytest.raises(IndexError):
_ = x[:, 9]
with pytest.raises(IndexError):
_ = x[:, 6]
ndvar_index(x, 'frequency', 10, 1)
ndvar_index(x, 'frequency', 10.1, 1, False)
ndvar_index(x, 'frequency', 9.9, 1, False)
ndvar_index(x, 'frequency', [8.1, 10.1], [0, 1], False)
ndvar_index(x, 'frequency', slice(8, 13), slice(0, 2))
ndvar_index(x, 'frequency', slice(8, 13.1), slice(0, 3), False)
ndvar_index(x, 'frequency', slice(8, 13.1, 2), slice(0, 3, 2), False)
# Categorial
x = NDVar(x.x, ('case', Categorial('cat', ['8', '10', '13', '17']), x.time))
with pytest.raises(TypeError):
_ = x[:, 9]
with pytest.raises(IndexError):
_ = x[:, '9']
ndvar_index(x, 'cat', '13', 2)
ndvar_index(x, 'cat', ['8', '13'], [0, 2])
ndvar_index(x, 'cat', slice('8', '13'), slice(0, 2))
ndvar_index(x, 'cat', slice('8', None, 2), slice(0, None, 2))
# SourceSpace
x = datasets.get_mne_stc(True, subject='fsaverage')
with pytest.raises(TypeError):
_ = x[:'insula-rh']
with pytest.raises(TypeError):
_ = x['insula-lh':'insula-rh']
with pytest.raises(TypeError):
_ = x['insula-lh', 'insula-rh']
ndvar_index(x, 'source', 'L90', 90)
ndvar_index(x, 'source', 'R90', 642 + 90)
ndvar_index(x, 'source', ['L90', 'R90'], [90, 642 + 90])
ndvar_index(x, 'source', slice('L90', 'R90'), slice(90, 642 + 90))
ndvar_index(x, 'source', 90, 90, False)
ndvar_index(x, 'source', [90, 95], [90, 95], False)
ndvar_index(x, 'source', slice(90, 95), slice(90, 95), False)
ndvar_index(x, 'source', 'insula-lh', x.source.parc == 'insula-lh', False)
ndvar_index(x, 'source', ('insula-lh', 'insula-rh'),
x.source.parc.isin(('insula-lh', 'insula-rh')), False)
n_lh = x.source.parc.endswith('lh').sum()
ndvar_index(x, 'source', 'lh', slice(n_lh), False)
ndvar_index(x, 'source', 'rh', slice(n_lh, None), False)
# index dim != dim
source_rh = x.source[x.source.lh_n:]
index = NDVar(np.arange(len(source_rh)) > 100, (source_rh,))
assert_dataobj_equal(x.sub(source=index), x.sub(source='rh').sub(source=index))
with pytest.raises(IndexError):
x.sub(source='lh').sub(index)
# multiple arguments
y = ds['utsnd'].sub(sensor=[1, 2], time=[0, 0.1])
assert y.shape == (60, 2, 2)
assert_array_equal(y.x, ds['utsnd'].x[:, 1:3, [20, 30]])
# argmax
x.x[10, 10] = 20
assert x.argmax() == ('L10', 0.1)
assert x[('L10', 0.1)] == 20
assert x.sub(source='L10').argmax() == 0.1
assert x.sub(time=0.1).argmax() == 'L10'
# broadcasting
u = ds[0, 'uts']
dim = Categorial('test_dim', ['a', 'b'])
v = NDVar([5, 1], dim)
for op, _, desc in OPERATORS:
y = op(v, u)
assert_array_equal(y['a'], op(5, u.x))
assert_array_equal(y['b'], op(1, u.x))
# with Case from Var
case = Var([4, 1])
for op, iop, desc in OPERATORS:
y = op(case, u)
assert_array_equal(y[0], op(4, u.x))
assert_array_equal(y[1], op(1, u.x))
# set NDVar elements
x = ds['uts'].copy()
x[:3, :.0] = 0
assert_array_equal(x.x[:3, :20], 0.)
assert_array_equal(x.x[3:, 20:], ds['uts'].x[3:, 20:])
# set with index NDVar
x = ds['uts'].copy()
index = x.mean('case') < 0
x[index] = -1
assert x.sum(index).sum() == -index.sum()
i_index = ~index
assert x.sum(i_index).sum() == ds['uts'].sum(i_index).sum()
with pytest.raises(DimensionMismatchError):
index[x != 0] = 0.
# set to NDVar
x = ds['utsnd'].copy()
x[0] = x[1]
assert_array_equal(x[0].x, x[1].x)
x3 = NDVar(x[3].x.swapaxes(0, 1), x.dims[:0:-1])
x[2] = x3
assert_array_equal(x[2].x, x[3].x)
x[:, '1'] = x[0, '2']
assert_array_equal(x.x[30, 1], x.x[0, 2])
with pytest.raises(ValueError):
x[:, '1'] = x[6]
def test_ndvar_summary_methods():
"Test NDVar methods for summarizing data over axes"
ds = datasets.get_uts(utsnd=True)
x = ds['utsnd']
x.info['test_item'] = 1
dim = 'sensor'
axis = x.get_axis(dim)
dims = ('case', 'sensor')
axes = tuple(x.get_axis(d) for d in dims)
idx = x > 0
x0 = x[0]
idx0 = idx[0]
xsub = x.sub(time=(0, 0.5))
idxsub = xsub > 0
idx1d = x.mean(('case', 'time')) > 0
# info inheritance
assert x.mean(('sensor', 'time')).info == x.info
# info update for booleans
assert x.any(('sensor', 'time')).info == {'test_item': 1}
# numpy functions
assert x.any() == x.x.any()
assert_array_equal(x.any(dim), x.x.any(axis))
assert_array_equal(x.any(dims), x.x.any(axes))
assert_array_equal(x.any(idx0), [x_[idx0.x].any() for x_ in x.x])
assert_array_equal(x.any(idx), [x_[i].any() for x_, i in zip(x.x, idx.x)])
assert_array_equal(x0.any(idx0), x0.x[idx0.x].any())
assert_array_equal(x.any(idxsub), xsub.any(idxsub))
assert_array_equal(x.any(idx1d), x.x[:, idx1d.x].any(1))
assert x.max() == x.x.max()
assert_array_equal(x.max(dim), x.x.max(axis))
assert_array_equal(x.max(dims), x.x.max(axes))
assert_array_equal(x.max(idx0), [x_[idx0.x].max() for x_ in x.x])
assert_array_equal(x.max(idx), x.x[idx.x].max())
assert_array_equal(x0.max(idx0), x0.x[idx0.x].max())
assert_array_equal(x.max(idxsub), xsub.max(idxsub))
assert_array_equal(x.max(idx1d), x.x[:, idx1d.x].max(1))
assert x.mean() == x.x.mean()
assert_array_equal(x.mean(dim), x.x.mean(axis))
assert_array_equal(x.mean(dims), x.x.mean(axes))
assert_array_almost_equal(x.mean(idx0), [x_[idx0.x].mean() for x_ in x.x])
assert_array_equal(x.mean(idx), x.x[idx.x].mean())
assert_array_equal(x0.mean(idx0), x0.x[idx0.x].mean())
assert_array_equal(x.mean(idxsub), xsub.mean(idxsub))
assert_array_equal(x.mean(idx1d), x.x[:, idx1d.x].mean(1))
assert x.min() == x.x.min()
assert_array_equal(x.min(dim), x.x.min(axis))
assert_array_equal(x.min(dims), x.x.min(axes))
assert_array_equal(x.min(idx0), [x_[idx0.x].min() for x_ in x.x])
assert_array_equal(x.min(idx), x.x[idx.x].min())
assert_array_equal(x0.min(idx0), x0.x[idx0.x].min())
assert_array_equal(x.min(idxsub), xsub.min(idxsub))
assert_array_equal(x.min(idx1d), x.x[:, idx1d.x].min(1))
assert x.var() == x.x.var()
assert x.var(ddof=1) == x.x.var(ddof=1)
assert_array_equal(x.var(dim), x.x.var(axis))
assert_array_equal(x.var(dims, ddof=1), x.x.var(axes, ddof=1))
assert_array_almost_equal(x.var(idx0), [x_[idx0.x].var() for x_ in x.x])
assert_array_equal(x.var(idx), x.x[idx.x].var())
assert_array_equal(x0.var(idx0), x0.x[idx0.x].var())
assert_array_equal(x.var(idxsub), xsub.var(idxsub))
assert_array_equal(x.var(idx1d), x.x[:, idx1d.x].var(1))
assert x.std() == x.x.std()
assert_array_equal(x.std(dim), x.x.std(axis))
assert_array_equal(x.std(dims), x.x.std(axes))
assert_array_almost_equal(x.std(idx0), [x_[idx0.x].std() for x_ in x.x])
assert_array_equal(x.std(idx), x.x[idx.x].std())
assert_array_equal(x0.std(idx0), x0.x[idx0.x].std())
assert_array_equal(x.std(idxsub), xsub.std(idxsub))
assert_array_equal(x.std(idx1d), x.x[:, idx1d.x].std(1))
# non-numpy
assert x.rms() == rms(x.x)
assert_array_equal(x.rms(dim), rms(x.x, axis))
assert_array_equal(x.rms(dims), rms(x.x, axes))
assert_array_almost_equal(x.rms(idx0), [rms(x_[idx0.x]) for x_ in x.x])
assert_array_equal(x.rms(idx), rms(x.x[idx.x]))
assert_array_equal(x0.rms(idx0), rms(x0.x[idx0.x]))
assert_array_equal(x.rms(idxsub), xsub.rms(idxsub))
assert_array_equal(x.rms(idx1d), rms(x.x[:, idx1d.x], 1))
assert x.extrema() == max(abs(x.min()), abs(x.max()))
def test_ndvar_timeseries_methods():
"Test NDVar time-series methods"
ds = datasets.get_uts(True)
x = ds['utsnd']
case, sensor, time = x.dims
xs = NDVar(x.x.swapaxes(1, 2), (case, time, sensor), x.info.copy(), x.name)
# envelope
env = x.envelope()
assert_array_equal(env.x >= 0, True)
envs = xs.envelope()
assert_array_equal(env.x, envs.x.swapaxes(1,2))
# indexing
assert len(ds[0, 'uts'][0.01:0.1].time) == 9
# smoothing
ma = x.smooth('time', 0.2, 'blackman')
assert_dataobj_equal(x.smooth('time', window='blackman', window_samples=20), ma)
with pytest.raises(TypeError):
x.smooth('time')
with pytest.raises(TypeError):
x.smooth('time', 0.2, 'blackman', window_samples=20)
mas = xs.smooth('time', 0.2, 'blackman')
assert_allclose(ma.x, mas.x.swapaxes(1, 2), 1e-10)
ma_mean = x.mean('case').smooth('time', 0.2, 'blackman')
assert_allclose(ma.mean('case').x, ma_mean.x)
# against raw scipy.signal
window = signal.get_window('blackman', 20, False)
window /= window.sum()
window.shape = (1, 1, 20)
assert_array_equal(ma.x, signal.convolve(x.x, window, 'same'))
# mode parameter
full = signal.convolve(x.x, window, 'full')
ma = x.smooth('time', 0.2, 'blackman', mode='left')
assert_array_equal(ma.x, full[:, :, :ma.shape[2]])
ma = x.smooth('time', 0.2, 'blackman', mode='right')
assert_array_equal(ma.x, full[:, :, -ma.shape[2]:])
# FFT
x = ds['uts'].mean('case')
np.sin(2 * np.pi * x.time.times, x.x)
f = x.fft()
assert_array_almost_equal(f.x, (f.frequency.values == 1) * (len(f) - 1))
np.sin(4 * np.pi * x.time.times, x.x)
f = x.fft()
assert_array_almost_equal(f.x, (f.frequency.values == 2) * (len(f) - 1))
# update tmin
assert x.time.times[0] == -0.2
x = set_tmin(x, 3.2)
assert x.time.times[0] == 3.2
def test_nested_effects():
"""Test nested effects"""
ds = datasets.get_uv(nrm=True)
nested = ds.eval("nrm(B)")
assert nested.cells == ds['nrm'].cells
# interaction
i = ds.eval("A % nrm(B)")
assert i.cells == tuple(product(*(ds[f].cells for f in ['A', 'nrm'])))
i = ds.eval("nrm(B) % A")
assert i.cells == tuple(product(*(ds[f].cells for f in ['nrm', 'A'])))
assert_has_no_empty_cells(ds.eval('A * B + nrm(B) + A % nrm(B)'))
@skip_on_windows # uses R
def test_ols():
"Test NDVar.ols() method"
from rpy2.robjects import r
# data-type
assert_array_equal(NDVar([1, 2, 3], Case).ols(Var([1, 2, 3])).x, [1.])
# simulate data
ds = datasets.get_uts(True)
n_times = len(ds['uts'].time)
x = np.zeros(n_times)
x[20:40] = np.hanning(20)
utsc = ds.eval("uts.copy()")
utsc.x += ds['Y'].x[:, None] * x[None, :]
ds_ = Dataset()
ds_['x'] = Var(ds['Y'].x)
ds_['x2'] = ds_['x'] + np.random.normal(0, 1, ds.n_cases)
# ols regression
m1 = ds_['x']
b1 = utsc.ols(m1)
res1 = utsc.residuals(m1)
t1 = utsc.ols_t(m1)
m2 = ds_.eval("x + x2")
b2 = utsc.ols(m2)
res2 = utsc.residuals(m2)
t2 = utsc.ols_t(m2)
# compare with R
for i in range(n_times):
ds_['y'] = Var(utsc.x[:, i])
ds_.to_r('ds')
# 1 predictor
r('lm1 <- lm(y ~ x, ds)')
beta = r('coef(lm1)')[1]
assert b1.x[0, i] == pytest.approx(beta)
res = r('residuals(lm1)')
assert_array_almost_equal(res1.x[:, i], res)
t = r('coef(summary(lm1))')[5]
assert t1.x[0, i] == pytest.approx(t)
# 2 predictors
r('lm2 <- lm(y ~ x + x2, ds)')
beta = r('coef(lm2)')[1:]
assert_array_almost_equal(b2.x[:, i], beta)
res = r('residuals(lm2)')
assert_array_almost_equal(res2.x[:, i], res)
lm2_coefs = r('coef(summary(lm2))')
t = [lm2_coefs[7], lm2_coefs[8]]
assert_array_almost_equal(t2.x[:, i], t)
# 3d
utsnd = ds['utsnd']
ds_['utsnd'] = utsnd
b1 = ds_.eval("utsnd.ols(x)")
res1 = ds_.eval("utsnd.residuals(x)")
t1 = ds_.eval("utsnd.ols_t(x)")
for i in range(len(b1.time)):
ds_['y'] = Var(utsnd.x[:, 1, i])
ds_.to_r('ds')
# 1 predictor
r('lm1 <- lm(y ~ x, ds)')
beta = r('coef(lm1)')[1]
assert b1.x[0, 1, i] == pytest.approx(beta)
res = r('residuals(lm1)')
assert_array_almost_equal(res1.x[:, 1, i], res)
t = r('coef(summary(lm1))')[5]
assert t1.x[0, 1, i] == pytest.approx(t)
def test_io_pickle():
"Test io by pickling"
ds = datasets.get_uts()
ds.info['info'] = "Some very useful information about the Dataset"
tempdir = tempfile.mkdtemp()
try:
dest = os.path.join(tempdir, 'test.pickled')
with open(dest, 'wb') as fid:
pickle.dump(ds, fid, protocol=pickle.HIGHEST_PROTOCOL)
with open(dest, 'rb') as fid:
ds2 = pickle.load(fid)
finally:
shutil.rmtree(tempdir)
assert_dataset_equal(ds, ds2)
def test_io_txt():
"Test Dataset io as text"
ds = datasets.get_uv()
# Var that has integer values as float
ds['intflt'] = ds.eval('intvar * 1.')
ds['intflt'].name = 'intflt'
# io test
tempdir = tempfile.mkdtemp()
try:
dest = os.path.join(tempdir, 'test.txt')
ds.save_txt(dest)
ds2 = load.tsv(dest)
finally:
shutil.rmtree(tempdir)
assert_dataset_equal(ds, ds2, decimal=6)
@skip_on_windows # uses R
def test_r():
"Test interaction with R through rpy2"
from rpy2.robjects import r
r("data(sleep)")
ds = Dataset.from_r("sleep")
assert ds.name == 'sleep'
extra = (0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0, 1.9, 0.8,
1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4)
assert_array_equal(ds.eval('extra'), extra)
assert_array_equal(ds.eval('ID'), list(map(str, range(1, 11))) * 2)
assert_array_equal(ds.eval('group'), ['1'] * 10 + ['2'] * 10)
# test putting
ds.to_r('sleep_copy')
ds_copy = Dataset.from_r('sleep_copy')
assert_dataset_equal(ds_copy, ds)
def test_sensor():
"Test Sensor dimension"
locs = np.array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]])
names = ['1', '2', '3']
sensor = Sensor(locs, names, 'test')
s1 = sensor[[0, 1]]
s2 = sensor[[1, 2]]
assert tuple(s1.names) == ('1', '2')
assert tuple(s2.names) == ('2', '3')
assert s1 == sensor[[0, 1]]
assert s1 != s2
assert s1.intersect(s2) == sensor[[1]]
assert sensor._dim_index(np.array([0, 1, 1], bool)) == ['2', '3']
def test_shuffle():
x = Factor('aabbaa')
for _ in range(3):
i = shuffled_index(6, x)
assert sorted(i[2:4]) == [2, 3]
assert sorted(i) == list(range(6))
@requires_mne_sample_data
def test_source_space():
"Test SourceSpace Dimension"
subject = 'fsaverage'
data_path = mne.datasets.sample.data_path()
mri_sdir = os.path.join(data_path, 'subjects')
mri_dir = os.path.join(mri_sdir, subject)
label_dir = os.path.join(mri_dir, 'label')
label_ba1 = mne.read_label(os.path.join(label_dir, 'lh.BA1.label'))
label_v1 = mne.read_label(os.path.join(label_dir, 'lh.V1.label'))
label_mt = mne.read_label(os.path.join(label_dir, 'lh.MT.label'))
label_ba1_v1 = label_ba1 + label_v1
label_v1_mt = label_v1 + label_mt
src = datasets._mne_source_space(subject, 'ico-5', mri_sdir)
source = SourceSpace.from_mne_source_spaces(src, 'ico-5', mri_sdir)
source_v1 = source[source._array_index(label_v1)]
assert source_v1 == SourceSpace.from_mne_source_spaces(src, 'ico-5', mri_sdir, label=label_v1)
source_ba1_v1 = source[source._array_index(label_ba1_v1)]
source_v1_mt = source[source._array_index(label_v1_mt)]
source_v1_intersection = source_ba1_v1.intersect(source_v1_mt)
assert_source_space_equal(source_v1, source_v1_intersection)
# persistence
assert pickle.loads(pickle.dumps(source, pickle.HIGHEST_PROTOCOL)) == source
assert pickle.loads(pickle.dumps(source_v1, pickle.HIGHEST_PROTOCOL)) == source_v1
# index from label
index = source.index_for_label(label_v1)
assert_array_equal(index.source[index.x].vertices[0],
np.intersect1d(source.lh_vertices, label_v1.vertices, 1))
# parcellation and cluster localization
parc = mne.read_labels_from_annot(subject, parc='aparc', subjects_dir=mri_sdir)
indexes = [source.index_for_label(label) for label in parc
if len(label) > 10]
x = np.vstack([index.x for index in indexes])
ds = source._cluster_properties(x)
for i in range(ds.n_cases):
assert ds[i, 'location'] == parc[i].name
# multiple labels
lingual_index = source._array_index('lingual-lh')
cuneus_index = source._array_index('cuneus-lh')
assert_array_equal(source._array_index(('cuneus-lh', 'lingual-lh')),
np.logical_or(cuneus_index, lingual_index))
lingual_source = source[lingual_index]
cuneus_source = source[cuneus_index]
with pytest.raises(IndexError):
_ = lingual_source._array_index(cuneus_source)
sub_source = source[source._array_index(('cuneus-lh', 'lingual-lh'))]
assert sub_source[sub_source._array_index('lingual-lh')] == lingual_source
assert sub_source[sub_source._array_index('cuneus-lh')] == cuneus_source
assert len(sub_source) == len(lingual_source) + len(cuneus_source)
# indexing
tgt = ['L%i' % i for i in chain(*sub_source.vertices)]
assert_array_equal([i for i in sub_source], tgt)
assert_array_equal([sub_source[i] for i in range(len(sub_source))], tgt)
# hemisphere indexing
lh = source._array_index('lh')
source_lh = source[lh]
assert source_lh._array_index('rh') == slice(0, 0)
assert source_lh._array_index('lh') == slice(len(source_lh))
def test_var():
"Test Var objects"
base = Factor('aabbcde')
# initialization
x = np.arange(4)
y = Var(x)
assert_array_equal(y, x)
y = Var(x, repeat=2)
assert_array_equal(y, x.repeat(2))
y = Var(x, repeat=x)
assert_array_equal(y, x.repeat(x))
y = Var.from_dict(base, {'a': 5, 'e': 8}, default=0)
assert_array_equal(y.x, [5, 5, 0, 0, 0, 0, 8])
with pytest.raises(TypeError):
Var(x, info=1)
# invalid dtypes
with pytest.raises(TypeError):
Var(np.array(['a', 'b', 'c']))
with pytest.raises(TypeError):
Var(np.array([None, 1, 2]))
# basic operations
info = {'a': 1}
v = Var([1., 2., 3., -4.], 'v', info=info)
c = 2
v2 = Var([2., 2., 3., 3.], 'w', info=info)
assert v.info == info
for op, iop, desc in OPERATORS:
target = op(v.x, c)
vtarget = op(v.x, v2.x)
# op
if desc == '+':
w = v.copy()
w.x = iop(w.x, c)
else:
w = op(v, c)
assert w.info == {'a': 1, 'longname': 'v %s %s' % (desc, c)}
assert_array_equal(w, target)
# with Var
w = op(v, v2)
assert w.info == {'a': 1, 'longname': 'v %s w' % desc}
assert_array_equal(w, vtarget)
# i-op
w = v.copy()
w = iop(w, c)
assert_array_equal(w, target)
# i-op with Var
w = v.copy()
w = iop(w, v2)
assert_array_equal(w, vtarget)
# methods
w = v.abs()
assert w.info == {'a': 1, 'longname': 'abs(v)'}
assert_array_equal(w, np.abs(v.x))
# log
x = w.log()
assert x.info == {'a': 1, 'longname': 'log(abs(v))'}
assert_array_equal(x, | np.log(w.x) | numpy.log |
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Nov 15 10:43:11 2018
@author: kyungdoehan
"""
#%% Required packages
import os
import numpy as np
#import multiprocessing as mp
from t2hlib import READDATA, LAKE, PACKAGES, PROPERTIES, GRID, PLOT, RCHRG
from os.path import expanduser
#%% Setting up directories
home = expanduser('~')
flopypth = os.path.join(home+'/anaconda3/lib/python3.6/site-packages')
#%% Initial variables
Ma = 12.5
nz = 40
nz_fixed = 10
inz = 30
dx = 1000
dy = 1000
dat = -10000
dat_var = -3000
idat = dat - dat_var
rech = 0.4 # background runoff
target = 75
Kconst = 100
perm_sed = Kconst * 2
hratio = 1.0
hydchr = Kconst / 10 # 100 m, thickness
iskip = 4
ivtk = 2
h_tol = 1E-4
Rflag = 1
CXrain = 0
CYrain = 0
Krain = 1
lakeK = 100
lakeb = 10.0
lamb = 1E-8
# sediment and rock density (arbitrary)
rho_sed = 1700
rho_rock1 = 3000
#%% Reading data file by specified Mas
class __main__:
def __init__(self, Ma, nz, nz_fixed, inz, dx, dy, dat, dat_var, idat\
, rech, perm_sed, target_row, Kconst, hratio, hydchr,\
iskip, ivtk, h_tol, Rflag, CXrain, CYrain, Krain,\
lakeK, lakeb, lamb, rho_rock1, rho_sed):
""" data checker """
datdef = READDATA.data(Ma)
self.topoT = datdef.topo
self.bdtopoT = datdef.bdtopo
self.sedT = datdef.sed
self.lakeT = datdef.lake
self.faultT = datdef.fault
print("console> data checker complete")
""" Reading topography """
topo = READDATA.topo_read(Ma)
self.x = topo.x
self.y = topo.y
self.z = topo.z
# Discretization variables (hydro. model specified)
grid = int(np.sqrt(len(self.x)))
self.nx = grid
self.ny = grid
griddata = GRID.XYZ(grid, self.x, self.y, self.z)
self.X = griddata.X
self.Y = griddata.Y
self.top = griddata.Z
self.top_l = self.top.copy()
self.top2 = self.top.copy()
self.top3 = self.top.copy()
""" Check optional files whether they are there or not there """
if self.sedT == True:
print("console> reading sed data")
sed = READDATA.sed_read(Ma)
self.sed_x = sed.x
self.sed_y = sed.y
self.sed_b = sed.z
elif self.sedT == False:
print("console> sed data is missing for this period")
self.sed_x = []
self.sed_y = []
self.sed_b = []
if self.faultT == True:
print("console> reading fault data")
fault = READDATA.fault_read(Ma)
self.fault_x = fault.x
self.fault_y = fault.y
self.fault_z = fault.z
fault_rearr = READDATA.fault_rearrange(Ma)
self.fault_x1 = fault_rearr.x
self.fault_y1 = fault_rearr.y
self.fault_z1 = fault_rearr.z
elif self.faultT == False:
print("console> fault data is missing for this period")
if self.faultT == True and self.sedT == True:
self.imodel = 1
elif self.faultT == True and self.sedT == False:
self.imodel = 2
elif self.faultT == False and self.sedT == True:
self.imodel = 3
elif self.faultT == False and self.sedT == False:
self.imodel = 4
# Exponentially increasing dz values
dzr = GRID.dzratio(inz)
self.dzratio = dzr.dzratio
bot = GRID.bot(inz, nz_fixed, grid, self.top, dat_var, idat, self.dzratio).bot
self.bot_l = bot.copy()
self.bot1 = bot.copy()
self.bot2 = bot.copy()
dzs = GRID.dzs(self.top, bot, nz, self.ny, self.nx).dzs
self.dzs_cumsum = np.cumsum(dzs, axis = 0)
node = GRID.node(bot, dzs, nz, self.ny, self.nx).node
self.nod = node.copy()
# * .9 # Initial value of water table according to the topo.
if self.lakeT == True:
lake = LAKE.lake(Ma, nz, self.ny, self.nx, grid, rech,\
dx, dy, lakeK, self.top_l, self.bot_l, lakeb)
self.lake_x = lake.x
self.lake_y = lake.y
self.lakarr = lake.lakarr
self.lake_level = lake.level
self.ilak = 1
self.nlakes = lake.nlakes
self.ghb = lake.ghb
#print(self.ghb)
elif self.lakeT == False:
self.ilak = 0
print("console> lake data is missing for this period \n")
conductivity = PROPERTIES.cond(nz, self.ny, self.nx, Kconst, hratio,\
node, self.top, lamb, rho_rock1)
self.h_ini = conductivity.h_ini
self.hk = conductivity.hk
self.dens = conductivity.dens
self.dens1 = self.dens.copy()
self.sediment = PROPERTIES.sed(self.dzs_cumsum, self.sed_b,\
self.sed_y, self.sed_x, grid,\
self.hk, nz, perm_sed, self.imodel,\
self.nod, self.top, self.ny, self.nx,\
Kconst, lamb, rho_rock1,\
self.dens1, rho_sed, self.bot1, dy, dx, dzs)
#print(self.hk[:, 85, 105])
if self.faultT == True:
fault = PROPERTIES.hfb(hydchr, grid, nz, self.ny, self.nx,\
self.fault_z,\
self.fault_y, self.fault_x,\
self.fault_x1, self.fault_y1,\
self.fault_z1, node, dat)
self.hfb_pair = fault.hfb_pair
self.hfb_info = fault.hfb_info
vfb = PROPERTIES.vfb(nz, self.ny, self.nx, self.fault_x1,\
self.fault_y1, self.fault_z1,\
node, grid, hydchr, self.dzratio)
self.vkcb_data = vfb.vkcb_data
self.vkcb_layers = vfb.layer
elif self.faultT == False:
self.hfb_pair = []
self.vkcb_data = []
self.hfb_info = []
switch = 2
laytyp = PROPERTIES.laytyp(switch, nz, inz).laytyp
self.xx = (0.5*(grid-1))*dx
self.xn = -(0.5*(grid-1))*dx
self.yx = (0.5*(grid-1))*dy
self.yn = -(0.5*(grid-1))*dy
self.topo = self.top.copy()
if self.lakeT == True:
prec = RCHRG.preci1(rech, Rflag, self.topo, self.nx, self.ny,\
self.lake_x, self.lake_y, CXrain, CYrain,\
self.lake_level, grid, self.xx,\
self.xn, self.yx, self.yn, dx, dy,\
Krain, self.ilak)
self.rchrg = prec.rchrg
self.prcp_t = prec.prcp_t
elif self.lakeT == False:
self.lake_x = []
self.lake_y = []
self.lake_level = []
prec = RCHRG.preci1(rech, Rflag, self.topo, self.nx, self.ny,\
self.lake_x, self.lake_y, CXrain, CYrain,\
self.lake_level, grid, self.xx,\
self.xn, self.yx, self.yn, dx, dy,\
Krain, self.ilak)
self.rchrg = prec.rchrg
self.prcp_t = prec.prcp_t
self.nlakes = 0
self.ghb = []
self.ibound = PROPERTIES.boundary(bot, nz, self.ny, self.nx, grid).ibound
self.conductance = PROPERTIES.cd(self.top3,\
self.bot2, dy, dx,\
self.ny, self.nx,\
self.hk, self.x, self.y,\
self.ibound, grid).conductance
self.condarr = PROPERTIES.cd(self.top3,\
self.bot2, dy, dx,\
self.ny, self.nx,\
self.hk, self.x, self.y,\
self.ibound, grid).condarr
# Model paths from external subroutine
self.path_info = PACKAGES.paths()
self.fdirmodel = self.path_info.fdirmodel
self.fnmmodel = self.path_info.fnmmodel
# Model packages from external subroutine
modelpackage = PACKAGES.packages(nz, self.ny, self.nx, dy, dx,\
self.top, bot, self.ibound,\
self.h_ini, self.hfb_pair,\
self.conductance, laytyp, self.hk,\
self.vkcb_data, self.rchrg, self.fdirmodel,\
self.fnmmodel, self.nlakes, self.ilak\
, self.ghb, self.imodel)
self.mf = modelpackage.mf
self.mfdis = modelpackage.mfdis
self.mfbas = modelpackage.mfbas
if self.faultT == True:
self.mfhfb = modelpackage.mfhfb
self.mfdrn = modelpackage.mfdrn
self.mfupw = modelpackage.mfupw
self.mfrch = modelpackage.mfrch
self.mfnwt = modelpackage.mfnwt
if self.lakeT == True:
self.mfghb = modelpackage.mfghb
self.output = modelpackage.output
def main(Ma, nz, nz_fixed, inz, dx, dy, dat, dat_var, idat\
, rech, perm_sed, target_row, Kconst, hratio, hydchr,\
iskip, ivtk, h_tol, Rflag, CXrain, CYrain, Krain,\
lakeK, lakeb, lamb, rho_rock1, rho_sed):
return __main__(Ma, nz, nz_fixed, inz, dx, dy, dat, dat_var, idat\
, rech, perm_sed, target_row, Kconst, hratio, hydchr,\
iskip, ivtk, h_tol, Rflag, CXrain, CYrain, Krain,\
lakeK, lakeb, lamb, rho_rock1, rho_sed)
#%% Model execution
model = main(Ma, nz, nz_fixed, inz, dx, dy, dat, dat_var, idat\
, rech, perm_sed, target, Kconst, hratio, hydchr,\
iskip, ivtk, h_tol, Rflag, CXrain, CYrain, Krain,\
lakeK, lakeb, lamb, rho_rock1, rho_sed)
#%% Model input checker
mf = model.mf
mf.dis.check()
mf.drn.check()
if model.lakeT == True:
mf.ghb.check()
mf.rch.check()
mf.upw.check()
mf.write_input()
mf.run_model()
#%%
print("model recharge average: ", np.mean(model.rchrg))
print("model topography average: ", np.mean(model.top))
print("model N/K: ", np.mean(model.rchrg)/np.mean(model.hk))
#%%
# Plot the grid, head contour, and discharge vector on a cross-section
target = 75
import matplotlib.pyplot as plt
import flopy
figheadxsect, axheadxsect = plt.subplots(figsize=(40,5))
mfxsect = PLOT.fmfxsect(mf, model.mfdis, target, axheadxsect).mfxsect
a = PLOT.head(mf, model.fdirmodel).a
headc = PLOT.headc(mfxsect, a)
if model.imodel > 4:
p = PLOT.pat(mfxsect, model.hk, Kconst, model.vkcb_data,\
model.hfb_info, nz, model.ny, model.nx, model.imodel)
#p1 = PLOT.wtable(mfxsect, model.top, a, nz, model.ny, model.nx)
#patch1 = p1.plarr
#patch1 = p.bcarray
# Plotting the grid mesh
#gdplot = mfxsect.plot_grid(color='r', linewidths=0.2)
# Plotting the BC (blue = const. head; noflow = black)
BCplot = mfxsect.plot_ibound(model.ibound, color_noflow = 'black',\
color_ch = 'blue', head = a)
wtable = PLOT.wt_f(nz, model.ny, model.nx, a, model.top)
wtf = wtable.wtf
wtplot = mfxsect.plot_surface(wtf[0,:,:])
topplot = mfxsect.plot_surface(model.top)
cellbudget = PLOT.cbc(model.fdirmodel, mf)
times = cellbudget.times
# Plot flux vector
qx = cellbudget.qx # right face
qy = cellbudget.qy # front face
qz = cellbudget.qz # lower face
# Average flows to cell centers
avgq = PLOT.qavg(qz, qy, qx, nz, model.ny, model.nx)
qx_avg = avgq.qx_avg
qy_avg = avgq.qy_avg
qz_avg = avgq.qz_avg
y, x, z = model.mfdis.get_node_coordinates()
#diagonal
# [0,0] [1, 1], [2,2] cross-section
# x = 1000*sqrt(2)/2 increment
# z =
zdiag = np.zeros((nz, model.nx), dtype=np.float32)
xdiag = np.zeros((nz, model.nx), dtype=np.float32)
hdiag = np.zeros((nz, model.nx), dtype=np.float32)
qxdiag = np.zeros((nz, model.nx), dtype=np.float32)
qydiag = | np.zeros((nz, model.nx), dtype=np.float32) | numpy.zeros |
''' CONFIDENTIAL
Copyright (c) 2021 <NAME>,
Department of Remote Sensing and Photogrammetry,
Finnish Geospatial Research Institute (FGI), National Land Survey of Finland (NLS)
PERMISSION IS HEREBY LIMITED TO FGI'S INTERNAL USE ONLY. THE CODE
MAY BE RE-LICENSED, SHARED, OR TAKEN INTO OTHER USE ONLY WITH
A WRITTEN CONSENT FROM THE HEAD OF THE DEPARTMENT.
The software is provided "as is", without warranty of any kind, express or
implied, including but not limited to the warranties of merchantability,
fitness for a particular purpose and noninfringement. In no event shall the
authors or copyright holders be liable for any claim, damages or other
liability, whether in an action of contract, tort or otherwise, arising from,
out of or in connection with the software or the use or other dealings in the
software.
'''
import numpy as np
import math
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.widgets import Slider, Button, RadioButtons, CheckButtons
try:
import pcl
from pyquaternion import Quaternion
except:
print('cannot import pcl -> change python version')
import matplotlib.cm as cmx
from scipy.spatial import distance_matrix
from scipy.optimize import leastsq
import matplotlib
import matplotlib.animation as animation
import open3d as o3d
import glob
import cv2
import cv2.aruco as aruco
import os
from mpl_toolkits.mplot3d.proj3d import proj_transform
from matplotlib.text import Annotation
import pickle
from matplotlib.lines import Line2D
import pandas as pd
import random
from scipy.spatial import ConvexHull
from math import sqrt
from math import atan2, cos, sin, pi
from collections import namedtuple
from matplotlib.patches import Circle
import mpl_toolkits.mplot3d.art3d as art3d
from pyquaternion import Quaternion
np.set_printoptions(suppress=True)
def eulerAnglesToRotationMatrix2(theta):
R_x = np.array([[1, 0, 0],
[0, math.cos(theta[0]), -math.sin(theta[0])],
[0, math.sin(theta[0]), math.cos(theta[0])]
])
R_y = np.array([[math.cos(theta[1]), 0, math.sin(theta[1])],
[0, 1, 0],
[-math.sin(theta[1]), 0, math.cos(theta[1])]
])
R_z = np.array([[math.cos(theta[2]), -math.sin(theta[2]), 0],
[math.sin(theta[2]), math.cos(theta[2]), 0],
[0, 0, 1]
])
R = np.dot(R_z, np.dot(R_y, R_x))
return R
Rot_matrix = eulerAnglesToRotationMatrix2([0, 0, np.deg2rad(-90)])
InitLidar = True
InitLidar = False
global globalTrigger
globalTrigger = True
stereoRectify = False# True
#stereoRectify = True
class Annotation3D(Annotation):
def __init__(self, s, xyz, *args, **kwargs):
Annotation.__init__(self, s, xy=(0, 0), *args, **kwargs)
self._verts3d = xyz
def draw(self, renderer):
xs3d, ys3d, zs3d = self._verts3d
xs, ys, zs = proj_transform(xs3d, ys3d, zs3d, renderer.M)
self.xy = (xs, ys)
Annotation.draw(self, renderer)
def save_obj(obj, name):
with open('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/' + name + '.pkl', 'wb') as f:
pickle.dump(obj, f, protocol=2)
print('{}.pkl Object saved'.format(name))
def load_obj(name):
with open('/home/eugeniu/Desktop/my_data/CameraCalibration/data/saved_files/' + name + '.pkl', 'rb') as f:
return pickle.load(f)
def showErros(_3DErros, IMageNames):
print('len(_3DErros)->{}'.format(np.shape(_3DErros)))
if len(_3DErros)>1:
_3DErros = np.array(_3DErros).squeeze()
# norm_total = np.array(_3DErros[:,0]).squeeze()
norm_axis = np.array(_3DErros).squeeze() * 1000
index, bar_width = np.arange(len(IMageNames)), 0.24
fig, ax = plt.subplots()
X = ax.bar(index, norm_axis[:, 0], bar_width, label="X")
Y = ax.bar(index + bar_width, norm_axis[:, 1], bar_width, label="Y")
Z = ax.bar(index + bar_width + bar_width, norm_axis[:, 2], bar_width, label="Z")
ax.set_xlabel('images')
ax.set_ylabel('errors in mm')
ax.set_title('3D error')
ax.set_xticks(index + bar_width / 3)
ax.set_xticklabels(IMageNames)
ax.legend()
plt.show()
def triangulation(kp1, kp2, T_1w, T_2w):
"""Triangulation to get 3D points
Args:
kp1 (Nx2): keypoint in view 1 (normalized)
kp2 (Nx2): keypoints in view 2 (normalized)
T_1w (4x4): pose of view 1 w.r.t i.e. T_1w (from w to 1)
T_2w (4x4): pose of view 2 w.r.t world, i.e. T_2w (from w to 2)
Returns:
X (3xN): 3D coordinates of the keypoints w.r.t world coordinate
X1 (3xN): 3D coordinates of the keypoints w.r.t view1 coordinate
X2 (3xN): 3D coordinates of the keypoints w.r.t view2 coordinate
"""
kp1_3D = np.ones((3, kp1.shape[0]))
kp2_3D = np.ones((3, kp2.shape[0]))
kp1_3D[0], kp1_3D[1] = kp1[:, 0].copy(), kp1[:, 1].copy()
kp2_3D[0], kp2_3D[1] = kp2[:, 0].copy(), kp2[:, 1].copy()
X = cv2.triangulatePoints(T_1w[:3], T_2w[:3], kp1_3D[:2], kp2_3D[:2])
X /= X[3]
X1 = T_1w[:3].dot(X)
X2 = T_2w[:3].dot(X)
return X[:3].T, X1.T, X2.T
def triangulate(R1,R2,t1,t2,K1,K2,D1,D2, pts1, pts2):
P1 = np.hstack([R1.T, -R1.T.dot(t1)])
P2 = np.hstack([R2.T, -R2.T.dot(t2)])
P1 = K1.dot(P1)
P2 = K2.dot(P2)
# Triangulate
_3d_points = []
for i,point in enumerate(pts1):
point3D = cv2.triangulatePoints(P1, P2, pts1[i], pts2[i]).T
point3D = point3D[:, :3] / point3D[:, 3:4]
_3d_points.append(point3D)
print('Triangulate _3d_points -> {}'.format(np.shape(_3d_points)))
return np.array(_3d_points).squeeze()
def mai(R1,R2,t1,t2,imagePoint1,imagePoint2, K2=None,K1=None, D2=None,D1=None):
# Set up two cameras near each other
if K1 is None:
K = np.array([
[718.856, 0., 607.1928],
[0., 718.856, 185.2157],
[0., 0., 1.],
])
R1 = np.array([
[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]
])
R2 = np.array([
[0.99999183, -0.00280829, -0.00290702],
[0.0028008, 0.99999276, -0.00257697],
[0.00291424, 0.00256881, 0.99999245]
])
t1 = np.array([[0.], [0.], [0.]])
t2 = np.array([[-0.02182627], [0.00733316], [0.99973488]])
# Corresponding image points
imagePoint1 = np.array([371.91915894, 221.53485107])
imagePoint2 = np.array([368.26071167, 224.86262512])
P1 = np.hstack([R1.T, -R1.T.dot(t1)])
P2 = np.hstack([R2.T, -R2.T.dot(t2)])
P1 = K1.dot(P1)
P2 = K2.dot(P2)
# Triangulate
point3D = cv2.triangulatePoints(P1, P2, imagePoint1, imagePoint2).T
point3D = point3D[:, :3] / point3D[:, 3:4]
print('Triangulate point3D -> {}'.format(point3D))
# Reproject back into the two cameras
rvec1, _ = cv2.Rodrigues(R1.T) # Change
rvec2, _ = cv2.Rodrigues(R2.T) # Change
p1, _ = cv2.projectPoints(point3D, rvec1, -t1, K1, distCoeffs=D1) # Change
p2, _ = cv2.projectPoints(point3D, rvec2, -t2, K2, distCoeffs=D2) # Change
# measure difference between original image point and reporjected image point
reprojection_error1 = np.linalg.norm(imagePoint1 - p1[0, :])
reprojection_error2 = np.linalg.norm(imagePoint2 - p2[0, :])
print('difference between original image point and reporjected image point')
print(reprojection_error1, reprojection_error2)
return p1,p2
class PointCloud_filter(object):
def __init__(self, file, img_file=None, img_file2=None, debug=True):
self.debug = debug
self.img_file = img_file
self.img_file2 = img_file2
self.name = os.path.basename(file).split('.')[0]
self.file = file
self.useVoxel, self.voxel_size = False, 0.15
self.lowerTemplate, self.showImage = False, True
self.showError = False
self.points_correspondences = None
self.OK = False
self.useInitialPointCloud = False #user all point to fit or only margins
self.chessBoard = False
self.applyICP_directly = False
self.s = .1 # scale
self.plotInit, self.axis_on, self.colour, self.Annotate = False, True, False, False
self.chess, self.corn, self.p1, self.p2, self.p3, self.ICP_finetune_plot = None, None, None, None, None, None
if self.showImage:
b = 1
self.pts = np.float32([[0, b, 0], [b, b, 0], [b, 0, 0], [-0.03, -0.03, 0]])
self.ImageNames = []
self._3DErros = []
self.criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 100, 0.0001)
self.axis = np.float32([[1, 0, 0], [0, 1, 0], [0, 0, -1]]).reshape(-1, 3)
self.objp = np.zeros((7 * 10, 3), np.float32)
self.objp[:, :2] = np.mgrid[0:10, 0:7].T.reshape(-1, 2) * self.s
self.fig = plt.figure(figsize=plt.figaspect(0.5))
self.fig.suptitle('Data collection', fontsize=16)
self.ax = self.fig.add_subplot(1, 2, 1, projection='3d')
#self.ax = self.fig.add_subplot(1, 2, 2, projection='3d')
self.readCameraIntrin()
self.QueryImg = cv2.imread(img_file)
self.ImageNames.append(os.path.basename(img_file))
if self.img_file2: # use stereo case
self.QueryImg2 = cv2.imread(img_file2)
if stereoRectify:
self.QueryImg = cv2.remap(src=self.QueryImg, map1=self.leftMapX, map2=self.leftMapY,
interpolation=cv2.INTER_LINEAR, dst=None, borderMode=cv2.BORDER_CONSTANT)
self.QueryImg2 = cv2.remap(src=self.QueryImg2, map1=self.rightMapX, map2=self.rightMapY,
interpolation=cv2.INTER_LINEAR, dst=None, borderMode=cv2.BORDER_CONSTANT)
gray_left = cv2.cvtColor(self.QueryImg, cv2.COLOR_BGR2GRAY)
ret_left, corners_left = cv2.findChessboardCorners(gray_left, (10, 7), None)
gray_right = cv2.cvtColor(self.QueryImg2, cv2.COLOR_BGR2GRAY)
ret_right, corners_right = cv2.findChessboardCorners(gray_right, (10, 7), None)
if ret_right and ret_left:
print('Found chessboard in both images')
self.chessBoard = True
corners2_left = cv2.cornerSubPix(gray_left, corners_left, (11, 11), (-1, -1), self.criteria)
self.corners2 = corners2_left
cv2.drawChessboardCorners(self.QueryImg, (10, 7), self.corners2, ret_left)
ret, self.rvecs, self.tvecs = cv2.solvePnP(self.objp, self.corners2, self.K_left, self.D_left)
imgpts, jac = cv2.projectPoints(self.axis, self.rvecs, self.tvecs, self.K_left, self.D_left)
self.QueryImg = self.draw(self.QueryImg, corners=corners2_left, imgpts=imgpts)
self.pixelsPoints = np.asarray(corners2_left).squeeze()
self.pixels_left = np.asarray(corners2_left).squeeze()
corners2_right = cv2.cornerSubPix(gray_right, corners_right, (11, 11), (-1, -1), self.criteria)
cv2.drawChessboardCorners(self.QueryImg2, (10, 7), corners2_right, ret_right)
self.pixels_right = np.asarray(corners2_right).squeeze()
self.T = np.array([-0.977, 0.004, 0.215])[:, np.newaxis]
angles = np.array([np.deg2rad(1.044), np.deg2rad(22.632), np.deg2rad(-.95)])
self.R = euler_matrix(angles)
#self.baseline =
self.T = np.array([-1.07, 0.004, 0.215])[:, np.newaxis]
self.baseline = abs(self.T[0])
print('baseline:{} m'.format(self.baseline))
self.focal_length, self.cx, self.cy = self.K[0, 0], self.K[0, 2], self.K[1, 2]
self.x_left, self.x_right = self.pixels_left, self.pixels_right
disparity = np.sum(np.sqrt((self.x_left - self.x_right) ** 2), axis=1)
# depth = baseline (meter) * focal length (pixel) / disparity-value (pixel) -> meter
self.depth = (self.baseline * self.focal_length / disparity)
print('depth:{}'.format(np.shape(self.depth)))
self.fxypxy = [self.K[0, 0], self.K[1, 1], self.cx, self.cy]
'''print('TRIANGULATE HERE==========================================')
P_1 = np.vstack((np.hstack((np.eye(3), np.zeros(3)[:, np.newaxis])), [0, 0, 0, 1])) # left camera
P_2 = np.vstack((np.hstack((self.R, self.T)), [0, 0, 0, 1])) # right camera
print('P1_{}, P_2{}, x_left:{}, x_right:{}'.format(np.shape(P_1), np.shape(P_2),
np.shape(self.x_left), np.shape(self.x_right)))
X_w, X1, X2 = triangulation(self.x_left,self.x_right,P_1,P_2)
print('X_w:{}, X1:{}, X2:{}, '.format(np.shape(X_w), np.shape(X1), np.shape(X2)))
print(X_w[0])
print(X1[0])
print(X2[0])'''
'''R1 = np.eye(3)
R2 = self.R
t1 = np.array([[0.], [0.], [0.]])
t2 = self.T
# Corresponding image points
imagePoint1 = np.array([371.91915894, 221.53485107])
imagePoint2 = np.array([368.26071167, 224.86262512])
imagePoint1 = self.x_left[0]
imagePoint2 = self.x_right[0]
print('imagePoint1:{}, imagePoint2:{}'.format(np.shape(imagePoint1), np.shape(imagePoint2)))
print('self.K_left ')
print(self.K_left)
print('self.K_right ')
print(self.K_right)
p1,p2 = test(R1,R2,t1,t2,imagePoint1,imagePoint2,K1=self.K_left,K2=self.K_right, D1=self.D_left,D2=self.D_right)
p1 = np.array(p1).squeeze().astype(int)
p2 = np.array(p2).squeeze().astype(int)
print('p1:{}, p2:{}'.format(np.shape(p1), np.shape(p2)))
#d2 = distance_matrix(X_w, X_w)
#print('d2:{}'.format(d2))
cv2.circle(self.QueryImg, (p1[0],p1[1]), 7, (255, 0, 0), 7)
cv2.circle(self.QueryImg2, (p2[0], p2[1]), 7, (255, 0, 0), 7)
cv2.imshow('QueryImg', cv2.resize(self.QueryImg,None,fx=.5,fy=.5))
cv2.imshow('QueryImg2', cv2.resize(self.QueryImg2, None, fx=.5, fy=.5))
cv2.waitKey(0)
cv2.destroyAllWindows()'''
else:
self.chessBoard = False
self.useVoxel = False
print('No chessboard ')
corners2_left, ids_left, rejectedImgPoints = aruco.detectMarkers(gray_left, self.ARUCO_DICT)
corners2_left, ids_left, _, _ = aruco.refineDetectedMarkers(image=gray_left,
board=self.calibation_board,
detectedCorners=corners2_left,
detectedIds=ids_left,
rejectedCorners=rejectedImgPoints,
cameraMatrix=self.K_left,
distCoeffs=self.D_left)
corners2_right, ids_right, rejectedImgPoints = aruco.detectMarkers(gray_right, self.ARUCO_DICT)
corners2_right, ids_right, _, _ = aruco.refineDetectedMarkers(image=gray_right,
board=self.calibation_board,
detectedCorners=corners2_right,
detectedIds=ids_right,
rejectedCorners=rejectedImgPoints,
cameraMatrix=self.K_right,
distCoeffs=self.D_right)
if np.all(ids_left != None) and np.all(ids_right != None):
print('found charuco board, in both images')
retval_left, self.rvecs, self.tvecs = aruco.estimatePoseBoard(corners2_left, ids_left,
self.calibation_board,
self.K_left, self.D_left, None,
None)
retval_right, self.rvecs_right, self.tvecs_right = aruco.estimatePoseBoard(corners2_right,
ids_right,
self.calibation_board,
self.K_right,
self.D_right, None,
None)
if retval_left and retval_right:
self.QueryImg = aruco.drawAxis(self.QueryImg, self.K_left, self.D_left, self.rvecs,
self.tvecs, 0.3)
self.QueryImg = aruco.drawDetectedMarkers(self.QueryImg, corners2_left, ids_left,
borderColor=(0, 0, 255))
b = 1
imgpts, _ = cv2.projectPoints(self.pts, self.rvecs_right, self.tvecs_right, self.K_right,
self.D_right)
self.corners2_right = np.append(imgpts, np.mean(imgpts, axis=0)).reshape(-1, 2)
self.dst, jacobian = cv2.Rodrigues(self.rvecs)
a, circle_tvec, b = .49, [], 1
circle_tvec.append(
np.asarray(self.tvecs).squeeze() + np.dot(self.dst, np.asarray([a, a, 0])))
circle_tvec = np.mean(circle_tvec, axis=0)
self.QueryImg = aruco.drawAxis(self.QueryImg, self.K_left, self.D_left, self.rvecs,
circle_tvec, 0.2)
imgpts, _ = cv2.projectPoints(self.pts, self.rvecs, self.tvecs, self.K_left, self.D_left)
self.corners2 = np.append(imgpts, np.mean(imgpts, axis=0)).reshape(-1, 2)
self.pt_dict = {}
for i in range(len(self.pts)):
self.pt_dict[tuple(self.pts[i])] = tuple(imgpts[i].ravel())
top_right = self.pt_dict[tuple(self.pts[0])]
bot_right = self.pt_dict[tuple(self.pts[1])]
bot_left = self.pt_dict[tuple(self.pts[2])]
top_left = self.pt_dict[tuple(self.pts[3])]
cv2.circle(self.QueryImg, top_right, 4, (0, 0, 255), 5)
cv2.circle(self.QueryImg, bot_right, 4, (0, 0, 255), 5)
cv2.circle(self.QueryImg, bot_left, 4, (0, 0, 255), 5)
cv2.circle(self.QueryImg, top_left, 4, (0, 0, 255), 5)
self.QueryImg = cv2.line(self.QueryImg, top_right, bot_right, (0, 255, 0), 4)
self.QueryImg = cv2.line(self.QueryImg, bot_right, bot_left, (0, 255, 0), 4)
self.QueryImg = cv2.line(self.QueryImg, bot_left, top_left, (0, 255, 0), 4)
self.QueryImg = cv2.line(self.QueryImg, top_left, top_right, (0, 255, 0), 4)
else:
print('Cannot estimate board position for both charuco')
self.pixelsPoints = self.corners2.squeeze()
self.pixels_left = self.pixelsPoints
self.pixels_right = self.corners2_right.squeeze()
self.T = np.array([-0.977, 0.004, 0.215])[:, np.newaxis]
angles = np.array([np.deg2rad(1.044), np.deg2rad(22.632), np.deg2rad(-.95)])
self.R = euler_matrix(angles)
# self.baseline =
self.T = np.array([-1.07, 0.004, 0.215])[:, np.newaxis]
self.baseline = abs(self.T[0])
print('baseline:{} m'.format(self.baseline))
self.focal_length, self.cx, self.cy = self.K[0, 0], self.K[0, 2], self.K[1, 2]
self.x_left, self.x_right = self.pixels_left, self.pixels_right
disparity = np.sum(np.sqrt((self.x_left - self.x_right) ** 2), axis=1)
print('disparity:{}'.format(np.shape(disparity)))
# depth = baseline (meter) * focal length (pixel) / disparity-value (pixel) -> meter
self.depth = (self.baseline * self.focal_length / disparity)
print('depth:{}'.format(np.shape(self.depth)))
self.fxypxy = [self.K[0, 0], self.K[1, 1], self.cx, self.cy]
else:
print('No any board found!!!')
else:
# Undistortion
h, w = self.QueryImg.shape[:2]
newcameramtx, roi = cv2.getOptimalNewCameraMatrix(self.K, self.D, (w, h), 1, (w, h))
dst = cv2.undistort(self.QueryImg, self.K, self.D, None, newcameramtx)
x, y, w, h = roi
self.QueryImg = dst[y:y + h, x:x + w]
gray = cv2.cvtColor(self.QueryImg, cv2.COLOR_BGR2GRAY)
ret, corners = cv2.findChessboardCorners(gray, (10, 7), None)
if ret: # found chessboard
print('Found chessboard')
self.chessBoard = True
self.corners2 = cv2.cornerSubPix(gray, corners, (11, 11), (-1, -1), self.criteria)
cv2.drawChessboardCorners(self.QueryImg, (10, 7), corners, ret)
ret, self.rvecs, self.tvecs = cv2.solvePnP(self.objp, self.corners2, self.K, self.D)
# ret, self.rvecs, self.tvecs, inliers = cv2.solvePnPRansac(self.objp, self.corners2, self.K, self.D)
self.imgpts, jac = cv2.projectPoints(self.axis, self.rvecs, self.tvecs, self.K, self.D)
self.QueryImg = self.draw(self.QueryImg, self.corners2, self.imgpts)
self.pixelsPoints = np.asarray(self.corners2).squeeze()
else: # check for charuco
self.chessBoard = False
self.useVoxel = False
corners, ids, rejectedImgPoints = aruco.detectMarkers(gray, self.ARUCO_DICT)
corners, ids, rejectedImgPoints, recoveredIds = aruco.refineDetectedMarkers(
image=gray, board=self.calibation_board, detectedCorners=corners, detectedIds=ids,
rejectedCorners=rejectedImgPoints, cameraMatrix=self.K, distCoeffs=self.D)
if np.all(ids != None):
print('found charuco board, ids:{}'.format(np.shape(ids)))
self.chessBoard = False
if len(ids) > 0:
retval, self.rvecs, self.tvecs = aruco.estimatePoseBoard(corners, ids,
self.calibation_board, self.K,
self.D, None, None)
if retval:
self.QueryImg = aruco.drawAxis(self.QueryImg, self.K, self.D, self.rvecs, self.tvecs,
0.3)
self.QueryImg = aruco.drawDetectedMarkers(self.QueryImg, corners, ids,
borderColor=(0, 0, 255))
self.dst, jacobian = cv2.Rodrigues(self.rvecs)
a, circle_tvec, b = .49, [], 1
circle_tvec.append(
np.asarray(self.tvecs).squeeze() + np.dot(self.dst, np.asarray([a, a, 0])))
circle_tvec = np.mean(circle_tvec, axis=0)
self.QueryImg = aruco.drawAxis(self.QueryImg, self.K, self.D, self.rvecs, circle_tvec,
0.2)
imgpts, _ = cv2.projectPoints(self.pts, self.rvecs, self.tvecs, self.K, self.D)
self.corners2 = np.append(imgpts, np.mean(imgpts, axis=0)).reshape(-1, 2)
self.pt_dict = {}
for i in range(len(self.pts)):
self.pt_dict[tuple(self.pts[i])] = tuple(imgpts[i].ravel())
top_right = self.pt_dict[tuple(self.pts[0])]
bot_right = self.pt_dict[tuple(self.pts[1])]
bot_left = self.pt_dict[tuple(self.pts[2])]
top_left = self.pt_dict[tuple(self.pts[3])]
cv2.circle(self.QueryImg, top_right, 4, (0, 0, 255), 5)
cv2.circle(self.QueryImg, bot_right, 4, (0, 0, 255), 5)
cv2.circle(self.QueryImg, bot_left, 4, (0, 0, 255), 5)
cv2.circle(self.QueryImg, top_left, 4, (0, 0, 255), 5)
self.QueryImg = cv2.line(self.QueryImg, top_right, bot_right, (0, 255, 0), 4)
self.QueryImg = cv2.line(self.QueryImg, bot_right, bot_left, (0, 255, 0), 4)
self.QueryImg = cv2.line(self.QueryImg, bot_left, top_left, (0, 255, 0), 4)
self.QueryImg = cv2.line(self.QueryImg, top_left, top_right, (0, 255, 0), 4)
else:
print('No board Found')
self.image_ax = self.fig.add_subplot(1, 2, 2)
#self.image_ax = self.fig.add_subplot(1, 2, 1)
self.image_ax.imshow(self.QueryImg)
self.image_ax.set_axis_off()
self.image_ax.set_xlabel('Y')
self.image_ax.set_ylabel('Z')
else:
self.fig = plt.figure()
self.ax = self.fig.add_subplot(111, projection="3d")
self.ax.set_xlabel('X', fontsize=10)
self.ax.set_ylabel('Y', fontsize=10)
self.ax.set_zlabel('Z', fontsize=10)
self.fig.tight_layout()
plt.subplots_adjust(left=.15, bottom=0.2)
#plt.subplots_adjust( bottom=0.2)
self.Rx, self.Ry, self.Rz = [np.deg2rad(-90), 0, np.deg2rad(-40)] if self.chessBoard else [0, 0, 0]
self.Tx, self.Ty, self.Tz = 0, 0, 0
self.board_origin = [self.Tx, self.Ty, self.Tz]
self.savePoints = Button(plt.axes([0.03, 0.45, 0.15, 0.04], ), 'filter points', color='white')
self.savePoints.on_clicked(self.getClosestPoints)
self.resetBtn = Button(plt.axes([0.03, 0.25, 0.15, 0.04], ), 'reset', color='white')
self.resetBtn.on_clicked(self.reset)
self.X_btn = Button(plt.axes([0.03, 0.9, 0.024, 0.04], ), 'X', color='red')
self.X_btn.on_clicked(self.Close)
self.OK_btn = Button(plt.axes([0.03, 0.83, 0.074, 0.04], ), 'OK', color='green')
self.OK_btn.on_clicked(self.OK_btnClick)
self.not_OK_btn = Button(plt.axes([0.105, 0.83, 0.074, 0.04], ), 'not OK', color='red')
self.not_OK_btn.on_clicked(self.not_OK_btnClick)
self.saveCorrespondences = Button(plt.axes([0.03, 0.76, 0.15, 0.04], ), 'Save points', color='white')
self.saveCorrespondences.on_clicked(self.savePointsCorrespondences)
self.fitChessboard = Button(plt.axes([0.03, 0.66, 0.15, 0.04], ), 'auto fit', color='white')
self.fitChessboard.on_clicked(self.auto_fitBoard)
# set up sliders
self.Rx_Slider = Slider(plt.axes([0.25, 0.15, 0.65, 0.03]), 'Rx', -180, 180.0, valinit=np.degrees(self.Rx))
self.Ry_Slider = Slider(plt.axes([0.25, 0.1, 0.65, 0.03]), 'Ry', -180, 180.0, valinit=np.degrees(self.Ry))
self.Rz_Slider = Slider(plt.axes([0.25, 0.05, 0.65, 0.03]), 'Rz', -180, 180.0, valinit=np.degrees(self.Rz))
self.Rx_Slider.on_changed(self.update_R)
self.Ry_Slider.on_changed(self.update_R)
self.Rz_Slider.on_changed(self.update_R)
self.check = CheckButtons(plt.axes([0.03, 0.3, 0.15, 0.12]), ('Axes', 'Black', 'Annotate'),
(self.axis_on, self.colour, self.Annotate))
self.check.on_clicked(self.func_CheckButtons)
# set up translation buttons
self.step = .1 # m
self.trigger = True
self.Tx_btn_plus = Button(plt.axes([0.05, 0.15, 0.04, 0.045]), '+Tx', color='white')
self.Tx_btn_plus.on_clicked(self.Tx_plus)
self.Tx_btn_minus = Button(plt.axes([0.12, 0.15, 0.04, 0.045]), '-Tx', color='white')
self.Tx_btn_minus.on_clicked(self.Tx_minus)
self.Ty_btn_plus = Button(plt.axes([0.05, 0.1, 0.04, 0.045]), '+Ty', color='white')
self.Ty_btn_plus.on_clicked(self.Ty_plus)
self.Ty_btn_minus = Button(plt.axes([0.12, 0.1, 0.04, 0.045]), '-Ty', color='white')
self.Ty_btn_minus.on_clicked(self.Ty_minus)
self.Tz_btn_plus = Button(plt.axes([0.05, 0.05, 0.04, 0.045]), '+Tz', color='white')
self.Tz_btn_plus.on_clicked(self.Tz_plus)
self.Tz_btn_minus = Button(plt.axes([0.12, 0.05, 0.04, 0.045]), '-Tz', color='white')
self.Tz_btn_minus.on_clicked(self.Tz_minus)
self.Tx_flip = Button(plt.axes([0.17, 0.15, 0.04, 0.045]), 'FlipX', color='white')
self.Tx_flip.on_clicked(self.flipX)
self.Ty_flip = Button(plt.axes([0.17, 0.1, 0.04, 0.045]), 'FlipY', color='white')
self.Ty_flip.on_clicked(self.flipY)
self.Tz_flip = Button(plt.axes([0.17, 0.05, 0.04, 0.045]), 'FlipZ', color='white')
self.Tz_flip.on_clicked(self.flipZ)
self.radio = RadioButtons(plt.axes([0.03, 0.5, 0.15, 0.15], ), ('Final', 'Init'), active=0)
self.radio.on_clicked(self.colorfunc)
self.tag = None
self.circle_center = None
self.errors = {0: "Improper input parameters were entered.",
1: "The solution converged.",
2: "The number of calls to function has "
"reached maxfev = %d.",
3: "xtol=%f is too small, no further improvement "
"in the approximate\n solution "
"is possible.",
4: "The iteration is not making good progress, as measured "
"by the \n improvement from the last five "
"Jacobian evaluations.",
5: "The iteration is not making good progress, "
"as measured by the \n improvement from the last "
"ten iterations.",
'unknown': "An error occurred."}
self.legend_elements = [
Line2D([0], [0], marker='o', color='w', label='Original pointcloud', markerfacecolor='g', markersize=4),
Line2D([0], [0], marker='o', color='w', label='Corners', markerfacecolor='k', markersize=4),
Line2D([0], [0], marker='o', color='w', label='Margins', markerfacecolor='r', markersize=4),
]
def setUp(self):
self.getPointCoud()
self.axisEqual3D(centers=np.mean(self.point_cloud, axis=0))
self.board()
self.ax.legend(handles=self.legend_elements, loc='best')
if self.showImage:
self.getDepth_Inside_Outside()
self.fitNewPlan()
def auto_fitBoard(self, args):
# estimate 3D-R and 3D-t between chess and PointCloud
# Inital guess of the transformation
x0 = np.array([np.degrees(self.Rx), np.degrees(self.Ry), np.degrees(self.Rz), self.Tx, self.Ty, self.Tz])
report = {"error": [], "template": []}
def f_min(x):
self.Rx, self.Ry, self.Rz = np.deg2rad(x[0]), np.deg2rad(x[1]), np.deg2rad(x[2])
self.Tx, self.Ty, self.Tz = x[3], x[4], x[5]
template = self.board(plot=False)
if self.useInitialPointCloud:
dist_mat = distance_matrix(template, self.point_cloud)
else:
dist_mat = distance_matrix(template, self.corners_)
err_func = dist_mat.sum(axis=1) # N x 1
# err_func = dist_mat.sum(axis=0) # N x 1
if self.debug:
print('errors = {}, dist_mat:{}, err_func:{}'.format(round(np.sum(err_func), 2), np.shape(dist_mat),
np.shape(err_func)))
report["error"].append(np.sum(err_func))
report["template"].append(template)
return err_func
maxIters = 700
sol, status = leastsq(f_min, x0, ftol=1.49012e-07, xtol=1.49012e-07, maxfev=maxIters)
print('sol:{}, status:{}'.format(sol, status))
print(self.errors[status])
if self.chess:
self.chess.remove()
if self.corn:
self.corn.remove()
if self.ICP_finetune_plot:
self.ICP_finetune_plot.remove()
self.lowerTemplate = False
self.board()
point_cloud = np.asarray(self.point_cloud, dtype=np.float32)
template = np.asarray(report["template"][0], dtype=np.float32) if self.applyICP_directly else np.asarray(
self.template_cloud, dtype=np.float32)
converged, self.transf, estimate, fitness = self.ICP_finetune(template, point_cloud)
# converged, self.transf, estimate, fitness = self.ICP_finetune(point_cloud,template)
self.estimate = np.array(estimate)
if self.chessBoard:
self.ICP_finetune_plot = self.ax.scatter(self.estimate[:, 0], self.estimate[:, 1], self.estimate[:, 2],
c='k', marker='o', alpha=0.8, s=4)
else:
idx = np.arange(start=0, stop=100, step=1)
idx = np.delete(idx, [44, 45, 54, 55])
cornersToPLot = self.estimate[idx, :]
self.ICP_finetune_plot = self.ax.scatter(cornersToPLot[:, 0], cornersToPLot[:, 1], cornersToPLot[:, 2],
c='k', marker='o', alpha=0.8, s=4)
self.trigger = False
# set values of sol to Sliders
self.Rx_Slider.set_val(np.rad2deg(self.Rx))
self.Ry_Slider.set_val(np.rad2deg(self.Ry))
self.Rz_Slider.set_val(np.rad2deg(self.Rz))
if self.chess:
self.chess.remove()
if self.corn:
self.corn.remove()
self.trigger = True
self.board()
self.AnnotateEdges()
self.fig.canvas.draw_idle()
if self.showError:
print('min error:{} , at index:{}'.format(np.min(report["error"]), np.argmin(report["error"])))
rep = plt.figure(figsize=(15, 8))
plt.xlim(0, len(report["error"]) + 1)
plt.xlabel('Iteration')
plt.ylabel('RMSE')
plt.yticks(color='w')
plt.plot(np.arange(len(report["error"])) + 1, report["error"])
print('Start animation gif')
def update_graph(num):
data = np.asarray(report["template"][num])
graph._offsets3d = (data[:, 0], data[:, 1], data[:, 2])
title.set_text('Iteration {}'.format(num))
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
title = ax.set_title('3D Test')
data = report["template"][0]
graph = ax.scatter(data[:, 0], data[:, 1], data[:, 2])
ax.scatter(self.point_cloud[:, 0], self.point_cloud[:, 1], self.point_cloud[:, 2])
ani = animation.FuncAnimation(fig, update_graph, 101, interval=2, blit=False, repeat=False)
ani.save('myAnimation.gif', writer='imagemagick', fps=30)
print('Animation done')
plt.show()
def flipX(self, event):
self.Rx_Slider.set_val(np.rad2deg(self.Rx + np.pi))
self.update_R(0)
def flipY(self, event):
self.Ry_Slider.set_val(np.rad2deg(self.Ry + np.pi))
self.update_R(0)
def flipZ(self, event):
self.Rz_Slider.set_val(np.rad2deg(self.Rz + np.pi))
self.update_R(0)
def update_R(self, val):
if self.trigger:
if self.chess:
self.chess.remove()
if self.corn:
self.corn.remove()
self.Rx = np.deg2rad(self.Rx_Slider.val)
self.Ry = np.deg2rad(self.Ry_Slider.val)
self.Rz = np.deg2rad(self.Rz_Slider.val)
self.board()
self.fig.canvas.draw_idle()
def board(self, plot=True, given_origin=None, angle=None):
self.board_origin = [self.Tx, self.Ty, self.Tz] if given_origin is None else given_origin
if self.chessBoard:
self.nCols, self.nRows, org = 7 + 2, 10 + 2, np.asarray(self.board_origin)
#org[0] -= self.nCols / 2
#org[1] -= self.nRows / 2
org[0] -= 4
org[1] -= 6
#org = np.zeros(3)
if self.lowerTemplate:
nrCols, nrRows = 2, 3
else:
nrCols, nrRows = self.nCols, self.nRows
#nrCols, nrRows = self.nCols+1, self.nRows+1 #remove later
print('org:{}, self.nCols - >{}, nrCols:{}'.format(org,self.nCols,nrCols))
X, Y = np.linspace(org[0], org[0] + self.nCols, num=nrCols), np.linspace(org[1], org[1] + self.nRows,num=nrRows)
X, Y = np.linspace(org[0], org[0] + self.nCols-1, num=nrCols), np.linspace(org[1], org[1] + self.nRows-1,
num=nrRows)
print('X:{}'.format(X))
X, Y = np.meshgrid(X, Y)
Z = np.full(np.shape(X), org[2])
colors, colortuple = np.empty(X.shape, dtype=str), ('k', 'w')
for y in range(nrCols):
for x in range(nrRows):
colors[x, y] = colortuple[(x + y) % len(colortuple)]
colors[0, 0] = 'r'
alpha = 0.65
else:
self.nCols, self.nRows, org = 10, 10, np.asarray(self.board_origin)
org[0] -= self.nCols / 2
org[1] -= self.nRows / 2
# nrCols, nrRows = 4,4z
nrCols, nrRows = self.nCols, self.nRows
# nrCols, nrRows = 20, 20
X, Y = np.linspace(org[0], org[0] + self.nCols, num=nrCols), np.linspace(org[1], org[1] + self.nRows,
num=nrRows)
X, Y = np.meshgrid(X, Y)
Z = np.full(np.shape(X), org[2])
alpha = 0.25
angles = np.array([self.Rx, self.Ry, self.Rz]) if angle is None else np.array(angle)
Rot_matrix = self.eulerAnglesToRotationMatrix(angles)
X, Y, Z = X * self.s, Y * self.s, Z * self.s
corners = np.transpose(np.array([X, Y, Z]), (1, 2, 0))
init = corners.reshape(-1, 3)
print('corners-----------------------------------------------------')
#print(init)
print('corners -> {}'.format(np.shape(init)))
dist_Lidar = distance_matrix(init, init)
print('dist_Lidar corners---------------------------------------------------------')
print(dist_Lidar[0, :11])
translation = np.mean(init, axis=0) # get the mean point
corners = np.subtract(corners, translation) # substract it from all the other points
X, Y, Z = np.transpose(np.add(np.dot(corners, Rot_matrix), translation), (2, 0, 1))
# corners = np.transpose(np.array([X, Y, Z]), (1, 2, 0)).reshape(-1, 3)
corners = np.transpose(np.array([X, Y, Z]), (2, 1, 0)).reshape(-1, 3)
if plot:
if self.chessBoard:
self.chess = self.ax.plot_surface(X, Y, Z, facecolors=colors, linewidth=0.2, cmap='gray', alpha=alpha)
else:
self.chess = self.ax.plot_surface(X, Y, Z, linewidth=0.2, cmap='gray', alpha=alpha)
idx = np.arange(start=0, stop=100, step=1)
idx = np.delete(idx, [44, 45, 54, 55])
cornersToPLot = corners[idx, :]
self.corn = self.ax.scatter(cornersToPLot[:, 0], cornersToPLot[:, 1], cornersToPLot[:, 2], c='tab:blue',
marker='o', s=5)
self.template_cloud = corners
return np.array(corners)
def getPointCoud(self, colorsMap='jet', skip=1, useRing = True):
# X, Y, Z, intensity, ring
if useRing:
originalCloud = np.array(np.load(self.file, mmap_mode='r'))[:,:5]
if InitLidar:
xyz = originalCloud[:, 0:3]
new_xyz = np.dot(xyz, Rot_matrix)
originalCloud[:, 0:3] = new_xyz
#mean_x = np.mean(originalCloud[:, 0])
#originalCloud[:, 0] = mean_x
df = pd.DataFrame(data=originalCloud, columns=["X", "Y", "Z","intens","ring"])
gp = df.groupby('ring')
keys = gp.groups.keys()
#groups = gp.groups
coolPoints, circlePoints = [],[]
for i in keys:
line = np.array(gp.get_group(i), dtype=np.float)
first,last = np.array(line[0], dtype=np.float)[:3],np.array(line[-1], dtype=np.float)[:3]
coolPoints.append(first)
coolPoints.append(last)
if self.chessBoard == False:
if len(line) > 50:
l = line[:,:3]
for i in range(2,len(l)-2,1):
d = np.linalg.norm(l[i]-l[i+1])
if d > 0.08: #half of the circle
circlePoints.append(l[i])
circlePoints.append(l[i+1])
self.coolPoints = np.array(coolPoints).squeeze()
self.ax.scatter(*self.coolPoints.T, color='r', marker='o', alpha=1, s=2)
print('coolPoints:{}, circlePoints:{}'.format(np.shape(self.coolPoints), np.shape(circlePoints)))
circlePoints = np.array(circlePoints)
if len(circlePoints)>0:
self.ax.scatter(*circlePoints.T, color='r', marker='o', alpha=1, s=5)
self.fitCircle(circlePoints)
#self.point_cloud = np.array(self.coolPoints, dtype=np.float32)
self.point_cloud = np.array(np.load(self.file, mmap_mode='r')[::skip, :3], dtype=np.float32)
if InitLidar:
xyz = self.point_cloud[:, 0:3]
new_xyz = np.dot(xyz, Rot_matrix)
self.point_cloud[:, 0:3] = new_xyz
# center the point_cloud
#mean_x = np.mean(self.point_cloud[:, 0])
#self.point_cloud[:, 0] = mean_x
self.point_cloud_mean = np.mean(self.point_cloud, axis=0)
self.Tx, self.Ty, self.Tz = self.point_cloud_mean
# self.point_cloud = self.point_cloud - self.point_cloud_mean
self.point_cloud_colors = np.array(np.load(self.file, mmap_mode='r'))[::skip, 3]
if self.plotInit:
cm = plt.get_cmap(colorsMap)
cNorm = matplotlib.colors.Normalize(vmin=min(self.point_cloud_colors), vmax=max(self.point_cloud_colors))
scalarMap = cmx.ScalarMappable(norm=cNorm, cmap=cm)
self.p1 = self.ax.scatter(self.point_cloud[:, 0], self.point_cloud[:, 1], self.point_cloud[:, 2],
color=scalarMap.to_rgba(self.point_cloud_colors), s=0.2)
else:
self.p = pcl.PointCloud(self.point_cloud)
inlier, outliner, coefficients = self.do_ransac_plane_segmentation(self.p, pcl.SACMODEL_PLANE,
pcl.SAC_RANSAC, 0.01)
#self.planeEquation(coef=np.array(coefficients).squeeze())
self.point_cloud_init = self.point_cloud.copy()
if self.useVoxel:
pcd = o3d.geometry.PointCloud()
pcd.points = o3d.utility.Vector3dVector(self.point_cloud)
self.point_cloud = np.array(pcd.voxel_down_sample(voxel_size=self.voxel_size).points)
# self.p1 = self.ax.scatter(outliner[:, 0], outliner[:, 1], outliner[:, 2], c='y', s=0.2)
self.p2 = self.ax.scatter(inlier[:, 0], inlier[:, 1], inlier[:, 2], c='g', s=0.2)
w, v = self.PCA(inlier)
point = np.mean(inlier, axis=0)
if self.chessBoard == False and self.circle_center:
#point[1:] = self.circle_center
point[[0,2]]= self.circle_center
w *= 2
if self.chessBoard==False and self.circle_center:
p = Circle(self.circle_center, self.circle_radius, alpha = .3, color='tab:blue')
self.ax.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=point[1], zdir="y")
self.p3 = self.ax.quiver([point[0]], [point[1]], [point[2]], [v[0, :] * np.sqrt(w[0])],
[v[1, :] * np.sqrt(w[0])],
[v[2, :] * np.sqrt(w[0])], linewidths=(1.8,))
def axisEqual3D(self, centers=None):
extents = np.array([getattr(self.ax, 'get_{}lim'.format(dim))() for dim in 'xyz'])
sz = extents[:, 1] - extents[:, 0]
# centers = np.mean(extents, axis=1) if centers is None
maxsize = max(abs(sz))
r = maxsize / 2
for ctr, dim in zip(centers, 'xyz'):
getattr(self.ax, 'set_{}lim'.format(dim))(ctr - r, ctr + r)
def planeEquation(self, coef):
a, b, c, d = coef
mean = np.mean(self.point_cloud, axis=0)
normal = [a, b, c]
d2 = -mean.dot(normal)
# print('d2:{}'.format(d2))
# print('mean:{}'.format(mean))
# print('The equation is {0}x + {1}y + {2}z = {3}'.format(a, b, c, d))
# plot the normal vector
startX, startY, startZ = mean[0], mean[1], mean[2]
startZ = (-normal[0] * startX - normal[1] * startY - d) * 1. / normal[2]
self.ax.quiver([startX], [startY], [startZ], [normal[0]], [normal[1]], [normal[2]], linewidths=(3,),edgecolor="red")
def PCA(self, data, correlation=False, sort=True):
# data = nx3
mean = np.mean(data, axis=0)
data_adjust = data - mean
#: the data is transposed due to np.cov/corrcoef syntax
if correlation:
matrix = np.corrcoef(data_adjust.T)
else:
matrix = np.cov(data_adjust.T)
eigenvalues, eigenvectors = np.linalg.eig(matrix)
if sort:
#: sort eigenvalues and eigenvectors
sort = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[sort]
eigenvectors = eigenvectors[:, sort]
return eigenvalues, eigenvectors
def eulerAnglesToRotationMatrix(self, theta):
R_x = np.array([[1, 0, 0],
[0, math.cos(theta[0]), -math.sin(theta[0])],
[0, math.sin(theta[0]), math.cos(theta[0])]
])
R_y = np.array([[math.cos(theta[1]), 0, math.sin(theta[1])],
[0, 1, 0],
[-math.sin(theta[1]), 0, math.cos(theta[1])]
])
R_z = np.array([[math.cos(theta[2]), -math.sin(theta[2]), 0],
[math.sin(theta[2]), math.cos(theta[2]), 0],
[0, 0, 1]
])
R = np.dot(R_z, np.dot(R_y, R_x))
return R
def do_ransac_plane_segmentation(self, pcl_data, pcl_sac_model_plane, pcl_sac_ransac, max_distance):
"""
Create the segmentation object
:param pcl_data: point could data subscriber
:param pcl_sac_model_plane: use to determine plane models
:param pcl_sac_ransac: RANdom SAmple Consensus
:param max_distance: Max distance for apoint to be considered fitting the model
:return: segmentation object
"""
seg = pcl_data.make_segmenter()
seg.set_model_type(pcl_sac_model_plane)
seg.set_method_type(pcl_sac_ransac)
seg.set_distance_threshold(max_distance)
inliers, coefficients = seg.segment()
inlier_object = pcl_data.extract(inliers, negative=False)
outlier_object = pcl_data.extract(inliers, negative=True)
if len(inliers) <= 1:
outlier_object = [0, 0, 0]
inlier_object, outlier_object = np.array(inlier_object), np.array(outlier_object)
return inlier_object, outlier_object, coefficients
def func_CheckButtons(self, label):
if label == 'Axes':
if self.axis_on:
self.ax.set_axis_off()
self.axis_on = False
else:
self.ax.set_axis_on()
self.axis_on = True
elif label == 'Black':
if self.colour:
self.colour = False
self.ax.set_facecolor((1, 1, 1))
else:
self.colour = True
self.ax.set_facecolor((0, 0, 0))
elif label == 'Annotate':
self.Annotate = not self.Annotate
self.AnnotateEdges()
self.fig.canvas.draw_idle()
def ICP_finetune(self, points_in, points_out):
cloud_in = pcl.PointCloud()
cloud_out = pcl.PointCloud()
cloud_in.from_array(points_in)
cloud_out.from_array(points_out)
# icp = cloud_in.make_IterativeClosestPoint()
icp = cloud_out.make_IterativeClosestPoint()
converged, transf, estimate, fitness = icp.icp(cloud_in, cloud_out)
print('fitness:{}, converged:{}, transf:{}, estimate:{}'.format(fitness, converged, np.shape(transf),
np.shape(estimate)))
return converged, transf, estimate, fitness
def colorfunc(self, label):
if label == 'Init':
self.plotInit = True
else:
self.plotInit = False
self.reset(0)
def OK_btnClick(self, args):
self.OK = True
plt.close()
def not_OK_btnClick(self, args):
self.OK = False
plt.close()
def Close(self, args):
global globalTrigger
globalTrigger = False
plt.close()
def reset(self, args):
self.ax.cla()
self.getPointCoud()
self.axisEqual3D(centers=np.mean(self.point_cloud, axis=0))
self.Rx, self.Ry, self.Rz = 0, 0, 0
self.Tx, self.Ty, self.Tz = 0, 0, 0
self.board_origin = [self.Tx, self.Ty, self.Tz]
self.board()
self.fig.canvas.draw_idle()
def getClosestPoints(self, arg):
dist_mat = distance_matrix(self.template_cloud, self.point_cloud_init)
self.neighbours = np.argsort(dist_mat, axis=1)[:, 0]
self.finaPoints = np.asarray(self.point_cloud_init[self.neighbours, :]).squeeze()
if self.chess:
self.chess.remove()
if self.corn:
self.corn.remove()
if self.p3:
self.p3.remove()
if self.p2:
self.p2.remove()
if self.p1:
self.p1.remove()
self.scatter_finalPoints = self.ax.scatter(self.finaPoints[:, 0], self.finaPoints[:, 1], self.finaPoints[:, 2],
c='k', marker='x', s=1)
self.corn = self.ax.scatter(self.template_cloud[:, 0], self.template_cloud[:, 1], self.template_cloud[:, 2],
c='blue', marker='o', s=5)
self.fig.canvas.draw_idle()
def Tz_plus(self, event):
self.Tz += self.step
self.update_R(0)
def Tz_minus(self, event):
self.Tz -= self.step
self.update_R(0)
def Ty_plus(self, event):
self.Ty += self.step
self.update_R(0)
def Ty_minus(self, event):
self.Ty -= self.step
self.update_R(0)
def Tx_plus(self, event):
self.Tx += self.step
self.update_R(0)
def Tx_minus(self, event):
self.Tx -= self.step
self.update_R(0)
def readCameraIntrin(self):
name = 'inside'
name = 'outside'
self.camera_model = load_obj('{}_combined_camera_model'.format(name))
self.camera_model_rectify = load_obj('{}_combined_camera_model_rectify'.format(name))
self.K_left = self.camera_model['K_left']
self.K_right = self.camera_model['K_right']
self.D_left = self.camera_model['D_left']
self.D_right = self.camera_model['D_right']
# self.K_left = self.camera_model['K_right']
# self.K_right = self.camera_model['K_left']
# self.D_left = self.camera_model['D_right']
# self.D_right = self.camera_model['D_left']
# print('K_left')
# print(self.K_left)
# print('K_right')
# print(self.K_right)
self.R = self.camera_model['R']
self.T = self.camera_model['T']
self.T = np.array([-0.977, 0.004, 0.215])[:, np.newaxis]
angles = np.array([np.deg2rad(1.044), np.deg2rad(22.632), np.deg2rad(-.95)])
self.R = euler_matrix(angles)
#self.T = np.array([-0.98, 0., 0.12])[:, np.newaxis]
#self.T = np.array([-.75, 0., 0.])[:, np.newaxis]
#print('self T after {}'.format(np.shape(self.T)))
#angles = np.array([np.deg2rad(0.68), np.deg2rad(22.66), np.deg2rad(-1.05)])
#self.R = euler_matrix(angles)
#Q = self.camera_model_rectify['Q']
#roi_left, roi_right = self.camera_model_rectify['roi_left'], self.camera_model_rectify['roi_right']
self.leftMapX, self.leftMapY = self.camera_model_rectify['leftMapX'], self.camera_model_rectify['leftMapY']
self.rightMapX, self.rightMapY = self.camera_model_rectify['rightMapX'], self.camera_model_rectify['rightMapY']
img_shape = (1936, 1216)
print('img_shape:{}'.format(img_shape))
R1, R2, P1, P2, Q, roi_left, roi_right = cv2.stereoRectify(self.K_left, self.D_left, self.K_right, self.D_right,
imageSize=img_shape,
R=self.camera_model['R'], T=self.camera_model['T'],
flags=cv2.CALIB_ZERO_DISPARITY,
alpha=-1
#alpha=0
)
self.leftMapX, self.leftMapY = cv2.initUndistortRectifyMap(
self.K_left, self.D_left, R1,
P1, img_shape, cv2.CV_32FC1)
self.rightMapX, self.rightMapY = cv2.initUndistortRectifyMap(
self.K_right, self.D_right, R2,
P2, img_shape, cv2.CV_32FC1)
self.K = self.K_right
self.D = self.D_right
try:
N = 5
aruco_dict = aruco.custom_dictionary(0, N, 1)
aruco_dict.bytesList = np.empty(shape=(4, N - 1, N - 1), dtype=np.uint8)
A = np.array([[0, 0, 1, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 0]],
dtype=np.uint8)
aruco_dict.bytesList[0] = aruco.Dictionary_getByteListFromBits(A)
R = np.array([[1, 1, 1, 1, 0], [1, 0, 0, 1, 0], [1, 1, 1, 0, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1]],
dtype=np.uint8)
aruco_dict.bytesList[1] = aruco.Dictionary_getByteListFromBits(R)
V = np.array([[1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [0, 1, 0, 1, 0], [0, 0, 1, 0, 0]],
dtype=np.uint8)
O = np.array([[0, 1, 1, 1, 0], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [0, 1, 1, 1, 0]],
dtype=np.uint8)
aruco_dict.bytesList[2] = aruco.Dictionary_getByteListFromBits(O)
aruco_dict.bytesList[3] = aruco.Dictionary_getByteListFromBits(V)
self.ARUCO_DICT = aruco_dict
self.calibation_board = aruco.GridBoard_create(
markersX=2, markersY=2,
markerLength=0.126, markerSeparation=0.74,
dictionary=self.ARUCO_DICT)
except:
print('Install Aruco')
def draw(self, img, corners, imgpts):
corner = tuple(corners[0].ravel())
cv2.line(img, corner, tuple(imgpts[0].ravel()), (255, 0, 0), 5)
cv2.line(img, corner, tuple(imgpts[1].ravel()), (0, 255, 0), 5)
cv2.line(img, corner, tuple(imgpts[2].ravel()), (0, 0, 255), 5)
return img
def annotate3D(self, ax, s, *args, **kwargs):
self.tag = Annotation3D(s, *args, **kwargs)
ax.add_artist(self.tag)
def AnnotateEdges(self, giveAX=None, givenPoints=None):
if self.Annotate:
# add vertices annotation.
if giveAX is None:
if self.lowerTemplate or self.chessBoard == False:
if self.chessBoard == False:
pts = np.asarray(self.template_cloud.copy()).reshape(self.nCols, self.nRows, 3)
idx = np.array([44, 45, 54, 55])
center = np.mean(self.template_cloud[idx], axis=0)
self.templatePoints = [pts[0, -1, :], pts[-1, -1, :], pts[-1, 0, :], pts[0, 0, :], center]
self.templatePoints = np.array(self.templatePoints).reshape(-1, 3)
cornersToPLot = self.estimate[idx, :]
for j, xyz_ in enumerate(self.templatePoints):
self.annotate3D(self.ax, s=str(j), xyz=xyz_, fontsize=12, xytext=(-1, 1),
textcoords='offset points', ha='right', va='bottom')
else:
for j, xyz_ in enumerate(self.template_cloud):
self.annotate3D(self.ax, s=str(j), xyz=xyz_, fontsize=8, xytext=(-1, 1),
textcoords='offset points', ha='right', va='bottom')
else:
try:
templatePoints = np.asarray(self.template_cloud.copy()).reshape(self.nCols, self.nRows, 3)[
1:self.nCols - 1, 1:self.nRows - 1, :]
except:
templatePoints = np.asarray(self.template_cloud.copy()).reshape(self.nCols+1, self.nRows+1, 3)[
1:self.nCols - 1, 1:self.nRows - 1, :]
# templatePoints = np.asarray(self.template_cloud.copy()).reshape(self.nRows,self.nCols, 3)[1:self.nRows-1,1:self.nCols-1,:]
self.templatePoints = np.array(templatePoints).reshape(-1, 3)
for j, xyz_ in enumerate(self.templatePoints):
self.annotate3D(self.ax, s=str(j), xyz=xyz_, fontsize=8, xytext=(-3, 3),
textcoords='offset points', ha='right', va='bottom')
else:
for j, xyz_ in enumerate(givenPoints):
self.annotate3D(giveAX, s=str(j), xyz=xyz_, fontsize=10, xytext=(-3, 3),
textcoords='offset points', ha='right', va='bottom')
if self.showImage:
# annotate image
points = np.asarray(self.corners2).squeeze()
font, lineType = cv2.FONT_HERSHEY_SIMPLEX, 2 if self.chessBoard else 10
for i, point in enumerate(points):
point = tuple(point.ravel())
cv2.putText(self.QueryImg, '{}'.format(i), point, font, 1 if self.chessBoard else 3, (0, 0, 0)
if self.chessBoard else (255, 0, 0), lineType)
self.image_ax.imshow(self.QueryImg)
def getCamera_XYZ_Stereo(self):
#cam_rot, jac = cv2.Rodrigues(self.rvecs)
#mR = np.matrix(cam_rot)
#mT = np.matrix(self.tvecs)
#cam_trans = -mR * mT
_3DPoints = []
for i, pixel in enumerate(self.x_left):
u, v = pixel.ravel()
u, v = int(u), int(v)
distance = self.depth[i]
pt = np.array([u, v, distance])
pt[0] = pt[2] * (pt[0] - self.fxypxy[2]) / self.fxypxy[0]
pt[1] = pt[2] * (pt[1] - self.fxypxy[3]) / self.fxypxy[1]
# pt = pt.dot(cam_rot.T) + self.tvecs
_3DPoints.append(pt)
print('_3DPoints {}'.format(np.shape(_3DPoints)))
print('tvec : {}'.format(np.asarray(self.tvecs).squeeze()))
print('Camera_XYZ_Stereo mean {}'.format(np.mean(_3DPoints, axis=0)))
_3DPoints = np.array(_3DPoints).squeeze()
print('from disparity getCamera_XYZ_Stereo ')
d = distance_matrix(_3DPoints,_3DPoints)
print(d)
return _3DPoints
def getCamera_XYZ(self):
R_mtx, jac = cv2.Rodrigues(self.rvecs)
inv_R_mtx = np.linalg.inv(R_mtx)
inv_K = np.linalg.inv(self.K)
def compute_XYZ(u, v): # from 2D pixels to 3D world
uv_ = np.array([[u, v, 1]], dtype=np.float32).T
suv_ = uv_
xyz_ = inv_K.dot(suv_) - self.tvecs
XYZ = inv_R_mtx.dot(xyz_)
pred = XYZ.T[0]
return pred
Camera_XYZ = []
for i, point in enumerate(self.pixelsPoints):
xyz = compute_XYZ(u=point[0], v=point[1])
# print 'xyz:{}'.format(xyz)
Camera_XYZ.append(xyz)
Camera_XYZ = np.array(Camera_XYZ)
print('init tvec : {}'.format(np.asarray(self.tvecs).squeeze()))
print('Camera_XYZ mean {}'.format(np.mean(Camera_XYZ, axis=0)))
if self.img_file2 is None:
for i, point in enumerate(Camera_XYZ):
imgpts, jac = cv2.projectPoints(point, self.rvecs, self.tvecs, self.K, self.D)
imgpts = np.asarray(imgpts).squeeze()
cv2.circle(self.QueryImg, (int(imgpts[0]), int(imgpts[1])), 7, (255, 0, 0), 7)
self.image_ax.imshow(self.QueryImg)
return Camera_XYZ
def getImagePixels(self):
img = cv2.imread(self.img_file) #left image
img2 = cv2.imread(self.img_file2) # left image
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
gray2 = cv2.cvtColor(img2, cv2.COLOR_BGR2GRAY)
pixelsPoints,pixelsPoints2, _3DreconstructedBoard = [],[],[]
if self.chessBoard:
ret, corners = cv2.findChessboardCorners(gray, (10, 7), None)
ret2, corners2 = cv2.findChessboardCorners(gray2, (10, 7), None)
if ret and ret2: # found chessboard
print('Found chessboard')
corners_2 = cv2.cornerSubPix(gray, corners, (11, 11), (-1, -1), self.criteria)
corners2_2 = cv2.cornerSubPix(gray2, corners2, (11, 11), (-1, -1), self.criteria)
pixelsPoints = np.asarray(corners_2).squeeze()
pixelsPoints2 = np.asarray(corners2_2).squeeze()
cv2.drawChessboardCorners(img, (10, 7), corners_2, ret)
cv2.drawChessboardCorners(img2, (10, 7), corners2_2, ret)
# Find the rotation and translation vectors.
success, rvecs, tvecs, inliers = cv2.solvePnPRansac(self.objp, corners_2, self.K, self.D)
rvecs, _ = cv2.Rodrigues(rvecs)
_3Dpoints = self.objp
# project 3D points to image plane
_2Dpoints, jac = cv2.projectPoints(_3Dpoints, rvecs, tvecs, self.K, self.D)
_2Dpoints = np.array(_2Dpoints, dtype=np.float32).squeeze()
print('_2Dpoints -> {}'.format(np.shape(_2Dpoints)))
for i in range(len(_2Dpoints)):
cv2.circle(img, tuple(_2Dpoints[i]), 5, (0, 255, 0), 3)
_3Dpoints = rvecs.dot(_3Dpoints.T) + tvecs
_3Dpoints = _3Dpoints.T
print('_3Dpoints->{}'.format(np.shape(_3Dpoints)))
dist_mat = distance_matrix(_3Dpoints, _3Dpoints)
print('dist_mat for OpencvReconstructed')
print(dist_mat[0, :11])
_3DreconstructedBoard = _3Dpoints
else:
return None,None
else:
corners, ids, rejectedImgPoints = aruco.detectMarkers(gray, self.ARUCO_DICT)
corners, ids, rejectedImgPoints, recoveredIds = aruco.refineDetectedMarkers(
image=gray, board=self.calibation_board, detectedCorners=corners, detectedIds=ids,
rejectedCorners=rejectedImgPoints, cameraMatrix=self.K, distCoeffs=self.D)
corners2, ids2, rejectedImgPoints2 = aruco.detectMarkers(gray2, self.ARUCO_DICT)
corners2, ids2, rejectedImgPoints2, recoveredIds2 = aruco.refineDetectedMarkers(
image=gray2, board=self.calibation_board, detectedCorners=corners2, detectedIds=ids2,
rejectedCorners=rejectedImgPoints2, cameraMatrix=self.K, distCoeffs=self.D)
if np.all(ids != None) and np.all(ids2 != None):
print('found charuco board, ids:{}'.format(np.shape(ids)))
if len(ids) and len(ids2) > 0:
retval, self.rvecs, self.tvecs = aruco.estimatePoseBoard(corners, ids,
self.calibation_board, self.K,
self.D, None, None)
retval2, self.rvecs2, self.tvecs2 = aruco.estimatePoseBoard(corners2, ids2,
self.calibation_board, self.K,
self.D, None, None)
img = aruco.drawDetectedMarkers(img, corners, ids,borderColor=(0, 0, 255))
img2 = aruco.drawDetectedMarkers(img2, corners2, ids2, borderColor=(0, 0, 255))
if retval and retval2:
self.dst, jacobian = cv2.Rodrigues(self.rvecs)
self.dst2, jacobian = cv2.Rodrigues(self.rvecs2)
#self.pts = np.float32([[0, b, 0], [b, b, 0], [b, 0, 0], [-0.03, -0.03, 0]])
b = 1
self.pts = np.float32([[0, b, 0], [b, b, 0], [b, 0, 0], [-0.03, -0.03, 0],[.5,.5,0]])
_3Dpoints = self.dst.T.dot(np.array(self.pts).squeeze().T) + self.tvecs
_3Dpoints = _3Dpoints.T
print('_3Dpoints->{}'.format(np.shape(_3Dpoints)))
dist_mat = distance_matrix(_3Dpoints, _3Dpoints)
print('dist_mat for OpencvReconstructed')
print(dist_mat)
_3DreconstructedBoard = _3Dpoints
imgpts, _ = cv2.projectPoints(self.pts, self.rvecs, self.tvecs, self.K, self.D)
#corners2 = np.append(imgpts, np.mean(imgpts, axis=0)).reshape(-1, 2)
corners2 = np.array(imgpts).squeeze()
self.pt_dict = {}
for i in range(len(self.pts)):
self.pt_dict[tuple(self.pts[i])] = tuple(imgpts[i].ravel())
top_right = self.pt_dict[tuple(self.pts[0])]
bot_right = self.pt_dict[tuple(self.pts[1])]
bot_left = self.pt_dict[tuple(self.pts[2])]
top_left = self.pt_dict[tuple(self.pts[3])]
img = cv2.line(img, top_right, bot_right, (0, 255, 0), 4)
img = cv2.line(img, bot_right, bot_left, (0, 255, 0), 4)
img = cv2.line(img, bot_left, top_left, (0, 255, 0), 4)
img = cv2.line(img, top_left, top_right, (0, 255, 0), 4)
cv2.circle(img, tuple(corners2[-1]), 5, (0, 255, 0), 3)
cv2.circle(img, tuple(corners2[-2]), 5, (0, 0, 255), 3)
pixelsPoints = np.asarray(corners2).squeeze()
imgpts, _ = cv2.projectPoints(self.pts, self.rvecs2, self.tvecs2, self.K, self.D)
#corners2 = np.append(imgpts, np.mean(imgpts, axis=0)).reshape(-1, 2)
corners2 = np.array(imgpts).squeeze()
self.pt_dict = {}
for i in range(len(self.pts)):
self.pt_dict[tuple(self.pts[i])] = tuple(imgpts[i].ravel())
top_right = self.pt_dict[tuple(self.pts[0])]
bot_right = self.pt_dict[tuple(self.pts[1])]
bot_left = self.pt_dict[tuple(self.pts[2])]
top_left = self.pt_dict[tuple(self.pts[3])]
img2 = cv2.line(img2, top_right, bot_right, (0, 255, 0), 4)
img2 = cv2.line(img2, bot_right, bot_left, (0, 255, 0), 4)
img2 = cv2.line(img2, bot_left, top_left, (0, 255, 0), 4)
img2 = cv2.line(img2, top_left, top_right, (0, 255, 0), 4)
cv2.circle(img2, tuple(corners2[-1]), 5, (0, 255, 0), 3)
#cv2.circle(img2, tuple(corners2[-2]), 5, (0, 0, 255), 3)
pixelsPoints2 = np.asarray(corners2).squeeze()
else:
return None,None
else:
return None,None
else:
return None,None
scale = .4
_horizontal = np.hstack(
(cv2.resize(img, None, fx=scale, fy=scale), cv2.resize(img2, None, fx=scale, fy=scale)))
cv2.imshow('_horizontal', _horizontal)
cv2.waitKey(0)
cv2.destroyAllWindows()
return pixelsPoints,pixelsPoints2, _3DreconstructedBoard
def savePointsCorrespondences(self, args):
display = True
fig = plt.figure(figsize=plt.figaspect(1))
ax = plt.axes(projection='3d')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
if self.chessBoard:
legend_elements = [
Line2D([0], [0], marker='o', label='board template', markerfacecolor='tab:blue', markersize=6),
Line2D([0], [0], marker='o', label='ICP finetuned', markerfacecolor='green', markersize=6),
Line2D([0], [0], marker='o', label='closest lidar points', markerfacecolor='k', markersize=6),
Line2D([0], [0], marker='o', label='Camera_XYZ', markerfacecolor='red', markersize=6),
]
board_template = self.template_cloud
board_template_ICP_finetuned = self.estimate
closest_lidar_points = self.finaPoints
try:
icp_finetuned_inside = np.asarray(self.estimate).reshape(self.nCols, self.nRows, 3)[1:self.nCols - 1,
1:self.nRows - 1, :]
board_template_inside = board_template.reshape(self.nCols, self.nRows, 3)[1:self.nCols - 1,
1:self.nRows - 1, :]
closest_lidar_points_inside = closest_lidar_points.reshape(self.nCols, self.nRows, 3)[1:self.nCols - 1,
1:self.nRows - 1, :]
except:
print('Second-----------------------------')
icp_finetuned_inside = np.asarray(self.estimate).reshape(self.nCols+1, self.nRows+1, 3)[1:self.nCols - 1,
1:self.nRows - 1, :]
board_template_inside = board_template.reshape(self.nCols+1, self.nRows+1, 3)[1:self.nCols - 1,
1:self.nRows - 1, :]
closest_lidar_points_inside = closest_lidar_points.reshape(self.nCols+1, self.nRows+1, 3)[1:self.nCols - 1,
1:self.nRows - 1, :]
icp_finetuned_inside = np.array(icp_finetuned_inside).reshape(-1, 3)
board_template_inside = np.array(board_template_inside).reshape(-1, 3)
print('board_template_inside-----------------------------------------------------')
print(board_template_inside)
print('board_template_inside -> {}'.format(np.shape(board_template_inside)))
dist_Lidar = distance_matrix(board_template_inside, board_template_inside)
print('dist_Lidar---------------------------------------------------------')
print(dist_Lidar[0, :11])
closest_lidar_points_inside = np.array(closest_lidar_points_inside).reshape(-1, 3)
Camera_XYZ = self.getCamera_XYZ()
if self.img_file2:
Camera_XYZ_Stereo = self.getCamera_XYZ_Stereo()
else:
Camera_XYZ_Stereo = np.array([[0, 0, 0]])
display = True
if display:
print('board_template:{}'.format(np.shape(board_template)))
print('board_template_ICP_finetuned:{}'.format(np.shape(board_template_ICP_finetuned)))
print('icp_finetuned_inside:{}'.format(np.shape(icp_finetuned_inside)))
print('board_template_inside:{}'.format(np.shape(board_template_inside)))
print('closest_lidar_points:{}'.format(np.shape(closest_lidar_points)))
print('closest_lidar_points_inside:{}'.format(np.shape(closest_lidar_points_inside)))
print('Camera_XYZ:{}'.format(np.shape(Camera_XYZ)))
print('Camera_XYZ_Stereo:{}'.format(np.shape(Camera_XYZ_Stereo)))
#dist = distance_matrix(Camera_XYZ_Stereo, Camera_XYZ_Stereo)
#print('distance matrix Camera_XYZ_Stereo:{}'.format(dist))
ax.scatter(*board_template.T, color='b', marker='o', alpha=.5, s=8)
ax.scatter(*board_template_ICP_finetuned.T, color='r', marker='o', alpha=.5, s=8)
ax.scatter(*board_template_inside.T, color='tab:blue', marker='x', alpha=1, s=10)
ax.scatter(*icp_finetuned_inside.T, color='g', marker='x', alpha=1, s=10)
ax.scatter(*closest_lidar_points.T, color='r', marker='x', alpha=.8, s=10)
ax.scatter(*closest_lidar_points_inside.T, color='k', marker='x', alpha=1, s=20)
ax.scatter(*Camera_XYZ.T, color='k', marker='x', alpha=1, s=30)
ax.scatter(*Camera_XYZ_Stereo.T, color='r', marker='o', alpha=1, s=3)
self.AnnotateEdges(giveAX=ax, givenPoints=board_template_inside)
extents = np.array([getattr(ax, 'get_{}lim'.format(dim))() for dim in 'xyz'])
sz = extents[:, 1] - extents[:, 0]
centers = np.mean(board_template, axis=0)
# centers = np.mean(Camera_XYZ_Stereo, axis=0) if self.img_file2 is not None else np.mean(board_template,axis=0)
maxsize = max(abs(sz))
r = maxsize / 2
for ctr, dim in zip(centers, 'xyz'):
getattr(ax, 'set_{}lim'.format(dim))(ctr - r, ctr + r)
self.pixelsPointsLeft, self.pixelsPointsRight, _3DreconstructedBoard = self.getImagePixels()
print('_3DreconstructedBoard -> {}'.format(np.shape(_3DreconstructedBoard)))
if len(self.pixelsPointsLeft)<=0:
print('Cannot get pixels points !!! ')
self.points_correspondences = dict([
('board_template', board_template),
('board_template_ICP_finetuned', board_template_ICP_finetuned),
('board_template_inside', board_template_inside),
('icp_finetuned_inside', icp_finetuned_inside),
('closest_lidar_points', closest_lidar_points),
('closest_lidar_points_inside', closest_lidar_points_inside),
('pixelsPointsLeft', self.pixelsPointsLeft),
('pixelsPointsRight', self.pixelsPointsRight),
('Camera_XYZ_Stereo', Camera_XYZ_Stereo),
('_3DreconstructedBoard',_3DreconstructedBoard),
('Camera_XYZ', Camera_XYZ)])
# save_obj(self.points_correspondences, self.name)
else:
legend_elements = [
Line2D([0], [0], marker='o', label='board template all', markerfacecolor='b', markersize=6),
Line2D([0], [0], marker='o', label='ICP finetuned', markerfacecolor='red', markersize=6),
Line2D([0], [0], marker='o', label='board template inside', markerfacecolor='tab:blue', markersize=6),
Line2D([0], [0], marker='o', label='closest lidar points', markerfacecolor='red', markersize=6),
]
pts = np.asarray(self.template_cloud.copy()).reshape(self.nCols, self.nRows, 3)
idx = np.array([44, 45, 54, 55])
center = np.mean(self.template_cloud[idx], axis=0)
board_template = np.array([pts[0, -1, :], pts[-1, -1, :], pts[-1, 0, :], pts[0, 0, :], center]).reshape(-1,
3)
board_template = board_template
pts = np.asarray(self.estimate.copy()).reshape(self.nCols, self.nRows, 3)
center = np.mean(self.estimate[idx], axis=0)
board_template_ICP_finetuned = np.array(
[pts[0, -1, :], pts[-1, -1, :], pts[-1, 0, :], pts[0, 0, :], center]).reshape(-1, 3)
board_template_inside = self.templatePoints
pts = np.asarray(self.finaPoints.copy()).reshape(self.nCols, self.nRows, 3)
center = np.mean(self.finaPoints[idx], axis=0)
closest_lidar_points = np.array(
[pts[0, -1, :], pts[-1, -1, :], pts[-1, 0, :], pts[0, 0, :], center]).reshape(-1, 3)
if self.img_file2:
Camera_XYZ_Stereo = self.getCamera_XYZ_Stereo()
else:
Camera_XYZ_Stereo = np.array([[0, 0, 0]])
if display:
print('board_template:{}'.format(np.shape(board_template)))
print('board_template_ICP_finetuned:{}'.format(np.shape(board_template_ICP_finetuned)))
print('board_template_inside:{}'.format(np.shape(board_template_inside)))
print('closest_lidar_points:{}'.format(np.shape(closest_lidar_points)))
print('Camera_XYZ_Stereo:{}'.format(np.shape(Camera_XYZ_Stereo)))
ax.scatter(*board_template.T, color='b', marker='o', alpha=.5, s=8)
ax.scatter(*board_template_ICP_finetuned.T, color='r', marker='o', alpha=.5, s=8)
ax.scatter(*board_template_inside.T, color='tab:blue', marker='x', alpha=1, s=10)
ax.scatter(*closest_lidar_points.T, color='r', marker='x', alpha=.8, s=10)
ax.scatter(*Camera_XYZ_Stereo.T, color='r', marker='o', alpha=.8, s=20)
self.AnnotateEdges(giveAX=ax, givenPoints=board_template_inside)
extents = np.array([getattr(ax, 'get_{}lim'.format(dim))() for dim in 'xyz'])
sz = extents[:, 1] - extents[:, 0]
centers = np.mean(board_template, axis=0)
# centers = np.mean(Camera_XYZ, axis=0) if self.img_file2 is not None else np.mean(board_template, axis=0)
maxsize = max(abs(sz))
r = maxsize / 2
for ctr, dim in zip(centers, 'xyz'):
getattr(ax, 'set_{}lim'.format(dim))(ctr - r, ctr + r)
self.pixelsPointsLeft, self.pixelsPointsRight, _3DreconstructedBoard = self.getImagePixels()
_3DreconstructedBoard = np.array(_3DreconstructedBoard).squeeze()
print('_3DreconstructedBoard -> {}'.format(np.shape(_3DreconstructedBoard)))
if len(self.pixelsPointsLeft) <= 0:
print('Cannot get pixels points !!! ')
ax.scatter(*_3DreconstructedBoard.T, color='b', marker='x', alpha=1, s=20)
print('pixelsPointsLeft:{}'.format(np.shape(self.pixelsPointsLeft)))
print('pixelsPointsRight:{}'.format(np.shape(self.pixelsPointsRight)))
print('_3DreconstructedBoard:{}'.format(np.shape(_3DreconstructedBoard)))
self.points_correspondences = dict([
('board_template', board_template),
('board_template_ICP_finetuned', board_template_ICP_finetuned),
('board_template_inside', board_template_inside),
('pixelsPointsLeft', self.pixelsPointsLeft),
('pixelsPointsRight', self.pixelsPointsRight),
('_3DreconstructedBoard',_3DreconstructedBoard),
('Camera_XYZ_Stereo', Camera_XYZ_Stereo),
('closest_lidar_points', closest_lidar_points)])
# save_obj(self.points_correspondences, self.name)
ax.legend(handles=legend_elements, loc='best')
plt.show()
def getDepth_Inside_Outside(self):
calibrations = ['inside', 'outside']
output = []
for calib in calibrations:
camera_model = load_obj('{}_combined_camera_model'.format(calib))
camera_model_rectify = load_obj('{}_combined_camera_model_rectify'.format(calib))
K_left = camera_model['K_right']
D_left = camera_model['D_right']
T = camera_model['T']
leftMapX, leftMapY = camera_model_rectify['leftMapX'], camera_model_rectify['leftMapY']
rightMapX, rightMapY = camera_model_rectify['rightMapX'], camera_model_rectify['rightMapY']
imgleft = cv2.imread(self.img_file)
imgright = cv2.imread(self.img_file2)
if stereoRectify:
imgleft = cv2.remap(src=imgleft, map1=leftMapX, map2=leftMapY, interpolation=cv2.INTER_LINEAR, dst=None,borderMode=cv2.BORDER_CONSTANT)
imgright = cv2.remap(src=imgright, map1=rightMapX, map2=rightMapY, interpolation=cv2.INTER_LINEAR, dst=None,borderMode=cv2.BORDER_CONSTANT)
gray_left = cv2.cvtColor(imgleft, cv2.COLOR_BGR2GRAY)
ret_left, corners_left = cv2.findChessboardCorners(gray_left, (10, 7), None)
gray_right = cv2.cvtColor(imgright, cv2.COLOR_BGR2GRAY)
ret_right, corners_right = cv2.findChessboardCorners(gray_right, (10, 7), None)
if ret_left and ret_right: # found chessboard
corners2_left = cv2.cornerSubPix(gray_left, corners_left, (11, 11), (-1, -1), self.criteria)
x_left = np.asarray(corners2_left).squeeze()
corners2_right = cv2.cornerSubPix(gray_right, corners_right, (11, 11), (-1, -1), self.criteria)
x_right = np.asarray(corners2_right).squeeze()
baseline = abs(T[0])
focal_length, cx, cy = K_left[0, 0], K_left[0, 2], K_left[1, 2]
disparity = np.sum(np.sqrt((x_left - x_right) ** 2), axis=1)
# depth = baseline (meter) * focal length (pixel) / disparity-value (pixel) -> meter
depth = (baseline * focal_length / disparity) # .reshape(10,7)
fxypxy = [K_left[0, 0], K_left[1, 1], cx, cy]
print('{} fx:{}, fy:{}'.format(calib, round(K_left[0, 0],2), round(K_left[1, 1],2)))
_3DPoints = []
for i, pixel in enumerate(x_left):
u, v = pixel.ravel()
u, v = int(u), int(v)
distance = depth[i]
# print('u:{},v:{},distance:{}'.format(u,v, distance))
pt = np.array([u, v, distance])
pt[0] = pt[2] * (pt[0] - fxypxy[2]) / fxypxy[0]
pt[1] = pt[2] * (pt[1] - fxypxy[3]) / fxypxy[1]
_3DPoints.append(pt)
_3DPoints = np.array(_3DPoints)
output.append(_3DPoints)
else:
print('cannot detect board in both images')
if len(output)>1:
inside_3D = np.array(output[0]).squeeze()
outisde_3D = np.array(output[1]).squeeze()
#get the error for each point
a_min_b = inside_3D - outisde_3D
norm_total = np.linalg.norm(a_min_b)/70
norm_axis = np.linalg.norm(a_min_b, axis=0)/70
print('norm_total:{}, norm_axis:{}'.format(norm_total,norm_axis))
self._3DErros.append(norm_axis)
def fitNewPlan(self):
coolPoints = self.coolPoints
def minimum_bounding_rectangle(points):
pi2 = np.pi / 2.
# get the convex hull for the points
hull = ConvexHull(points)
hull_points = points[hull.vertices]
y_saved = []
for simplex in hull.simplices:
y = coolPoints[simplex,1]
x = points[simplex, 0]
z = points[simplex, 1]
self.ax.plot(x, y, z, 'k-', alpha = .5)
y_saved.append(y)
y_saved = np.array(y_saved)
# calculate edge angles
edges = hull_points[1:] - hull_points[:-1]
angles = np.arctan2(edges[:, 1], edges[:, 0])
angles = np.abs(np.mod(angles, pi2))
angles = np.unique(angles)
rotations = np.vstack([
np.cos(angles),np.cos(angles - pi2),
np.cos(angles + pi2),np.cos(angles)]).T
rotations = rotations.reshape((-1, 2, 2))
# apply rotations to the hull
rot_points = np.dot(rotations, hull_points.T)
# find the bounding points
min_x = np.nanmin(rot_points[:, 0], axis=1)
max_x = np.nanmax(rot_points[:, 0], axis=1)
min_y = np.nanmin(rot_points[:, 1], axis=1)
max_y = np.nanmax(rot_points[:, 1], axis=1)
# find the box with the best area
areas = (max_x - min_x) * (max_y - min_y)
best_idx = np.argmin(areas)
# return the best box
x1 = max_x[best_idx]
x2 = min_x[best_idx]
y1 = max_y[best_idx]
y2 = min_y[best_idx]
r = rotations[best_idx]
rval = np.zeros((4, 2))
rval[0] = np.dot([x1, y2], r)
rval[1] = np.dot([x2, y2], r)
rval[2] = np.dot([x2, y1], r)
rval[3] = np.dot([x1, y1], r)
rval = np.array(rval)
d_matrix = distance_matrix(rval, points)
neighbours = np.argsort(d_matrix, axis=1)[:, 0]
rval2 = np.asarray(coolPoints[neighbours, 1]).squeeze()
return rval, rval2
points = list(self.coolPoints[:, [0, -1]])
y = np.mean(self.coolPoints[:, 1])
c, c2 = minimum_bounding_rectangle(np.array(points))
self.corners_ = []
for i,point in enumerate(c):
#self.corners_.append([point[0],y, point[1]])
self.corners_.append([point[0],c2[i], point[1]])
if self.chessBoard==False and self.circle_center:
self.corners_.append([self.circle_center[0],y,self.circle_center[1]])
self.corners_ = np.array(self.corners_)
self.ax.scatter(*self.corners_.T, color='k', marker='x', alpha=1, s=50)
def fitCircle(self, points):
if len(points)>0:
def calc_R(x, y, xc, yc):
"""calculate the distance of each 2D points from the center (xc, yc)"""
return np.sqrt((x - xc) ** 2 + (y - yc) ** 2)
def f(c, x, y):
"""calculate the algebraic distance between the data points
and the mean circle centered at c=(xc, yc)"""
Ri = calc_R(x, y, *c)
return Ri - Ri.mean()
def sigma(coords, x, y, r):
"""Computes Sigma for circle fit."""
dx, dy, sum_ = 0., 0., 0.
for i in range(len(coords)):
dx = coords[i][1] - x
dy = coords[i][0] - y
sum_ += (sqrt(dx * dx + dy * dy) - r) ** 2
return sqrt(sum_ / len(coords))
def hyper_fit(coords, IterMax=99, verbose=False):
"""
Fits coords to circle using hyperfit algorithm.
Inputs:
- coords, list or numpy array with len>2 of the form:
[
[x_coord, y_coord],
...,
[x_coord, y_coord]
]
or numpy array of shape (n, 2)
Outputs:
- xc : x-coordinate of solution center (float)
- yc : y-coordinate of solution center (float)
- R : Radius of solution (float)
- residu : s, sigma - variance of data wrt solution (float)
"""
X, Y = None, None
if isinstance(coords, np.ndarray):
X = coords[:, 0]
Y = coords[:, 1]
elif isinstance(coords, list):
X = np.array([x[0] for x in coords])
Y = np.array([x[1] for x in coords])
else:
raise Exception("Parameter 'coords' is an unsupported type: " + str(type(coords)))
n = X.shape[0]
Xi = X - X.mean()
Yi = Y - Y.mean()
Zi = Xi * Xi + Yi * Yi
# compute moments
Mxy = (Xi * Yi).sum() / n
Mxx = (Xi * Xi).sum() / n
Myy = (Yi * Yi).sum() / n
Mxz = (Xi * Zi).sum() / n
Myz = (Yi * Zi).sum() / n
Mzz = (Zi * Zi).sum() / n
# computing the coefficients of characteristic polynomial
Mz = Mxx + Myy
Cov_xy = Mxx * Myy - Mxy * Mxy
Var_z = Mzz - Mz * Mz
A2 = 4 * Cov_xy - 3 * Mz * Mz - Mzz
A1 = Var_z * Mz + 4. * Cov_xy * Mz - Mxz * Mxz - Myz * Myz
A0 = Mxz * (Mxz * Myy - Myz * Mxy) + Myz * (Myz * Mxx - Mxz * Mxy) - Var_z * Cov_xy
A22 = A2 + A2
# finding the root of the characteristic polynomial
y = A0
x = 0.
for i in range(IterMax):
Dy = A1 + x * (A22 + 16. * x * x)
xnew = x - y / Dy
if xnew == x or not np.isfinite(xnew):
break
ynew = A0 + xnew * (A1 + xnew * (A2 + 4. * xnew * xnew))
if abs(ynew) >= abs(y):
break
x, y = xnew, ynew
det = x * x - x * Mz + Cov_xy
Xcenter = (Mxz * (Myy - x) - Myz * Mxy) / det / 2.
Ycenter = (Myz * (Mxx - x) - Mxz * Mxy) / det / 2.
x = Xcenter + X.mean()
y = Ycenter + Y.mean()
r = sqrt(abs(Xcenter ** 2 + Ycenter ** 2 + Mz))
s = sigma(coords, x, y, r)
iter_ = i
if verbose:
print('Regression complete in {} iterations.'.format(iter_))
print('Sigma computed: ', s)
return x, y, r, s
def least_squares_circle(coords):
"""Circle fit using least-squares solver.
Inputs:
- coords, list or numpy array with len>2 of the form:
[
[x_coord, y_coord],
...,
[x_coord, y_coord]
]
or numpy array of shape (n, 2)
Outputs:
- xc : x-coordinate of solution center (float)
- yc : y-coordinate of solution center (float)
- R : Radius of solution (float)
- residu : MSE of solution against training data (float)
"""
x, y = None, None
if isinstance(coords, np.ndarray):
x = coords[:, 0]
y = coords[:, 1]
elif isinstance(coords, list):
x = np.array([point[0] for point in coords])
y = np.array([point[1] for point in coords])
else:
raise Exception("Parameter 'coords' is an unsupported type: " + str(type(coords)))
# coordinates of the barycenter
x_m = np.mean(x)
y_m = np.mean(y)
center_estimate = x_m, y_m
center, _ = leastsq(f, center_estimate, args=(x, y))
xc, yc = center
Ri = calc_R(x, y, *center)
R = Ri.mean()
residu = np.sum((Ri - R) ** 2)
return xc, yc, R, residu
def plot_data_circle(x, y, xc, yc, R):
"""
Plot data and a fitted circle.
Inputs:
x : data, x values (array)
y : data, y values (array)
xc : fit circle center (x-value) (float)
yc : fit circle center (y-value) (float)
R : fir circle radius (float)
Output:
None (generates matplotlib plot).
"""
f = plt.figure(facecolor='white')
plt.axis('equal')
theta_fit = np.linspace(-pi, pi, 180)
x_fit = xc + R * np.cos(theta_fit)
y_fit = yc + R * np.sin(theta_fit)
plt.plot(x_fit, y_fit, 'b-', label="fitted circle", lw=2)
plt.plot([xc], [yc], 'bD', mec='y', mew=1)
plt.xlabel('x')
plt.ylabel('y')
# plot data
plt.scatter(x, y, c='red', label='data')
plt.legend(loc='best', labelspacing=0.1)
plt.grid()
plt.title('Fit Circle')
x1, y1, r1, resid1 = hyper_fit(points[:,[0,2]])
x2, y2, r2, resid2 = least_squares_circle(points[:,[0,2]])
#plot_data_circle(points[:,1], points[:,2],x,y,r)
if resid1>resid2:
x, y, r = x2, y2, r2
else:
x, y, r = x1, y1, r1
self.circle_center = (x, y)
self.circle_radius = r
def getData(chess=True):
pcl_files = glob.glob('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/{}/*.npy'.format('chess' if chess else 'charuco'))
imgleft_files = glob.glob('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/{}/left/*.png'.format('chess' if chess else 'charuco'))
imgright_files = glob.glob('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/{}/right/*.png'.format('chess' if chess else 'charuco'))
pcl_files.sort()
imgleft_files.sort()
imgright_files.sort()
GoodPoints,_3DErros, IMageNames = [],[],[]
for i, file in enumerate(pcl_files):
if globalTrigger:
print('work with {}'.format(file))
image_left = imgleft_files[i]
image_right = imgright_files[i]
filt = PointCloud_filter(file=file, img_file=image_left, img_file2=image_right, debug=False)
filt.setUp()
plt.show()
plt.close()
print('\n OK:{}, Save points_correspondences : {}'.format(filt.OK, np.shape(filt.points_correspondences)))
if filt.OK:
GoodPoints.append(filt.points_correspondences)
print('save data {} '.format(np.shape(GoodPoints)))
_3DErros.append(filt._3DErros)
IMageNames.append(os.path.basename(image_left))
else:
print('Close')
break
#save_obj(GoodPoints, 'GoodPoints2_{}'.format('chess' if chess else 'charuco'))
print('Data saved in GoodPoints')
showErros(_3DErros, IMageNames)
def euler_from_matrix(R):
beta = -np.arcsin(R[2, 0])
alpha = np.arctan2(R[2, 1] / np.cos(beta), R[2, 2] / np.cos(beta))
gamma = np.arctan2(R[1, 0] / np.cos(beta), R[0, 0] / np.cos(beta))
return np.array((alpha, beta, gamma))
def euler_matrix(theta):
R = np.array([[np.cos(theta[1]) * np.cos(theta[2]),
np.sin(theta[0]) * np.sin(theta[1]) * np.cos(theta[2]) - np.sin(theta[2]) * np.cos(theta[0]),
np.sin(theta[1]) * np.cos(theta[0]) * np.cos(theta[2]) + np.sin(theta[0]) * np.sin(
theta[2])],
[np.sin(theta[2]) * np.cos(theta[1]),
np.sin(theta[0]) * np.sin(theta[1]) * np.sin(theta[2]) + np.cos(theta[0]) * np.cos(theta[2]),
np.sin(theta[1]) * np.sin(theta[2]) * np.cos(theta[0]) - np.sin(theta[0]) * np.cos(
theta[2])],
[-np.sin(theta[1]), np.sin(theta[0]) * np.cos(theta[1]),
np.cos(theta[0]) * np.cos(theta[1])]])
return R
class LiDAR_Camera_Calibration(object):
def __init__(self, file, chess = True, debug=True):
self.criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 100, 0.0001)
self.objp = np.zeros((7 * 10, 3), np.float32)
self.objp[:, :2] = np.mgrid[0:10, 0:7].T.reshape(-1, 2) * .1
self.debug = debug
self.file = file
self.chess = chess
if chess:
self.data_key = ['board_template','board_template_ICP_finetuned','board_template_inside',
'icp_finetuned_inside','closest_lidar_points','closest_lidar_points_inside',
'pixelsPoints','Camera_XYZ_Stereo','Camera_XYZ']
else:
self.data_key = ['board_template','board_template_ICP_finetuned','board_template_inside','pixelsPoints',
'Camera_XYZ_Stereo','closest_lidar_points']
self.readIntrinsics()
try:
self.load_points()
except:
print('cannot load data points')
'''self.Rotation = np.array([[ 0.94901505, 0.01681284, 0.3147821 ],
[-0.01003801, 0.99968204, -0.02313113],
[-0.31507091, 0.018792, 0.94888207]]).squeeze()
self.Translation = np.array([[-0.98078971],
[ 0.00600202],
[ 0.19497569]]).squeeze()
#self.Translation[0] = -.64
euler = euler_from_matrix(self.Rotation)
# print('euler1->{}'.format(euler))
angles = euler_from_matrix(self.Rotation)
print('rotation1: ', [(180.0 / math.pi) * i for i in angles])
euler[1] = np.deg2rad(22.598)
self.Rotation = euler_matrix(euler)'''
def rmse(self, objp, imgp, K, D, rvec, tvec):
print('objp:{}, imgp:{}'.format(np.shape(objp), np.shape(imgp)))
predicted, _ = cv2.projectPoints(objp, rvec, tvec, K, D)
print('rmse=====================================================')
print('predicted -> {}, type - >{}'.format(np.shape(predicted), type(predicted)))
predicted = cv2.undistortPoints(predicted, K, D, P=K)
predicted = predicted.squeeze()
pix_serr = []
for i in range(len(predicted)):
xp = predicted[i, 0]
yp = predicted[i, 1]
xo = imgp[i, 0]
yo = imgp[i, 1]
pix_serr.append((xp - xo) ** 2 + (yp - yo) ** 2)
ssum = sum(pix_serr)
return math.sqrt(ssum / len(pix_serr))
def readIntrinsics(self):
name = 'inside'
name = 'outside'
self.camera_model = load_obj('{}_combined_camera_model'.format(name))
self.camera_model_rectify = load_obj('{}_combined_camera_model_rectify'.format(name))
self.K_right = self.camera_model['K_left']
self.K_left = self.camera_model['K_right']
self.D_right = self.camera_model['D_left']
self.D_left = self.camera_model['D_right']
print(' self.K_right')
print( self.K_right)
print(' self.K_left')
print(self.K_left)
self.R = self.camera_model['R']
self.T = self.camera_model['T']
self.K = self.K_right
self.D = self.D_right
print('self T before {}'.format(np.shape(self.T)))
self.T = np.array([-0.96, 0., 0.12])[:, np.newaxis]
print('self T after {}'.format(np.shape(self.T)))
angles = np.array([np.deg2rad(0.68), np.deg2rad(22.66), np.deg2rad(-1.05)])
self.R = euler_matrix(angles)
#-----------------------------------------------------
self.T = np.array([-0.977, 0.004, 0.215])[:, np.newaxis]
angles = np.array([np.deg2rad(1.044), np.deg2rad(22.632), np.deg2rad(-.95)])
self.R = euler_matrix(angles)
#print(self.R)
print('translation is {}-----------------------------'.format(self.T))
img_shape = (1936, 1216)
print('img_shape:{}'.format(img_shape))
R1, R2, P1, P2, Q, roi_left, roi_right = cv2.stereoRectify(self.K_left, self.D_left, self.K_right, self.D_right,
imageSize=img_shape,
R=self.camera_model['R'], T=self.camera_model['T'],
flags=cv2.CALIB_ZERO_DISPARITY,
alpha=-1
#alpha=0
)
#print('R1:{}'.format(R1))
#print('R2:{}'.format(R2))
# print('euler1->{}'.format(euler))
angles = euler_from_matrix(self.R)
print('self.R: ', [(180.0 / math.pi) * i for i in angles])
euler = euler_from_matrix(R1)
#print('euler1->{}'.format(euler))
angles = euler_from_matrix(R1)
#print('rotation1: ', [(180.0 / math.pi) * i for i in angles])
euler = euler_from_matrix(R2)
#print('euler2->{}'.format(euler))
angles = euler_from_matrix(R2)
#print('rotation2: ', [(180.0 / math.pi) * i for i in angles])
self.R1 = R1
self.R2 = R2
self.P1 = P1
self.leftMapX, self.leftMapY = cv2.initUndistortRectifyMap(
self.K_left, self.D_left, R1,
P1, img_shape, cv2.CV_32FC1)
self.rightMapX, self.rightMapY = cv2.initUndistortRectifyMap(
self.K_right, self.D_right, R2,
P2, img_shape, cv2.CV_32FC1)
print('Got camera intrinsic')
print('Got camera-lidar extrinsics')
def load_points(self):
self.Lidar_3D, self.Image_2D,self.Image_2D2, self.Image_3D,self.Camera_XYZ = [],[],[],[],[]
with open(self.file, 'rb') as f:
self.dataPoinst = pickle.load(f, encoding='latin1')
#with open(self.file,'rb') as f:
#self.dataPoinst = pickle.load(f)
self.N = len(self.dataPoinst)
print('Got {} data views'.format(self.N))
#self.N = 1
for i in range(self.N):
try:
dictionary_data = self.dataPoinst[i]
LiDAR_3D_points = dictionary_data['board_template_inside'] #N x 3
#pixelsPoints = dictionary_data['pixelsPoints'] #N x 2
#StereoCam_3D_points = dictionary_data['Camera_XYZ_Stereo'] #N x 3
pixelsPointsLeft = dictionary_data['pixelsPointsLeft']
pixelsPointsRight = dictionary_data['pixelsPointsRight']
StereoCam_3D_points = dictionary_data['_3DreconstructedBoard'] #N x 3
self.Lidar_3D.append(LiDAR_3D_points)
self.Image_2D.append(pixelsPointsLeft)
self.Image_2D2.append(pixelsPointsRight)
self.Image_3D.append(StereoCam_3D_points)
if self.chess:
self.Camera_XYZ.append(dictionary_data['Camera_XYZ'])
except:
#print('Cannot read data')
pass
#self.Lidar_3D = np.array(self.Lidar_3D).reshape(-1,3)
#self.Image_2D = np.array(self.Image_2D).reshape(-1,2)
#self.Image_3D = np.array( self.Image_3D).reshape(-1,3)
print('Lidar_3D:{}, Image_2D:{}, Image_2D2:{}, Image_3D:{}'.format(np.shape(self.Lidar_3D),
np.shape(self.Image_2D),np.shape(self.Image_2D2),
np.shape(self.Image_3D)))
def plotData(self):
self.fig = plt.figure(figsize=plt.figaspect(0.33))
self.fig.tight_layout()
for i in range(self.N):
print('{}/{}'.format(i+1,self.N))
ax1 = self.fig.add_subplot(1, 3, 1, projection='3d')
#ax1.set_title('3D LiDAR')
ax1.set_xlabel('X', fontsize=8)
ax1.set_ylabel('Y', fontsize=8)
ax1.set_zlabel('Z', fontsize=8)
ax2 = self.fig.add_subplot(1, 3, 2, projection='3d')
ax2.set_title('3D Stereo cameras')
ax2.set_xlabel('X', fontsize=8)
ax2.set_ylabel('Y', fontsize=8)
ax2.set_zlabel('Z', fontsize=8)
ax3 = self.fig.add_subplot(1, 3, 3, projection='3d')
ax3.set_title('2D pixels')
ax3.set_xlabel('X', fontsize=8)
ax3.set_ylabel('Y', fontsize=8)
ax3.set_zlabel('Z', fontsize=8)
_3d_LIDAR = np.array(self.Lidar_3D[i])
ax1.scatter(*_3d_LIDAR.T)
self.axisEqual3D(ax1, _3d_LIDAR)
_3d_cam = np.array(self.Image_3D[i])
ax2.scatter(*_3d_cam.T, c='r')
self.axisEqual3D(ax2,_3d_cam)
_2d_cam = np.array(self.Image_2D[i])
ax3.scatter(*_2d_cam.T, c='g')
self.axisEqual3D(ax3, _2d_cam)
plt.show()
def axisEqual3D(self,ax,data):
extents = np.array([getattr(ax, 'get_{}lim'.format(dim))() for dim in 'xyz'])
sz = extents[:, 1] - extents[:, 0]
centers = np.mean(data, axis=0)
maxsize = max(abs(sz))
r = maxsize / 2
for ctr, dim in zip(centers, 'xyz'):
getattr(ax, 'set_{}lim'.format(dim))(ctr - r, ctr + r)
def get3D_3D_homography(self, src, dst): #both or Nx3 matrices
src_mean = np.mean(src, axis=0)
dst_mean = np.mean(dst, axis=0)
# Compute covariance
"""try:
H = reduce(lambda s, (a, b): s + np.outer(a, b), zip(src - src_mean, dst - dst_mean), np.zeros((3, 3)))
u, s, v = np.linalg.svd(H)
R = v.T.dot(u.T) # Rotation
T = - R.dot(src_mean) + dst_mean # Translation
H = np.hstack((R, T[:, np.newaxis]))
return H,R.T,T
except:
print('switch to python 2')"""
def calibrate_3D_3D_old(self):
print('3D-3D ========================================================================================')
file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/GoodPoints_3D3D_{}.pkl'.format('chess')
file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/GoodPoints_{}.pkl'.format('chess')
self.Lidar_3D, self.Image_2D, self.Image_3D, self.Camera_XYZ = [], [], [], []
with open(file, 'rb') as f:
self.dataPoinst = pickle.load(f)
self.N = len(self.dataPoinst)
print('Got {} data views'.format(self.N))
for i in range(self.N):
try:
dictionary_data = self.dataPoinst[i]
LiDAR_3D_points = dictionary_data['board_template_inside'] # N x 3
pixelsPoints = dictionary_data['pixelsPoints'] # N x 2
StereoCam_3D_points = dictionary_data['Camera_XYZ_Stereo'] # N x 3
#StereoCam_3D_points = dictionary_data['point3D_trianguate']
self.Lidar_3D.append(LiDAR_3D_points)
self.Image_2D.append(pixelsPoints)
self.Image_3D.append(StereoCam_3D_points)
if self.chess:
self.Camera_XYZ.append(dictionary_data['Camera_XYZ'])
except:
print('Cannot read data===================================================')
break
print('Lidar_3D:{}, Image_2D:{}, Image_3D:{}'.format(np.shape(self.Lidar_3D),
np.shape(self.Image_2D),
np.shape(self.Image_3D)))
Lidar_3D = np.array(self.Lidar_3D).reshape(-1, 3)
Image_3D = np.array( self.Image_3D).reshape(-1,3)
print('Lidar_3D:{}, Image_3D:{}'.format(np.shape(Lidar_3D),np.shape(Image_3D)))
#-------------------------------------#-------------------------------------
c_, R_, t_ = self.estimate(Lidar_3D,Image_3D)
#import superpose3d as super
#(RMSD, R_, t_, c_) = super.Superpose3D(Lidar_3D, Image_3D)
#print('RMSD -> {}, t_{}, c_->{}'.format(RMSD, t_, c_))
# -------------------------------------#-------------------------------------
def similarity_transform(from_points, to_points):
assert len(from_points.shape) == 2, \
"from_points must be a m x n array"
assert from_points.shape == to_points.shape, \
"from_points and to_points must have the same shape"
N, m = from_points.shape
mean_from = from_points.mean(axis=0)
mean_to = to_points.mean(axis=0)
delta_from = from_points - mean_from # N x m
delta_to = to_points - mean_to # N x m
sigma_from = (delta_from * delta_from).sum(axis=1).mean()
sigma_to = (delta_to * delta_to).sum(axis=1).mean()
cov_matrix = delta_to.T.dot(delta_from) / N
U, d, V_t = np.linalg.svd(cov_matrix, full_matrices=True)
cov_rank = np.linalg.matrix_rank(cov_matrix)
S = np.eye(m)
if cov_rank >= m - 1 and np.linalg.det(cov_matrix) < 0:
S[m - 1, m - 1] = -1
elif cov_rank < m - 1:
raise ValueError("colinearility detected in covariance matrix:\n{}".format(cov_matrix))
R = U.dot(S).dot(V_t)
c = (d * S.diagonal()).sum() / sigma_from
t = mean_to - c * R.dot(mean_from)
print('R:{},t:{},c:{}'.format(R,t,c))
return c * R, t
print('similarity_transform===============================')
from_points = Lidar_3D
to_points = Image_3D
M_ans, t_ans = similarity_transform(from_points, to_points)
H, R, T = self.get3D_3D_homography(src = Lidar_3D, dst=Image_3D)
print('H:{}, R:{}, T:{}'.format(np.shape(H), np.shape(R), np.shape(T)))
print(H)
self.fig = plt.figure(figsize=plt.figaspect(1.))
ax1 = self.fig.add_subplot(1, 1, 1, projection='3d')
#ax1.set_title('3D LiDAR')
ax1.set_xlabel('X', fontsize=8)
ax1.set_ylabel('Y', fontsize=8)
ax1.set_zlabel('Z', fontsize=8)
ax1.set_axis_off()
_3d_LIDAR = self.Lidar_3D[0]
ax1.scatter(*_3d_LIDAR.T, label = 'LiDAR')
_3d_Image = self.Image_3D[0]
ax1.scatter(*_3d_Image.T, s=25, label = 'Stereo Cam')
T = _3d_LIDAR.dot(c_ * R_) + t_
print('T -> {}'.format(np.shape(T)))
ax1.scatter(*T.T, marker='x', label='T')
d2 = distance_matrix(_3d_Image,_3d_Image)
print('d2:{}'.format(d2))
print('d2 shape :{}'.format(np.shape(d2)))
ones = np.ones(len(_3d_LIDAR))[:, np.newaxis]
transformed_ = np.hstack((_3d_LIDAR,ones))
transformed = np.dot(H, transformed_.T).T #transformation estimated with SVD
print(np.shape(transformed))
ax1.scatter(*transformed.T, s=25, label = 'ICP sol')
#ax1.set_axis_off()
primary = Lidar_3D# _3d_LIDAR
secondary = Image_3D# _3d_Image
pad = lambda x: np.hstack([x, np.ones((x.shape[0], 1))])
unpad = lambda x: x[:, :-1]
X = pad(primary)
Y = pad(secondary)
# Solve the least squares problem X * A = Y # to find our transformation matrix A
A, res, rank, s = np.linalg.lstsq(X, Y)
transform = lambda x: unpad(np.dot(pad(x), A))
#print transform(primary)
print("Max error:", np.abs(secondary - transform(primary)).max())
trns2 = transform(_3d_LIDAR) #transformation estimated with LS
ax1.scatter(*trns2.T, label = 'least square sol')
to_points = M_ans.dot(_3d_LIDAR.T).T + t_ans
print('to_points ->{}'.format(np.shape(to_points)))
ax1.scatter(*to_points.T, label = 'to_points')
self.axisEqual3D(ax1, transformed)
ax1.legend()
plt.show()
#----------------------------------
if True:
img = cv2.imread('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/left/left_4.png')
img2 = cv2.imread('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/right/right_4.png')
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/cloud_4.npy'
else:
img = cv2.imread('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/left/left_4.png')
img2 = cv2.imread('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/right/right_4.png')
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/cloud_4.npy'
i = 12
l = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/cool/left_{}.png'.format(i)
r = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/cool/right_{}.png'.format(i)
#img, img2 = cv2.imread(l), cv2.imread(r)
#cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/cool/cloud_{}.npy'.format(i)
if stereoRectify and True:
img = cv2.remap(src=img, map1=self.leftMapX, map2=self.leftMapY,
interpolation=cv2.INTER_LINEAR, dst=None, borderMode=cv2.BORDER_CONSTANT)
img2 = cv2.remap(src=img2, map1=self.rightMapX, map2=self.rightMapY,
interpolation=cv2.INTER_LINEAR, dst=None, borderMode=cv2.BORDER_CONSTANT)
#Points in LiDAR frame
LiDAR_points3D = np.array(np.load(cloud_file, mmap_mode='r'), dtype=np.float32)[:, :3] #
print('LiDAR_points3D:{}'.format(np.shape(LiDAR_points3D)))
#converted in camera frame
ones = np.ones(len(LiDAR_points3D))[:, np.newaxis]
transformed_ = np.hstack((LiDAR_points3D, ones))
Camera_points3D = np.dot(H, transformed_.T).T
#Camera_points3D = transform(LiDAR_points3D)
#print('Camera_points3D:{}'.format(np.shape(Camera_points3D)))
#Camera_points3D = LiDAR_points3D.dot(c_ * R_) + t_
#Camera_points3D = LiDAR_points3D.dot(R_) + t_
#Camera_points3D = transform(LiDAR_points3D) #transformation estimated with LS
print('Camera_points3D -> {}'.format(Camera_points3D))
rvec, _ = cv2.Rodrigues(np.eye(3))
tvec = np.zeros(3)
#Camera_points3D = LiDAR_points3D#.dot(R_) + t_
#rvec = R_
#tran = t_
#tran[0] = -0.02
#tran[1] = -0.03
print('rvec -> {}, tvec->{}'.format(np.shape(rvec),np.shape(tvec)))
print('Camera_points3D -> {}'.format(np.shape(Camera_points3D)))
# Reproject back into the two cameras
rvec1, _ = cv2.Rodrigues(np.eye(3).T) # Change
rvec2, _ = cv2.Rodrigues(self.R.T) # Change
t1 = np.array([[0.], [0.], [0.]])
t2 = self.T
p1, _ = cv2.projectPoints(Camera_points3D[:, :3], rvec1, -t1, self.K, distCoeffs=self.D) # Change
p2, _ = cv2.projectPoints(Camera_points3D[:, :3], rvec2, -t2, self.K, distCoeffs=self.D) # Change
#points2D = [cv2.projectPoints(point, rvec, tvec, self.K, self.D)[0] for point in Camera_points3D[:, :3]]
points2D, _ = cv2.projectPoints(Camera_points3D[:, :3], np.identity(3), np.array([0., 0., 0.]), self.K, self.D)
points2D = np.asarray(points2D).squeeze()
points2D = np.asarray(p1).squeeze()
print('points2D:{}, img.shape[1]:{}'.format(np.shape(points2D), img.shape[1]))
inrange = np.where(
(points2D[:, 0] >= 0) &
(points2D[:, 1] >= 0) &
(points2D[:, 0] < img.shape[1]) &
(points2D[:, 1] < img.shape[0])
)
points2D = points2D[inrange[0]].round().astype('int')
# Draw the projected 2D points
for i in range(len(points2D)):
cv2.circle(img, tuple(points2D[i]), 2, (0, 255, 0), -1)
#cv2.circle(img2, tuple(points2D[i]), 2, (0, 255, 0), -1)
print('rvec -> {}, tvec->{}'.format(np.shape(rvec),np.shape(tvec)))
T_01 = np.vstack((np.hstack((np.eye(3), tvec[:,np.newaxis])), [0, 0, 0, 1])) # from lidar to right camera
T_12 = np.vstack((np.hstack((self.R, self.T)), [0, 0, 0, 1])) # between cameras
T_final = np.dot(T_01,T_12)
rotation, translation = T_final[:3, :3], T_final[:3, -1]
points2D = [cv2.projectPoints(point, rotation, translation, self.K, self.D)[0] for point in Camera_points3D[:, :3]]
points2D = np.asarray(points2D).squeeze()
points2D = np.asarray(p2).squeeze()
print('points2D:{}, img.shape[1]:{}'.format(np.shape(points2D), img.shape[1]))
inrange = np.where(
(points2D[:, 0] >= 0) &
(points2D[:, 1] >= 0) &
(points2D[:, 0] < img.shape[1]) &
(points2D[:, 1] < img.shape[0])
)
points2D = points2D[inrange[0]].round().astype('int')
# Draw the projected 2D points
for i in range(len(points2D)):
cv2.circle(img2, tuple(points2D[i]), 2, (0, 255, 0), -1)
cv2.imshow('left', cv2.resize(img,None, fx=.4, fy=.4))
cv2.imshow('right', cv2.resize(img2, None, fx=.4, fy=.4))
cv2.waitKey()
cv2.destroyAllWindows()
def drawCharuco(self, QueryImg):
points2D = np.array(self.Image_2D[0]).reshape(-1, 2)
for p in points2D:
cv2.circle(QueryImg, tuple(p), 4, (0, 0, 255), 5)
return QueryImg
def calibrate_3D_2D(self, userRansac = False):
points3D = np.array(self.Lidar_3D).reshape(-1, 3)
points2D = np.array(self.Image_2D).reshape(-1,2)
print('points3D:{}, points2D:{}'.format(np.shape(points3D),np.shape(points2D)))
# Estimate extrinsics
if userRansac:
success, rotation_vector, translation_vector, inliers = cv2.solvePnPRansac(points3D,
points2D, self.K, self.D,
flags=cv2.SOLVEPNP_ITERATIVE)
print('success:{},rotation_vector:{},translation_vector:{},inliers:{}'.format(success, np.shape(rotation_vector),
np.shape(translation_vector), np.shape(inliers)))
# Compute re-projection error.
points2D_reproj = cv2.projectPoints(points3D, rotation_vector,
translation_vector, self.K, self.D)[0].squeeze(1)
error = (points2D_reproj - points2D)[inliers] # Compute error only over inliers.
error = np.asarray(error).squeeze()
print('points2D_reproj:{}, points2D:{},error:{}'.format(np.shape(points2D_reproj), np.shape(points2D), np.shape(error)))
rmse = np.sqrt(np.mean(error[:, 0] ** 2 + error[:, 1] ** 2))
print('Re-projection error before LM refinement (RMSE) in px: ' + str(rmse))
# Refine estimate using LM
if not success:
print('Initial estimation unsuccessful, skipping refinement')
elif not hasattr(cv2, 'solvePnPRefineLM'):
print('solvePnPRefineLM requires OpenCV >= 4.1.1, skipping refinement')
else:
assert len(inliers) >= 3, 'LM refinement requires at least 3 inlier points'
rotation_vector, translation_vector = cv2.solvePnPRefineLM(points3D[inliers],
points2D[inliers], self.K, self.D,
rotation_vector, translation_vector)
# Compute re-projection error.
points2D_reproj = cv2.projectPoints(points3D, rotation_vector,
translation_vector, self.K, self.D)[0].squeeze(1)
assert (points2D_reproj.shape == points2D.shape)
error = (points2D_reproj - points2D)[inliers] # Compute error only over inliers.
error = np.array(error).squeeze()
rmse = np.sqrt(np.mean(error[:, 0] ** 2 + error[:, 1] ** 2))
print('Re-projection error after LM refinement (RMSE) in px: ' + str(rmse))
# Convert rotation vector
#from tf.transformations import euler_from_matrix
rotation_matrix = cv2.Rodrigues(rotation_vector)[0]
euler = euler_from_matrix(rotation_matrix)
# Save extrinsics
np.savez('extrinsics{}.npz'.format('chess' if self.chess else 'charuco'),euler=euler,Rodrigues=rotation_matrix, R=rotation_vector, T=translation_vector)
# Display results
print('Euler angles (RPY):', euler)
print('Rotation Matrix Rodrigues :', rotation_matrix)
print('rotation_vector:', rotation_vector)
print('Translation Offsets:', translation_vector)
points2D = cv2.projectPoints(points3D, rotation_vector, translation_vector, self.K, self.D)[0].squeeze(1)
print('========points3D:{}, points2D:{}=================================================='.format(np.shape(points3D),np.shape(points2D)))
else:
#-------------------------------------------------------------------------------------------------
imgp = np.array([points2D], dtype=np.float32).squeeze()
objp = np.array([points3D], dtype=np.float32).squeeze()
retval, rvec, tvec = cv2.solvePnP(objp, imgp, self.K, self.D, flags=cv2.SOLVEPNP_ITERATIVE)
rmat, jac = cv2.Rodrigues(rvec)
q = Quaternion(matrix=rmat)
print("Transform from camera to laser")
print("T = ")
print(tvec)
print("R = ")
print(rmat)
print("Quaternion = ")
print(q)
print("RMSE in pixel = %f" % self.rmse(objp, imgp, self.K, self.D, rvec, tvec))
result_file = 'solvePnP_extrinsics{}.npz'.format('chess' if self.chess else 'charuco')
with open(result_file, 'w') as f:
f.write("%f %f %f %f %f %f %f" % (q.x, q.y, q.z, q.w, tvec[0], tvec[1], tvec[2]))
print("Result output format: qx qy qz qw tx ty tz")
#refine results
print('refine results------------------------------------>')
rvec, tvec = cv2.solvePnPRefineLM(objp,imgp, self.K, self.D, rvec, tvec)
rmat, jac = cv2.Rodrigues(rvec)
q = Quaternion(matrix=rmat)
print("Transform from camera to laser")
print("T = ")
print(tvec)
print("R = ")
print(rmat)
print("Quaternion = ")
print(q)
print('Euler angles')
angles = euler_from_matrix(rmat)
print(angles)
print('euler angles ', [(180.0 / math.pi) * i for i in angles])
print("RMSE in pixel = %f" % self.rmse(objp, imgp, self.K, self.D, rvec, tvec))
result_file = 'refined_solvePnP_extrinsics{}.npz'.format('chess' if self.chess else 'charuco')
with open(result_file, 'w') as f:
f.write("%f %f %f %f %f %f %f" % (q.x, q.y, q.z, q.w, tvec[0], tvec[1], tvec[2]))
def get_z(self, T_cam_world, T_world_pc, K):
R = T_cam_world[:3, :3]
t = T_cam_world[:3, 3]
proj_mat = np.dot(K, np.hstack((R, t[:, np.newaxis])))
xyz_hom = np.hstack((T_world_pc, np.ones((T_world_pc.shape[0], 1))))
xy_hom = np.dot(proj_mat, xyz_hom.T).T
z = xy_hom[:, -1]
z = np.asarray(z).squeeze()
return z
def callback_solvePnP(self, img, cloud_file):
#init calibraiton
calib_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/solvePnP_extrinsics{}.npz'.format(
'chess' if self.chess else 'charuco')
calib_file_ = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/combined_extrinsics{}.npz'
with open(calib_file, 'r') as f:
data = f.read().split()
#print('data:{}'.format(data))
qx = float(data[0])
qy = float(data[1])
qz = float(data[2])
qw = float(data[3])
tx = float(data[4])
ty = float(data[5])
tz = float(data[6])
q = Quaternion(qw, qx, qy, qz).transformation_matrix
q[0, 3] = tx
q[1, 3] = ty
q[2, 3] = tz
print("Extrinsic parameter - camera to laser")
print(q)
tvec = q[:3, 3]
rot_mat = q[:3, :3]
rvec, _ = cv2.Rodrigues(rot_mat)
try:
objPoints = np.array(np.load(cloud_file, mmap_mode='r'), dtype=np.float32)[:, :3]
print('objPoints:{}'.format(np.shape(objPoints)))
Z = self.get_z(q, objPoints, self.K)
objPoints = objPoints[Z > 0]
#print('objPoints:{}'.format(objPoints))
img_points, _ = cv2.projectPoints(objPoints, rvec, tvec, self.K, self.D)
img_points = np.squeeze(img_points)
for i in range(len(img_points)):
try:
cv2.circle(img, (int(round(img_points[i][0])), int(round(img_points[i][1]))), 3,
(0, 255, 0), 1)
except OverflowError:
continue
if self.chess:
cv2.drawChessboardCorners(img, (10, 7), np.array(self.Image_2D).reshape(-1,2), True)
else:
self.drawCharuco(img)
except:
print('callback_solvePnP - error')
image = cv2.resize(img, None, fx=.6, fy=.6)
return image
def callback_solvePnP_Ransac(self, img, cloud_file):
points3D = np.array(np.load(cloud_file, mmap_mode='r'), dtype=np.float32)[:, :3]
print('points3D:{}'.format(np.shape(points3D)))
file = np.load('extrinsics{}.npz'.format('chess' if self.chess else 'charuco'))
euler = np.array(file["euler"])
rotation_matrix = np.array(file["Rodrigues"])
rotation_vector = np.array(file["R"])
translation_vector = np.array(file["T"])
print('Euler angles (RPY):', euler)
print('Rotation Matrix Rodrigues :', rotation_matrix)
print('rotation_vector:', rotation_vector)
print('Translation Offsets:', translation_vector)
rvec = rotation_matrix
#rvec, _ = cv2.Rodrigues(rotation_matrix)
print('========points3D:{}=================================================='.format(
np.shape(points3D)))
#points2D = cv2.projectPoints(points3D, rotation_vector, translation_vector, self.K, self.D)[0].squeeze(1)
#print('points2D:{}'.format(np.shape(points2D)))
points2D = [cv2.projectPoints(point, rvec, translation_vector, self.K, self.D)[0] for point in points3D[:, :3]]
points2D = np.asarray(points2D).squeeze()
print('points2D:{}, img.shape[1]:{}'.format(np.shape(points2D),img.shape[1]))
inrange = np.where(
(points2D[:, 0] >= 0) &
(points2D[:, 1] >= 0) &
(points2D[:, 0] < img.shape[1]) &
(points2D[:, 1] < img.shape[0])
)
points2D = points2D[inrange[0]].round().astype('int')
# Draw the projected 2D points
for i in range(len(points2D)):
cv2.circle(img, tuple(points2D[i]), 2, (0, 255, 0), -1)
if self.chess:
cv2.drawChessboardCorners(img, (10, 7), np.array(self.Image_2D).reshape(-1,2), True)
else:
self.drawCharuco(img)
image = cv2.resize(img, None, fx=.6, fy=.6)
return image
def callback(self):
if self.chess:
img = cv2.imread('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/left/left_0.png')
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/cloud_0.npy'
else:
img = cv2.imread('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/left/left_0.png')
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/cloud_0.npy'
#img = cv2.imread('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/left/left_0.png')
#cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/cloud_0.npy'
#img = cv2.imread('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/left/left_0.png')
#cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/cloud_0.npy'
#solvePnP_Ransac_image = self.callback_solvePnP_Ransac(img=img.copy(),cloud_file=cloud_file)
cv2.imshow('solvePnP_Ransac', cv2.resize(img,None,fx=.4,fy=.4))
cv2.waitKey()
solvePnP_image = self.callback_solvePnP(img=img.copy(),cloud_file=cloud_file)
cv2.imshow('solvePnP', solvePnP_image)
cv2.waitKey()
cv2.destroyAllWindows()
def combine_both_boards_and_train(self):
#get data from chessboard
name = 'chess'
self.file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/GoodPoints_{}.pkl'.format(name)
self.load_points()
Lidar_3D, Image_2D, Image_3D = np.array(self.Lidar_3D).reshape(-1,3), np.array(self.Image_2D).reshape(-1,2), np.array(self.Image_3D).reshape(-1,3)
#get data from charuco
name = 'charuco'
self.file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/GoodPoints_{}.pkl'.format(name)
self.load_points()
Lidar_3D, Image_2D = np.vstack((Lidar_3D, np.array(self.Lidar_3D).reshape(-1,3))), np.vstack((Image_2D, np.array(self.Image_2D).reshape(-1,2)))
print('Lidar_3D:->{}, Image_2D:->{}'.format(np.shape(Lidar_3D), np.shape(Image_2D)))
imgp = np.array([Image_2D], dtype=np.float32).squeeze()
objp = np.array([Lidar_3D], dtype=np.float32).squeeze()
retval, rvec, tvec = cv2.solvePnP(objp, imgp, self.K, self.D, flags=cv2.SOLVEPNP_ITERATIVE)
print('tvec -> {}'.format(tvec.ravel()))
rmat, jac = cv2.Rodrigues(rvec)
q = Quaternion(matrix=rmat)
angles = euler_from_matrix(rmat)
print(angles)
print('euler angles ', [(180.0 / math.pi) * i for i in angles])
print("RMSE in pixel = %f" % self.rmse(objp, imgp, self.K, self.D, rvec, tvec))
result_file = 'combined_extrinsics{}.npz'
with open(result_file, 'w') as f:
f.write("%f %f %f %f %f %f %f" % (q.x, q.y, q.z, q.w, tvec[0], tvec[1], tvec[2]))
print('Combined calibration done!!!')
def computeTransformation(self):
i = 5
l = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/cool/left_{}.png'.format(i)
r = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/cool/right_{}.png'.format(i)
img1 = cv2.imread(l)
img2 = cv2.imread(r)
#sift = cv2.SIFT_create()
sift = cv2.xfeatures2d.SIFT_create()
# find the keypoints and descriptors with SIFT
kp1, des1 = sift.detectAndCompute(img1, None)
kp2, des2 = sift.detectAndCompute(img2, None)
# FLANN parameters
FLANN_INDEX_KDTREE = 1
index_params = dict(algorithm=FLANN_INDEX_KDTREE, trees=5)
search_params = dict(checks=50)
flann = cv2.FlannBasedMatcher(index_params, search_params)
matches = flann.knnMatch(des1, des2, k=2)
pts1 = []
pts2 = []
# ratio test as per Lowe's paper
for i, (m, n) in enumerate(matches):
if m.distance < 0.8 * n.distance:
pts2.append(kp2[m.trainIdx].pt)
pts1.append(kp1[m.queryIdx].pt)
pts1 = np.int32(pts1)
pts2 = np.int32(pts2)
#F, mask = cv2.findFundamentalMat(pts1, pts2, cv2.FM_LMEDS)
E, mask = cv2.findEssentialMat(pts1, pts2, self.K, cv2.RANSAC, 0.999, 1.0, None)
print(E)
points, R, t, mask = cv2.recoverPose(E, pts1, pts2, self.K)
print('R')
print(R)
angles = euler_from_matrix(R)
print('rotation angles: ', [(180.0 / math.pi) * i for i in angles])
print('t')
print(t)
for pt1, pt2 in zip(pts1, pts2):
color = tuple(np.random.randint(0, 255, 3).tolist())
img1 = cv2.circle(img1, tuple(pt1), 5, color, -1)
img2 = cv2.circle(img2, tuple(pt2), 5, color, -1)
cv2.imshow('imgL', cv2.resize(img1, None, fx=.4, fy=.4))
cv2.imshow('imgR', cv2.resize(img2, None, fx=.4, fy=.4))
cv2.waitKey(0)
cv2.destroyAllWindows()
def write_ply(self, fn, verts, colors):
ply_header = '''ply
format ascii 1.0
element vertex %(vert_num)d
property float x
property float y
property float z
property uchar red
property uchar green
property uchar blue
end_header
'''
out_colors = colors.copy()
verts = verts.reshape(-1, 3)
verts = np.hstack([verts, out_colors])
with open(fn, 'wb') as f:
f.write((ply_header % dict(vert_num=len(verts))).encode('utf-8'))
np.savetxt(f, verts, fmt='%f %f %f %d %d %d ')
def view(self):
import glob
import open3d
file = glob.glob('/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/*.ply')
pcda = []
for i, file_path in enumerate(file):
print("{} Load a ply point cloud, print it, and render it".format(file_path))
pcd = open3d.io.read_point_cloud(file_path)
pcda.append(pcd)
open3d.visualization.draw_geometries([pcd])
#o3d.visualization.draw_geometries([pcda[1], pcda[-1]])
def reproject_on_3D(self, useUnique = True):
def readCalibrationExtrinsic():
calib_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/solvePnP_extrinsics{}.npz'.format(
'chess' if self.chess else 'charuco')
calib_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/combined_extrinsics{}.npz'
with open(calib_file, 'r') as f:
data = f.read().split()
#print('data:{}'.format(data))
qx = float(data[0])
qy = float(data[1])
qz = float(data[2])
qw = float(data[3])
tx = float(data[4])
ty = float(data[5])
tz = float(data[6])
q = Quaternion(qw, qx, qy, qz).transformation_matrix
q[0, 3],q[1, 3],q[2, 3] = tx,ty,tz
tvec = q[:3, 3]
rot_mat = q[:3, :3]
#rvec, _ = cv2.Rodrigues(rot_mat)
rvec = rot_mat
print('tvec -> {}'.format(tvec))
return rvec, tvec, q
rvec, tvec, q = readCalibrationExtrinsic()
print(self.K)
print(self.D)
print(rvec)
print(tvec)
i=1
i=11
l = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/cool/left_{}.png'.format(i)
r = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/cool/right_{}.png'.format(i)
imgLeft, imgRight = cv2.imread(l),cv2.imread(r)
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/cool/cloud_{}.npy'.format(i)
_3DPoints = np.array(np.load(cloud_file, mmap_mode='r'), dtype=np.float32)[:, :3]
#Left image--------------------------------------------------------------------------------------------
objPoints_left = _3DPoints.copy()
Z = self.get_z(q, objPoints_left, self.K)
objPoints_left = objPoints_left[Z > 0]
print('objPoints_left:{}'.format(np.shape(objPoints_left)))
points2D_left, _ = cv2.projectPoints(objPoints_left, rvec, tvec, self.K, self.D)
points2D_left = np.squeeze(points2D_left)
print('objPoints_left -> {}, points2D_left -> {}, '.format(np.shape(objPoints_left), np.shape(points2D_left)))
inrange_left = np.where((points2D_left[:, 0] > 0) & (points2D_left[:, 1] > 0) &
(points2D_left[:, 0] < imgLeft.shape[1]-1) & (points2D_left[:, 1] < imgLeft.shape[0]-1))
print('inrange_left : {}'.format(np.shape(inrange_left)))
points2D_left = points2D_left[inrange_left[0]].round().astype('int')
print('points2D_left:{}, '.format(np.shape(points2D_left)))
#Right image ----------------------------------------------------------------------------------------
objPoints_right = _3DPoints.copy()
Z = self.get_z(q, objPoints_right, self.K_left)
objPoints_right = objPoints_right[Z > 0]
T_01 = np.vstack((np.hstack((rvec, tvec[:, np.newaxis])), [0,0,0,1])) #from lidar to right camera
T_12 = np.vstack((np.hstack((self.R, self.T)), [0,0,0,1])) #between cameras
T_final = np.dot(T_12, T_01)
rotation, translation = T_final[:3,:3], T_final[:3,-1]
points2D_right, _ = cv2.projectPoints(objPoints_right, rotation, translation, self.K_left, self.D_left)
points2D_right = np.squeeze(points2D_right)
inrange_right = np.where((points2D_right[:, 0] >= 0) &(points2D_right[:, 1] >= 0) &
(points2D_right[:, 0] < imgRight.shape[1]-1) &(points2D_right[:, 1] < imgRight.shape[0]-1))
print('points2D_right init ->{}'.format(np.shape(points2D_right)))
points2D_right = points2D_right[inrange_right[0]].round().astype('int')
print('points2D_right now ->{}'.format(np.shape(points2D_right)))
#columns=["X", "Y", "Z","intens","ring"]
colors = np.array(np.load(cloud_file, mmap_mode='r'))[:, 3] #
# Color map for the points
colors = colors[inrange_left[0]]
cmap = matplotlib.cm.get_cmap('hsv')
colors = cmap(colors / np.max(colors))
print('colors -> {}, min:{}, max:{}'.format(np.shape(colors), np.min(colors), np.max(colors)))
colorImageLeft,colorImageRight = imgLeft.copy(),imgRight.copy()
fig, axs = plt.subplots(1, 2)
fig.set_size_inches(20, 10.5, forward=True)
axs[0].imshow(imgLeft)
#axs[0].scatter(points2D_left[:,0],points2D_left[:,1], s=.1, c='green')
axs[0].scatter(points2D_left[:,0],points2D_left[:,1], s=.3, c=colors)
axs[0].set_title("Left image")
axs[1].set_title("Right image")
axs[1].imshow(imgRight)
#axs[1].scatter(points2D_right[:,0],points2D_right[:,1], s=.1, c='red')
# Color map for the points
colors = np.array(np.load(cloud_file, mmap_mode='r'))[:, 3] #
colors = colors[inrange_right[0]]
colors = cmap(colors / np.max(colors))
print('points2D_right->{}, colors->{}'.format(np.shape(points2D_right), np.shape(colors)))
axs[1].scatter(points2D_right[:,0],points2D_right[:,1], s=.1, c=colors)
fig.tight_layout()
plt.show()
points_left = objPoints_left[inrange_left[0]]
points_right = objPoints_right[inrange_right[0]]
print('points_left -> {}, colorImageLeft->{}'.format(np.shape(points_left), np.shape(colorImageLeft)))
print('points_right -> {}, colorImageRight->{}'.format(np.shape(points_right), np.shape(colorImageRight)))
colors_left = colorImageLeft[points2D_left[:, 1], points2D_left[:, 0], :]
colors_right = colorImageRight[points2D_right[:, 1], points2D_right[:, 0], :]
print('colors_left -> {}'.format(np.shape(colors_left)))
print('colors_right -> {}'.format(np.shape(colors_right)))
points = np.vstack((points_left,points_right))
color = np.vstack((colors_left,colors_right))
print('points->{}, color->{}'.format(np.shape(points), np.shape(color)))
#plt.show()
#self.write_ply('Lidar_cam.ply', points, color)
#self.view()
#plt.show()
def hsv_to_rgb(h, s, v):
if s == 0.0:
return v, v, v
i = int(h * 6.0)
f = (h * 6.0) - i
p = v * (1.0 - s)
q = v * (1.0 - s * f)
t = v * (1.0 - s * (1.0 - f))
i = i % 6
if i == 0:
return v, t, p
if i == 1:
return q, v, p
if i == 2:
return p, v, t
if i == 3:
return p, q, v
if i == 4:
return t, p, v
if i == 5:
return v, p, q
def filterOcclusion(data):
print('data -> {}'.format(np.shape(data)))
# ---create a pandas Dataframe with X,Y,Z
print('Create a DataFrame')
df = pd.DataFrame(data, columns=['X','Y','Z','X3D','Y3X','Z3D','R','G','B'])
# ---sort it ascend by Z
print('Sort by Z')
df = df.sort_values(by=['Z'],kind='quicksort')
print('Data point after sorting------------------------------')
#---For each point create rectangle centered in current point
xGap,yGap = 20, 50
xOffset, yOffset = int(xGap / 2), int(yGap / 2)
def create_rectange(x,y,depth):
bl = [x-xOffset, y+yOffset] #bottom left
tr = [x+xOffset, y-yOffset] #top right
return [bl,tr,depth]
print('Adding rectangles')
#Rectangles = np.array([create_rectange(x=row['X'],y=row['Y'], depth = row['Z']) for index, row in df.iterrows()])
vfunc = np.vectorize(create_rectange)
Rectangles = vfunc(df['X'].values, df['Y'].values, df['Z'].values)
df['Rectangles'] = Rectangles
#Rectangles = np.asarray(Rectangles.tolist())
#print('Rectangles -> {}'.format(np.shape(Rectangles)))
#bl,tr = np.asarray(Rectangles[:,0].tolist()),np.asarray(Rectangles[:,0].tolist())
# 'bl0 -> {}'.format(np.shape(bl), np.shape(tr))
#df['bl0'] = bl[:,0]
#df['bl1'] = bl[:, 1]
#df['tr0'] = tr[:, 0]
#df['tr1'] = tr[:, 1]
# For each point, project it if it does not belong in prev 5 points
t = .5
def lies_inside(bl, tr, p, dist): #bottom_left, top_right, poin, distance_left, distance_right
if (p[0] > bl[0] and p[0] < tr[0] and p[1] < bl[1] and p[1] > tr[1]):
if abs(p[-1]-dist)>t:
return True
else:
return False
else:
return False
def lies_inside_(bl0,bl1, tr0,tr1, p0,p1,p2, dist): #bottom_left, top_right, poin, distance_left, distance_right
if (p0 > bl0 and p0 < tr0 and p1 < bl1 and p1 > tr1):
if abs(p2-dist)>t:
return True
else:
return False
else:
return False
lies_inside_ = np.vectorize(lies_inside_)
occluded = np.zeros_like(Z, dtype=bool)
projected = np.zeros_like(Z, dtype=bool)
df['occluded'] = occluded
df['projected'] = projected
idx = range(len(df))
df['idx'] = idx
df = df.set_index(['idx'])
# for each point check if the prev 5 points belongs to its rectangle -> if yes-> discard it
print('Compute neighbors')
from sklearn.neighbors import NearestNeighbors
X = np.array(df.iloc[:,0:2])
k=10
print('X -> {}'.format(np.shape(X)))
nbrs = NearestNeighbors(n_neighbors=k, algorithm='ball_tree').fit(X)
distances, indices = nbrs.kneighbors(X)
print('distances -> {}, indices->{}, df->{}'.format(np.shape(distances), np.shape(indices), np.shape(df)))
df['nbrs_indices'] = indices[:,1:].tolist()
print(df.head())
import time
start = time.time()
print('Start projection')
def soc_iter(i):
print(i)
# take the neighbours that are already projected and not occluded
nbrs = df.iloc[i, -1]
prev_points = df.iloc[nbrs] # .query('projected == 1 & occluded == 0') #5.82813405991 s
condition = (prev_points.projected == True) & (prev_points.occluded == False)
prev_points = prev_points[condition] # time = 156.481780052 s
# print('nbrs -> {}, prev_points->{}, condition1->{}'.format(np.shape(nbrs), np.shape(prev_points), np.shape(condition)))
if len(prev_points) > 0:
p = np.array(df.iloc[i, 0:3]) # current_point
# time = 156.481780052 s
Rectangles = prev_points['Rectangles']
occlusion = [lies_inside(bl=point[0], tr=point[1], p=p, dist=point[-1]) for point in Rectangles]
# time = 156.481780052 s
#occlusion = lies_inside_(prev_points['bl0'].values, prev_points['bl1'].values, prev_points['tr0'].values, prev_points['tr1'].values, p[0], p[1], p[-1], prev_points['Z'].values)
if np.any(occlusion):
# print('point {} is occluded'.format(p))
df.loc[i, 'occluded'] = True
df.loc[i, 'projected'] = True
soc_iter_vect = np.vectorize(soc_iter)
N = len(df)
m = np.linspace(start=1, stop=N-1, num=N-1, dtype=int)
print('m->{}, N:{}'.format(np.shape(m),N))
soc_iter_vect(m) # uncomment this
'''for i in range(1,2): #len(df)
print i
# take the neighbours that are already projected and not occluded
nbrs = df.iloc[i, -1]
prev_points = df.iloc[nbrs]#.query('projected == 1 & occluded == 0') #5.82813405991 s
condition = (prev_points.projected == True) & (prev_points.occluded == False)
prev_points = prev_points[condition] #time = 156.481780052 s
#print('nbrs -> {}, prev_points->{}, condition1->{}'.format(np.shape(nbrs), np.shape(prev_points), np.shape(condition)))
if len(prev_points)>0:
p = np.array(df.iloc[i, 0:3]) #current_point
# time = 303.82229900
#occlusion = (p[0] > (prev_points.X-xOffset)) & (p[0] < (prev_points.X+xOffset)) & (p[1] < (prev_points.Y+yOffset)) & (p[1] > (prev_points.Y-yOffset)) & (abs(p[-1] - prev_points.Z) > .3)
#time = 156.481780052 s
Rectangles = prev_points['Rectangles']
occlusion = np.array([lies_inside(bl=point[0], tr=point[1], p=p, dist=point[-1]) for point in Rectangles])
if np.any(occlusion):
#print('point {} is occluded'.format(p))
df.loc[i,'occluded'] = True
df.loc[i, 'projected'] = True'''
#soc_iter_vect(1)
end = time.time()
print('the publish took {}'.format(end - start))
print(df.head())
Points = np.array(df[df['occluded']==False]).squeeze()
good_points = Points[:,0:2].astype('int')
distance = Points[:,2]
_3Dpoint = Points[:,3:6]
_3Dcolor = Points[:, 6:9]
MIN_DISTANCE, MAX_DISTANCE = np.min(distance), np.max(distance)
colours = (distance - MIN_DISTANCE) / (MAX_DISTANCE - MIN_DISTANCE)
colours = np.asarray([np.asarray(hsv_to_rgb( c, np.sqrt(1), 1.0)) for c in colours])
cols = 255 * colours
return good_points, cols,_3Dpoint, _3Dcolor
def filterOcclusion_(data):
print('data -> {}'.format(np.shape(data)))
# ---create a pandas Dataframe with X,Y,Z
print('Create a DataFrame')
df = pd.DataFrame(data, columns=['X','Y','Z','X3D','Y3X','Z3D','R','G','B'])
# ---sort it ascend by Z
print('Sort by Z')
df = df.sort_values(by=['Z'],kind='quicksort')
print('Data point after sorting------------------------------')
#---For each point create rectangle centered in current point
xGap,yGap = 20, 50
xOffset, yOffset = int(xGap / 2), int(yGap / 2)
def create_rectange(x,y,depth):
bl = [x-xOffset, y+yOffset] #bottom left
tr = [x+xOffset, y-yOffset] #top right
return [bl,tr,depth]
print('Adding rectangles')
#Rectangles = np.array([create_rectange(x=row['X'],y=row['Y'], depth = row['Z']) for index, row in df.iterrows()])
vfunc = np.vectorize(create_rectange)
Rectangles = vfunc(df['X'].values, df['Y'].values, df['Z'].values)
df['Rectangles'] = Rectangles
t = .5
def lies_inside(bl, tr, p, dist): #bottom_left, top_right, poin, distance_left, distance_right
if (p[0] > bl[0] and p[0] < tr[0] and p[1] < bl[1] and p[1] > tr[1]):
if abs(p[-1]-dist)>t:
return True
else:
return False
else:
return False
def lies_inside_(bl0,bl1, tr0,tr1, p0,p1,p2, dist): #bottom_left, top_right, poin, distance_left, distance_right
if (p0 > bl0 and p0 < tr0 and p1 < bl1 and p1 > tr1):
if abs(p2-dist)>t:
return True
else:
return False
else:
return False
lies_inside_ = np.vectorize(lies_inside_)
occluded = np.zeros_like(Z, dtype=bool)
projected = np.zeros_like(Z, dtype=bool)
df['occluded'] = occluded
df['projected'] = projected
idx = range(len(df))
df['idx'] = idx
df = df.set_index(['idx'])
# for each point check if the prev 5 points belongs to its rectangle -> if yes-> discard it
print('Compute neighbors')
from sklearn.neighbors import NearestNeighbors
#X = np.array(df.iloc[:,0:2])
X = np.array(df.iloc[:, 1])
nbrs = NearestNeighbors(n_neighbors=3, algorithm='ball_tree').fit(X)
distances, indices = nbrs.kneighbors(X)
print('distances -> {}, indices->{}, df->{}'.format(np.shape(distances), np.shape(indices), np.shape(df)))
df['nbrs_indices'] = indices[:,1:].tolist()
print(df.head())
import time
start = time.time()
print('Start projection')
def soc_iter(i):
print(i)
# take the neighbours that are already projected and not occluded
nbrs = df.iloc[i, -1]
prev_points = df.iloc[nbrs] # .query('projected == 1 & occluded == 0') #5.82813405991 s
condition = (prev_points.projected == True) & (prev_points.occluded == False)
prev_points = prev_points[condition] # time = 156.481780052 s
# print('nbrs -> {}, prev_points->{}, condition1->{}'.format(np.shape(nbrs), np.shape(prev_points), np.shape(condition)))
if len(prev_points) > 0:
p = np.array(df.iloc[i, 0:3]) # current_point
# time = 156.481780052 s
Rectangles = prev_points['Rectangles']
occlusion = [lies_inside(bl=point[0], tr=point[1], p=p, dist=point[-1]) for point in Rectangles]
# time = 156.481780052 s
#occlusion = lies_inside_(prev_points['bl0'].values, prev_points['bl1'].values, prev_points['tr0'].values, prev_points['tr1'].values, p[0], p[1], p[-1], prev_points['Z'].values)
if np.any(occlusion):
# print('point {} is occluded'.format(p))
df.loc[i, 'occluded'] = True
df.loc[i, 'projected'] = True
soc_iter_vect = np.vectorize(soc_iter)
N = len(df)
m = np.linspace(start=1, stop=N-1, num=N-1, dtype=int)
print('m->{}, N:{}'.format(np.shape(m),N))
soc_iter_vect(m) # uncomment this
'''for i in range(1,2): #len(df)
print i
# take the neighbours that are already projected and not occluded
nbrs = df.iloc[i, -1]
prev_points = df.iloc[nbrs]#.query('projected == 1 & occluded == 0') #5.82813405991 s
condition = (prev_points.projected == True) & (prev_points.occluded == False)
prev_points = prev_points[condition] #time = 156.481780052 s
#print('nbrs -> {}, prev_points->{}, condition1->{}'.format(np.shape(nbrs), np.shape(prev_points), np.shape(condition)))
if len(prev_points)>0:
p = np.array(df.iloc[i, 0:3]) #current_point
# time = 303.82229900
#occlusion = (p[0] > (prev_points.X-xOffset)) & (p[0] < (prev_points.X+xOffset)) & (p[1] < (prev_points.Y+yOffset)) & (p[1] > (prev_points.Y-yOffset)) & (abs(p[-1] - prev_points.Z) > .3)
#time = 156.481780052 s
Rectangles = prev_points['Rectangles']
occlusion = np.array([lies_inside(bl=point[0], tr=point[1], p=p, dist=point[-1]) for point in Rectangles])
if np.any(occlusion):
#print('point {} is occluded'.format(p))
df.loc[i,'occluded'] = True
df.loc[i, 'projected'] = True'''
#soc_iter_vect(1)
end = time.time()
print('the publish took {}'.format(end - start))
print(df.head())
Points = np.array(df[df['occluded']==False]).squeeze()
good_points = Points[:,0:2].astype('int')
distance = Points[:,2]
_3Dpoint = Points[:,3:6]
_3Dcolor = Points[:, 6:9]
MIN_DISTANCE, MAX_DISTANCE = np.min(distance), np.max(distance)
colours = (distance - MIN_DISTANCE) / (MAX_DISTANCE - MIN_DISTANCE)
colours = np.asarray([np.asarray(hsv_to_rgb( c, np.sqrt(1), 1.0)) for c in colours])
cols = 255 * colours
return good_points, cols,_3Dpoint, _3Dcolor
#points left
"""Z = np.linalg.norm(points_left, axis=1)[:, np.newaxis]
data = np.hstack((points2D_left, Z)) # N x 3 (x,y,distance)
data = np.hstack((data,points_left)) # N x 6
data = np.hstack((data,colors_left)) # N x 9 (x,y,distance, X,Y,Z,R,G,B)
good_points, cols,_3Dpoint, _3Dcolor = filterOcclusion(data = data)
print('good_points->{}, cols->{}, _3Dpoint->{}, _3Dcolor->{}'.format(
np.shape(good_points), np.shape(cols), np.shape(_3Dpoint), np.shape(_3Dcolor)))
for i in range(len(good_points)):
cv2.circle(imgLeft, tuple(good_points[i]), 2, cols[i], -1)
'''Z = np.linalg.norm(points_right, axis=1)[:, np.newaxis]
data = np.hstack((points2D_right, Z)) # N x 3 (x,y,distance)
data = np.hstack((data,points_right)) # N x 6 (x,y,distance)
data = np.hstack((data,colors_right)) # N x 9 (x,y,distance, X,Y,Z,R,G,B)
_good_points, _cols,_3Dpoint_, _3Dcolor_ = filterOcclusion(data=data)
print('good_points->{}, cols->{}, _3Dpoint->{}'.format(np.shape(good_points), np.shape(cols), np.shape(_3Dpoint)))
for i in range(len(_good_points)):
cv2.circle(imgRight, tuple(_good_points[i]), 2, _cols[i], -1)'''
cv2.imshow('imgLeft', cv2.resize(imgLeft,None, fx=.4,fy=.4))
cv2.imshow('imgRight', cv2.resize(imgRight,None, fx=.4,fy=.4))
cv2.waitKey(0)
cv2.destroyAllWindows()"""
#create a combined pointcloud
#print('_3Dpoint->{}, _3Dpoint_->{}'.format(np.shape(_3Dpoint), np.shape(_3Dpoint_)))
#print('_3Dcolor->{}, _3Dcolor_->{}'.format(np.shape(_3Dcolor), np.shape(_3Dcolor_)))
#points = np.vstack((_3Dpoint, _3Dpoint_))
#color = np.vstack((_3Dcolor, _3Dcolor_))
#points = np.vstack((_3Dpoint_, _3Dpoint))
#color = np.vstack((_3Dcolor_, _3Dcolor))
#points = _3Dpoint #np.vstack((_3Dpoint, _3Dpoint_))
#color = _3Dcolor #np.vstack((_3Dcolor, _3Dcolor_))
#print('points->{}, color->{}'.format(np.shape(points), np.shape(color)))
#self.write_ply('Lidar_cam_filtered.ply', points, color)
#self.view()
plt.show()
print('----------------------------------------------------------------------------------------')
def occlus(t=.3):
# columns=["X", "Y", "Z","intens","ring", time]
_3DPoints = np.array(np.load(cloud_file, mmap_mode='r'), dtype=np.float32) #[:,6] # N x 6
print('_3DPoints -> {}'.format(np.shape(_3DPoints)))
# Left image--------------------------------------------------------------------------------------------
objPoints_left = _3DPoints.copy()
Z = self.get_z(q, objPoints_left[:,:3], self.K)
objPoints_left = objPoints_left[Z > 0]
print('objPoints_left:{}'.format(np.shape(objPoints_left)))
points2D_left, _ = cv2.projectPoints(np.array(objPoints_left[:,:3]).squeeze(), rvec, tvec, self.K, self.D)
points2D_left = np.squeeze(points2D_left)
print('objPoints_left -> {}, points2D_left -> {}, '.format(np.shape(objPoints_left), np.shape(points2D_left)))
inrange_left = np.where((points2D_left[:, 0] > 0) & (points2D_left[:, 1] > 0) &
(points2D_left[:, 0] < imgLeft.shape[1] - 1) & (points2D_left[:, 1] < imgLeft.shape[0] - 1))
points2D_left = points2D_left[inrange_left[0]].round().astype('int')
print('points2D_left:{}, '.format(np.shape(points2D_left)))
points_left = objPoints_left[inrange_left[0]]
colors_left = colorImageLeft[points2D_left[:, 1], points2D_left[:, 0], :]
print('points->{}, color->{}'.format(np.shape(points_left), np.shape(colors_left)))
distance = np.linalg.norm(points_left[:,:3], axis=1)[:, np.newaxis]
MIN_DISTANCE, MAX_DISTANCE = np.min(distance), np.max(distance)
colours = np.asarray((distance - MIN_DISTANCE) / (MAX_DISTANCE - MIN_DISTANCE)).squeeze()
colours = np.asarray([hsv_to_rgb(0.75 * c, np.sqrt(1), 1.0) for c in colours])
cols = 255 * colours
df = pd.DataFrame(data=points_left, columns=["X", "Y", "Z", "intens", "ring", "time"])
df['RGB'] = colors_left.tolist()
df['pixels'] = points2D_left.tolist()
df['distance'] = distance #.round()
df['color'] = cols.tolist()
print(df.head())
gp = df.groupby('ring')
keys = gp.groups.keys()
print('keys -> {}'.format(np.shape(keys)))
_3Dcolor,_3Dpoint = [],[]
k=0
for i in keys:
group = gp.get_group(i).to_numpy() # X,Y,Z,intens,ring,time,RGB,pixels,distance,color
#group = gp.get_group(i+b).to_numpy()
N = len(group)
print('Ring ->{}, {}'.format(i, np.shape(group)))
#take x pixels
pixels = np.concatenate(group[:,7]).reshape(-1,2)
sorted_idx = pixels[:, 0].argsort(kind='mergesort') #sort by x pixel
#sorted_idx = np.linspace(start = 0, stop = N-1, num = N, dtype = int)
pixels = pixels[sorted_idx]
distance = group[sorted_idx,8]
points, colors = np.asarray(group[:, :3]), np.asarray(group[:, 6])
k+=1
collours = []
for j in range(1, N):
d = distance[j] - distance[j - 1]
s = np.sign(d)
if abs(d) > t:
if s < 0:
col, col_ = 'b', (255, 0, 0)
_3Dcolor.append(colors[j])
_3Dpoint.append(points[j])
size = 3
l=2
else:
col, col_ = 'r', (0, 0, 255)
#col, col_ = 'g', (0, 255, 0)
size = 2
l=-1
else:
col, col_ = 'g', (0, 255, 0)
_3Dcolor.append(colors[j])
_3Dpoint.append(points[j])
size = 2
l = -1
collours.append(col)
#cv2.circle(imgLeft, tuple(pixels[j]), size, col_, l)
cv2.circle(imgLeft, tuple(pixels[j]), size, (0,255,0), l)
#plt.scatter(pixels[j,0], distance[j], c=col, s=2)
#plt.plot(pixels[:, 0], distance, c='blue', alpha=0.2)
plt.scatter(pixels[:, 0], distance, c=collours, s=.5)
#if k%3==0:
#plt.grid()
#plt.show()
#distance = group[:,8] #unsorted
#m = np.linspace(start = 0, stop = N-1, num = N, dtype = int)
#plt.scatter(m, distance,s=2)
#plt.grid()
#plt.show()
cv2.imshow('imgLeft', cv2.resize(imgLeft, None, fx=.5, fy=.5))
cv2.waitKey(0)
cv2.imshow('imgLeft', cv2.resize(imgLeft, None, fx=.5, fy=.5))
plt.grid()
plt.show()
cv2.waitKey(0)
print('_3Dpoint -> {}, _3Dcolor->{}'.format(np.shape(_3Dpoint), np.shape(_3Dcolor)))
#self.write_ply('0Lidar_cam_filter2.ply', np.array(_3Dpoint), np.array(_3Dcolor))
#self.view()
cv2.waitKey(0)
cv2.destroyAllWindows()
#occlus()
#self.view()
def DLT(self):
def vgg_rq(S):
S = S.T
Q, U = np.linalg.qr(np.fliplr(np.flipud(S)))
Q = np.fliplr(np.flipud(Q.T))
U = np.fliplr(np.flipud(U.T))
return U, Q
def vgg_KR_from_P(P, noscale=False):
N = P.shape[0]
H = P[:, :N]
K, R = vgg_rq(H)
if not noscale:
K = K / K[N - 1, N - 1]
if K[0, 0] < 0:
D = np.diag(np.hstack((np.array([-1, -1]), np.ones(N - 2))))
K = np.dot(K, D)
R = np.dot(D, R)
t = np.linalg.lstsq(-P[:, 0:N], P[:, -1])[0]
return K, R, t
def camcalibDLT(Xworld, Xim):
# Xworld - (8, 4)
# Xim - (8, 3)
n, d = np.shape(Xworld)
zeros_1x4 = np.zeros((1, 4))
saved_data = []
for j in range(n):
world_point = np.array(Xworld[j]).reshape(1, -1)
image_point = np.array(Xim[j]).reshape(-1, 1)
image2world = image_point.dot(world_point) # (3, 4)
minus_row1 = -(image2world[0]).reshape(1, -1) # (1, 4)
minus_row2 = -(image2world[1]).reshape(1, -1) # (1, 4)
row3 = image2world[2].reshape(1, -1) # (1, 4)
stack = np.stack((zeros_1x4, row3, minus_row2)).reshape(1, -1) # (1, 12)
saved_data.append(stack[0])
stack = np.stack((row3, zeros_1x4, minus_row1)).reshape(1, -1) # (1, 12)
saved_data.append(stack[0])
saved_data = np.array(saved_data)
print('saved_data ', np.shape(saved_data))
_, Sigma, V = np.linalg.svd(saved_data)
P = V[np.argmin(Sigma)].reshape((3, 4))
return P
def GET_DATA():
# get data from chessboard
'''name = 'chess'
self.file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/GoodPoints_{}.pkl'.format(name)
self.load_points()
Lidar_3D, Image_2D, Image_3D = np.array(self.Lidar_3D).reshape(-1, 3), np.array(self.Image_2D).reshape(-1,
2), np.array(
self.Image_3D).reshape(-1, 3)
# get data from charuco'''
name = 'charuco'
self.file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/GoodPoints_{}.pkl'.format(name)
self.load_points()
#Lidar_3D, Image_2D = np.vstack((Lidar_3D, np.array(self.Lidar_3D).reshape(-1, 3))), np.vstack(
# (Image_2D, np.array(self.Image_2D).reshape(-1, 2)))
#print('Lidar_3D:->{}, Image_2D:->{}'.format(np.shape(Lidar_3D), np.shape(Image_2D)))
Lidar_3D, Image_2D, Image_3D = np.array(self.Lidar_3D).reshape(-1, 3), np.array(self.Image_2D).reshape(-1,
2), np.array(
self.Image_3D).reshape(-1, 3)
imgp = np.array([Image_2D], dtype=np.float32).squeeze()
objp = np.array([Lidar_3D], dtype=np.float32).squeeze()
return objp, imgp
_3D_points, _2D_points = GET_DATA()
print('_3D_points->{}, _2D_points->{}'.format(np.shape(_3D_points), np.shape(_2D_points)))
P1 = camcalibDLT(np.hstack((_3D_points, np.ones((len(_3D_points), 1)))),
np.hstack((_2D_points, np.ones((len(_3D_points), 1)))))
print('P1 -> {}'.format(P1))
# Check the results by projecting the world points with the estimated P.
# The projected points should overlap with manually localized points
fig, axes = plt.subplots(nrows=1, ncols=1, figsize=(15, 15))
# plot manually localized
axes.plot(_2D_points[:,0], _2D_points[:,1], 'c+', markersize=10)
# plot projected
pproj1 = np.dot(P1, np.hstack((_3D_points, np.ones((len(_3D_points), 1)))).T)
for i in range(len(_3D_points)):
axes.plot(pproj1[0, i] / pproj1[2, i], pproj1[1, i] / pproj1[2, i], 'rx', markersize=12)
plt.show()
print('intrinsic camera calibration matrices')
K1, R1, t1 = vgg_KR_from_P(P1)
print('K1')
print(K1)
def estimate(self, a1=None,a2=None):
import numpy as np
import numpy.linalg
# Relevant links:
# - http://stackoverflow.com/a/32244818/263061 (solution with scale)
# - "Least-Squares Rigid Motion Using SVD" (no scale but easy proofs and explains how weights could be added)
# Rigidly (+scale) aligns two point clouds with know point-to-point correspondences
# with least-squares error.
# Returns (scale factor c, rotation matrix R, translation vector t) such that
# Q = P*cR + t
# if they align perfectly, or such that
# SUM over point i ( | P_i*cR + t - Q_i |^2 )
# is minimised if they don't align perfectly.
def umeyama(P, Q):
assert P.shape == Q.shape
n, dim = P.shape
centeredP = P - P.mean(axis=0)
centeredQ = Q - Q.mean(axis=0)
C = np.dot(np.transpose(centeredP), centeredQ) / n
V, S, W = np.linalg.svd(C)
d = (np.linalg.det(V) * np.linalg.det(W)) < 0.0
if d:
S[-1] = -S[-1]
V[:, -1] = -V[:, -1]
R = np.dot(V, W)
varP = np.var(a1, axis=0).sum()
c = 1 / varP * np.sum(S) # scale factor
t = Q.mean(axis=0) - P.mean(axis=0).dot(c * R)
return c, R, t
# Testing
np.set_printoptions(precision=3)
if a1 is None and a2 is None:
a1 = np.array([
[0, 0, -1],
[0, 0, 0],
[0, 0, 1],
[0, 1, 0],
[1, 0, 0],
])
a2 = np.array([
[0, 0, 1],
[0, 0, 0],
[0, 0, -1],
[0, 1, 0],
[-1, 0, 0],
])
a2 *= 2 # for testing the scale calculation
a2 += 3 # for testing the translation calculation
c, R, t = umeyama(a1, a2)
print ("R =\n", R)
print ("c =", c)
print ("t =\n", t)
print ("Check: a1*cR + t = a2 is", np.allclose(a1.dot(c * R) + t, a2))
err = ((a1.dot(c * R) + t - a2) ** 2).sum()
print ("Residual error", err)
return c, R, t
def project3D_2D_onImage(self, imgLeft, _3DPoints):
def readCalibrationExtrinsic():
calib_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/solvePnP_extrinsics{}.npz'.format(
'chess' if self.chess else 'charuco')
calib_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/combined_extrinsics{}.npz'
with open(calib_file, 'r') as f:
data = f.read().split()
#print('data:{}'.format(data))
qx = float(data[0])
qy = float(data[1])
qz = float(data[2])
qw = float(data[3])
tx = float(data[4])
ty = float(data[5])
tz = float(data[6])
q = Quaternion(qw, qx, qy, qz).transformation_matrix
q[0, 3],q[1, 3],q[2, 3] = tx,ty,tz
tvec = q[:3, 3]
rot_mat = q[:3, :3]
#rvec, _ = cv2.Rodrigues(rot_mat)
rvec = rot_mat
print('tvec -> {}'.format(tvec))
return rvec, tvec, q
rvec, tvec, q = readCalibrationExtrinsic()
#Left image--------------------------------------------------------------------------------------------
objPoints_left = _3DPoints.copy()
Z = self.get_z(q, objPoints_left, self.K)
objPoints_left = objPoints_left[Z > 0]
points2D_left, _ = cv2.projectPoints(objPoints_left, rvec, tvec, self.K, self.D)
points2D_left = np.squeeze(points2D_left)
inrange_left = np.where((points2D_left[:, 0] > 0) & (points2D_left[:, 1] > 0) &
(points2D_left[:, 0] < imgLeft.shape[1]-1) & (points2D_left[:, 1] < imgLeft.shape[0]-1))
points2D_left = points2D_left[inrange_left[0]].round().astype('int')
for i in range(len(points2D_left)):
cv2.circle(imgLeft, tuple(points2D_left[i]), 2, (0, 255, 0), -1)
return imgLeft
def calibrate_3D_3D(self):
def rot2eul(R):
beta = -np.arcsin(R[2, 0])
alpha = np.arctan2(R[2, 1] / np.cos(beta), R[2, 2] / np.cos(beta))
gamma = np.arctan2(R[1, 0] / np.cos(beta), R[0, 0] / np.cos(beta))
return np.array((np.rad2deg(alpha), np.rad2deg(beta), np.rad2deg(gamma)))
print('3D-3D ========================================================================================')
Lidar_3D = np.array(self.Lidar_3D).reshape(-1, 3)
Image_3D = np.array(self.Image_3D).reshape(-1, 3)
print('Lidar_3D:{}, Image_3D:{}'.format(np.shape(Lidar_3D), np.shape(Image_3D)))
self.fig = plt.figure(figsize=plt.figaspect(1.))
ax1 = self.fig.add_subplot(1, 1, 1, projection='3d')
ax1.set_xlabel('X', fontsize=8)
ax1.set_ylabel('Y', fontsize=8)
ax1.set_zlabel('Z', fontsize=8)
ax1.set_xlim([-3, 3])
ax1.set_ylim([-3, 3])
ax1.set_zlim([-5, 10])
#ax1.set_axis_off()
#plot all data
#ax1.scatter(*Lidar_3D.T, c='blue', label = 'LiDAR points')
#ax1.scatter(*Image_3D.T, s=25, c='red', label = 'Stereo Cam points')
ax1.scatter(*self.Lidar_3D[0].T, c='blue', label='LiDAR points')
ax1.scatter(*self.Image_3D[0].T, s=25, c='red', label='Stereo Cam points')
dist_mat = distance_matrix(self.Image_3D[0],self.Image_3D[0])
print('distance_matrix cam')
print(dist_mat)
dist_mat = distance_matrix(self.Lidar_3D[0], self.Lidar_3D[0])
print('distance_matrix LiDAR')
print(dist_mat)
#ax1.legend()
#plt.show()
#estimate transformation ====================================================
c, R, t = self.estimate(Lidar_3D,Image_3D)
print('t:{}'.format(t))
angles = rot2eul(R)
print('angles:{}'.format(angles))
Camera_points3D = self.Lidar_3D[0].dot(c * R) + t
#Camera_points3D = self.Lidar_3D[0].dot(R) + t
ax1.scatter(*Camera_points3D.T, label='Transformed LiDAR')
ax1.legend()
plt.show()
#project on image ===========================================================
l = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/left/left_4.png'
img = cv2.imread(l)
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/cloud_4.npy'
i = 12
#l = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/cool/left_{}.png'.format(i)
#img = cv2.imread(l)
#cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/cool/cloud_{}.npy'.format(i)
img = cv2.remap(src=img, map1=self.leftMapX, map2=self.leftMapY,interpolation=cv2.INTER_LINEAR, dst=None, borderMode=cv2.BORDER_CONSTANT)
LiDAR_points3D = np.array(np.load(cloud_file, mmap_mode='r'), dtype=np.float32)[:, :3] #
Camera_points3D = LiDAR_points3D.dot(c * R) + t #LiDAR points in camera frame
print('LiDAR_points3D:{}, Camera_points3D:{}'.format(np.shape(LiDAR_points3D), np.shape(Camera_points3D)))
homogen = lambda x: np.array([x[0],x[1],x[2],1])
invhomogen = lambda x: np.array([x[0]/x[-1], x[1]/x[-1]])
cam = np.array([homogen(x) for x in Camera_points3D[:, :3]])
points2D = self.P1.dot(cam.T).T
points2D = np.array([invhomogen(x) for x in points2D[:]])
print('points2D -> {}'.format(np.shape(points2D)))
inrange = np.where(
(points2D[:, 0] >= 0) & (points2D[:, 1] >= 0) &
(points2D[:, 0] < img.shape[1]) & (points2D[:, 1] < img.shape[0])
)
points2D = points2D[inrange[0]].round().astype('int')
for i in range(len(points2D)):
cv2.circle(img, tuple(points2D[i]), 2, (0, 255, 0), -1)
projection_2D_3D = self.project3D_2D_onImage(cv2.imread(l), LiDAR_points3D)
#cv2.imshow('3D-3D estimation', cv2.resize(img,None,fx=.4,fy=.4))
#cv2.imshow('2D-3D estimation', cv2.resize(projection_2D_3D,None,fx=.4,fy=.4))
cv2.putText(img, '3D-3D', (20, 1200), cv2.FONT_HERSHEY_SIMPLEX, 2, (0, 0, 255), 3)
cv2.putText(projection_2D_3D, '3D-2D', (20, 1200), cv2.FONT_HERSHEY_SIMPLEX, 2, (0, 0, 255), 3)
scale = .4
_horizontal = np.hstack(
(cv2.resize(img, None, fx=scale, fy=scale), cv2.resize(projection_2D_3D, None, fx=scale, fy=scale)))
cv2.imshow('Estimation', _horizontal)
cv2.waitKey(0)
cv2.destroyAllWindows()
print('self.P1->{}'.format(np.shape(self.P1)))
print(self.P1)
#-------------------------------------------------------------
l = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/left/left_5.png'
img = cv2.imread(l)
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
ret, corners = cv2.findChessboardCorners(gray, (10, 7), None)
print('ret ->{}'.format(ret))
if ret == True:
corners2 = cv2.cornerSubPix(gray, corners, (11, 11), (-1, -1), self.criteria)
# Find the rotation and translation vectors.
success, rvecs, tvecs, inliers = cv2.solvePnPRansac(self.objp, corners2, self.K, self.D)
print('success->{} rvecs:{}, tvecs:{}, inliers:{}'.format(success, np.shape(rvecs), np.shape(tvecs), np.shape(inliers)))
#print(rvecs)
#print(tvecs)
rvecs,_ = cv2.Rodrigues(rvecs)
print('self.objp->{}'.format(np.shape(self.objp)))
_3Dpoints = self.objp
# project 3D points to image plane
_2Dpoints, jac = cv2.projectPoints(_3Dpoints, rvecs, tvecs, self.K, self.D)
_2Dpoints = np.array(_2Dpoints, dtype=np.float32).squeeze()
print('_2Dpoints -> {}'.format(np.shape(_2Dpoints)))
for i in range(len(_2Dpoints)):
cv2.circle(img, tuple(_2Dpoints[i]), 5, (0, 255, 0), 3)
_3Dpoints = rvecs.dot(_3Dpoints.T)+tvecs
_3Dpoints = _3Dpoints.T
#rvecs, tvecs, _3Dpoints, _2Dpoints
print('_3Dpoints->{}'.format(np.shape(_3Dpoints)))
print(_3Dpoints)
dist_mat = distance_matrix(_3Dpoints,_3Dpoints)
print('dist_mat')
print(dist_mat)
self.fig = plt.figure(figsize=plt.figaspect(1.))
ax1 = self.fig.add_subplot(1, 1, 1, projection='3d')
ax1.scatter(*_3Dpoints.T, label='OpenCV')
#ax1.scatter(*self.Image_3D[0].T, s=25, c='red', label='Stereo Cam points')
ax1.legend()
cv2.imshow('img', cv2.resize(img, None, fx=.4, fy=.4))
cv2.waitKey(0)
plt.show()
cv2.destroyAllWindows()
def doSomePlots(self):
points3D = np.array(self.Lidar_3D).reshape(-1, 3)
points2D = np.array(self.Image_2D).reshape(-1, 2)
print('points3D:{}, points2D:{}'.format(np.shape(points3D), np.shape(points2D)))
def readCalibrationExtrinsic():
calib_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/solvePnP_extrinsics{}.npz'.format(
'chess' if self.chess else 'charuco')
calib_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/combined_extrinsics{}.npz'
with open(calib_file, 'r') as f:
data = f.read().split()
#print('data:{}'.format(data))
qx = float(data[0])
qy = float(data[1])
qz = float(data[2])
qw = float(data[3])
tx = float(data[4])
ty = float(data[5])
tz = float(data[6])
q = Quaternion(qw, qx, qy, qz).transformation_matrix
q[0, 3],q[1, 3],q[2, 3] = tx,ty,tz
tvec = q[:3, 3]
rot_mat = q[:3, :3]
#rvec, _ = cv2.Rodrigues(rot_mat)
rvec = rot_mat
print('tvec -> {}'.format(tvec))
return rvec, tvec, q
#ground truth estimation
rvec, tvec, q = readCalibrationExtrinsic()
ground_truth_rotation = euler_from_matrix(rvec)
ground_truth_translation = np.array(tvec).squeeze()
ground_truth_rotation = np.array([(180.0 / math.pi) * i for i in ground_truth_rotation]).squeeze()
print('ground_truth_rotation: ', ground_truth_rotation)
print('ground_truth_translation: ', ground_truth_translation)
#randomly select 5%, 10%, 15%, ..., 100% of data points
#compute the transformation
#estimate the error between the ground truth
#save for later plot and plot it
percentage = np.linspace(2,100,20)
N = len(points3D) #
Idx = np.arange(0,len(points3D))
print('N -> {}'.format(N))
print('percentage -> {}'.format(percentage))
rot_, tran_ = [], []
for i in range(20):
rot, tran = [], []
for p in percentage:
nr_points = int(p*N/100)
#print(nr_points)
idx_points = np.random.choice(Idx, nr_points)
train_lidar = points3D[idx_points]
train_camera = points2D[idx_points]
imgp = np.array([train_camera], dtype=np.float32).squeeze()
objp = np.array([train_lidar], dtype=np.float32).squeeze()
retval, rvec, tvec = cv2.solvePnP(objp, imgp, self.K, self.D, flags=cv2.SOLVEPNP_ITERATIVE)
rvec,_ = cv2.Rodrigues(rvec)
tvec = np.array(tvec).squeeze()
_rotation = euler_from_matrix(rvec)
_rotation = np.array([(180.0 / math.pi) * i for i in _rotation])
err_rotation = np.abs(_rotation-ground_truth_rotation)
err_translation = np.abs(tvec - ground_truth_translation)
#print('err_rotation->{}, err_translation->{}'.format(np.shape(err_rotation), np.shape(err_translation)))
rot.append(err_rotation)
tran.append(err_translation)
print('rot->{}, tran->{}'.format(np.shape(rot), np.shape(tran)))
rot_.append(rot)
tran_.append(tran)
print('rot_->{}, tran_->{}'.format(np.shape(rot_), np.shape(tran_)))
rot_ = np.mean(rot_, axis=0)
tran_ = np.mean(tran_, axis=0)
print('rot_->{}, tran_->{}'.format(np.shape(rot_), np.shape(tran_)))
ticks = percentage * N / 100
print('ticks -> {}'.format(np.shape(ticks)))
plt.plot(ticks,rot_[:,0], label='X')
plt.plot(ticks,rot_[:, 1], label='Y')
plt.plot(ticks,rot_[:, 2], label='Z')
plt.legend()
plt.xlabel("n-points")
plt.ylabel("mean rotation error (degree)")
plt.xticks(ticks)
plt.show()
plt.plot(ticks,tran_[:, 0], label='X')
plt.plot(ticks,tran_[:, 1], label='Y')
plt.plot(ticks,tran_[:, 2], label='Z')
plt.xlabel("n-points")
plt.ylabel("mean translation error (m)")
plt.legend()
plt.show()
def do_holy_Final_calibration(self,viewData = False):
#get data
self.Lidar_3D = np.array(self.Lidar_3D)[:,-1,:]
self.Image_3D = np.array(self.Image_3D)[:, -1, :]
self.Image_2D = np.array(self.Image_2D)[:, -1, :]
self.Image_2D2 = np.array(self.Image_2D2)[:, -1, :]
print('self.Lidar_3D ->{}, self.Image_3D->{}'.format(np.shape(self.Lidar_3D), np.shape(self.Image_3D)))
points3D_Lidar = np.array(self.Lidar_3D, dtype=np.float32).reshape(-1, 3)
points3D_Camera = np.array(self.Image_3D, dtype=np.float32).reshape(-1, 3)
points2DLeft = np.array(self.Image_2D, dtype=np.float32).reshape(-1, 2)
points2DRight = np.array(self.Image_2D2, dtype=np.float32).reshape(-1, 2)
print('points3D_Lidar:{},points3D_Camera:{}, points2DLeft:{}, points2DRight:{}'.format(np.shape(points3D_Lidar),np.shape(points3D_Camera), np.shape(points2DLeft), np.shape(points2DRight)))
#visualize the data
if viewData:
for i in range(len(self.Lidar_3D)):
fig = plt.figure()
ax0 = fig.add_subplot(2, 2, 1, projection='3d') # Lidar
ax0.set_title('Lidar points')
ax1 = fig.add_subplot(2, 2, 2, projection='3d') # camera 3d
ax1.set_title('Camera 3D')
ax2 = fig.add_subplot(2, 2, 3) # left pixels
ax2.set_title('Left px')
ax3 = fig.add_subplot(2, 2, 4) # right pixels
ax3.set_title('Right px')
print(i)
ax0.clear()
ax0.scatter(*self.Lidar_3D[i].T)
ax0.set_title('Lidar points')
dist_Lidar = distance_matrix(self.Lidar_3D[i],self.Lidar_3D[i])
print('dist_Lidar---------------------------------------------------------')
print(dist_Lidar[0,:11])
ax1.clear()
ax1 = plt.axes(projection='3d')
ax1.scatter(*self.Image_3D[i].T, c='k', marker='v', alpha=1)
ax1.set_title('Camera 3D')
dist_Cam = distance_matrix(self.Image_3D[i], self.Image_3D[i])
print('dist_Cam---------------------------------------------------------')
print(dist_Cam[0,:11])
data = np.array(self.Image_3D).squeeze()
#ax1.plot_wireframe(data[i,:,0], data[i,:,1], data[i,:,2], rstride=1, cstride=1)
ax1.plot_trisurf(data[i,:,0], data[i,:,1], data[i,:,2],
alpha=.4, color='grey', shade=False)
ax1.set_xlabel('X')
ax1.set_ylabel('Y')
ax1.set_zlabel('Z')
ax1.set_xticks([])
ax1.set_yticks([])
ax1.set_zticks([])
ax1.set_axis_off()
plt.show()
ax2.clear()
ax2.scatter(*self.Image_2D[i].T)
ax2.set_title('Left px')
ax3.clear()
ax3.scatter(*self.Image_2D2[i].T)
ax3.set_title('Right px')
plt.show()
break
#Calibrate LiDAR3d-Camera3D
self.fig = plt.figure(figsize=plt.figaspect(1.))
ax1 = self.fig.add_subplot(1, 1, 1, projection='3d')
ax1.set_xlabel('X', fontsize=8)
ax1.set_ylabel('Y', fontsize=8)
ax1.set_zlabel('Z', fontsize=8)
ax1.set_xlim([-3, 3])
ax1.set_ylim([-3, 3])
ax1.set_zlim([-3, 3])
# ax1.set_axis_off()
ax1.scatter(*self.Lidar_3D[0].T, c='blue', label='LiDAR points')
ax1.scatter(*self.Image_3D[0].T, s=25, c='red', label='Stereo Cam points')
#ax1.scatter(*points3D_Lidar.T, c='blue', label='LiDAR points2')
#ax1.scatter(*points3D_Camera.T, s=25, c='red', label='Stereo Cam points2')
# estimate transformation ====================================================
c, R, t = self.estimate(points3D_Lidar, points3D_Camera)
pad = lambda x: np.hstack([x, np.ones((x.shape[0], 1))])
unpad = lambda x: x[:, :-1]
# Solve the least squares problem X * A = Y # to find our transformation matrix A
A, res, rank, s = np.linalg.lstsq(pad(points3D_Lidar), pad(points3D_Camera))
transform = lambda x: unpad(np.dot(pad(x), A))
#Camera_points3D = transform(np.array(self.Lidar_3D[0])) # transformation estimated with LS
#ax1.scatter(*Camera_points3D.T, label='least square sol')
print('t:{}'.format(t))
angles = euler_from_matrix(R)
print('euler angles ', [(180.0 / math.pi) * i for i in angles])
Camera_points3D = self.Lidar_3D[0].dot(c * R) + t
#Camera_points3D = self.Lidar_3D[0].dot(R) + t
ax1.scatter(*Camera_points3D.T, label='SVD')
ax1.legend()
plt.show()
left_src = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/left/left_0.png'
left_src = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/left/left_4.png'
left_img = cv2.imread(left_src)
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/cloud_0.npy'
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/cloud_4.npy'
_3DPoints = np.array(np.load(cloud_file, mmap_mode='r'), dtype=np.float32)[:, :3]
# Left image--------------------------------------------------------------------------------------------
objPoints_left = _3DPoints.copy()
objPoints_left = objPoints_left.dot(c * R) + t
#objPoints_left = np.array(transform(_3DPoints), dtype=np.float32).squeeze() # transformation estimated with LS
#objPoints_left = Camera_points3D
print('objPoints_left ->{}'.format(np.shape(objPoints_left)))
print(objPoints_left)
points2D_left, _ = cv2.projectPoints(objPoints_left, np.eye(3), np.zeros(3), self.K_left, self.D_left)
points2D_left = np.squeeze(points2D_left)
print('objPoints_left -> {}, points2D_left -> {}, '.format(np.shape(objPoints_left), np.shape(points2D_left)))
inrange_left = np.where((points2D_left[:, 0] > 0) & (points2D_left[:, 1] > 0) &
(points2D_left[:, 0] < left_img.shape[1] - 1) & (
points2D_left[:, 1] < left_img.shape[0] - 1))
points2D_left = points2D_left[inrange_left[0]].round().astype('int')
for i in range(len(points2D_left)):
cv2.circle(left_img, tuple(points2D_left[i]), 2, (0, 255, 0), -1)
cv2.imshow('left_img 3D-3D estimation', cv2.resize(left_img, None, fx=.4, fy=.4))
cv2.waitKey(0)
# cv2.destroyAllWindows()
#calibrate Lidar-> left camera
print('Calibrate LiDAR->Left camera===============================================================')
imgp = np.array([points2DLeft], dtype=np.float32).squeeze()
objp = np.array([points3D_Lidar], dtype=np.float32).squeeze()
print('imgp->{},objp->{}'.format(np.shape(imgp), np.shape(objp)))
retval, rvec, tvec = cv2.solvePnP(objp, imgp, self.K, self.D, flags=cv2.SOLVEPNP_ITERATIVE)
#success, rvec, tvec, inliers = cv2.solvePnPRansac(objp,imgp, self.K, self.D,flags=cv2.SOLVEPNP_ITERATIVE)
rvec, tvec = cv2.solvePnPRefineLM(objp, imgp, self.K, self.D, rvec, tvec)
print('rvec is {}=============='.format(rvec))
rvec, jac = cv2.Rodrigues(rvec)
print("RMSE in pixel = %f" % self.rmse(objp, imgp, self.K_left, self.D_left, rvec, tvec))
print("T = ")
print(tvec)
print('Euler angles')
angles = euler_from_matrix(rvec)
self.Lidar_left_tvec = tvec
self.Lidar_left_rvec = rvec
print('euler angles ', [(180.0 / math.pi) * i for i in angles])
#test calibration LiDAR->Left camera
left_src = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/left/left_0.png'
left_src = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/left/left_4.png'
left_img = cv2.imread(left_src)
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/cloud_0.npy'
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/cloud_4.npy'
_3DPoints = np.array(np.load(cloud_file, mmap_mode='r'), dtype=np.float32)[:, :3]
#Left image--------------------------------------------------------------------------------------------
objPoints_left = _3DPoints.copy()
points2D_left, _ = cv2.projectPoints(objPoints_left, rvec, tvec, self.K_right, self.D_right)
points2D_left = np.squeeze(points2D_left)
print('objPoints_left -> {}, points2D_left -> {}, '.format(np.shape(objPoints_left), np.shape(points2D_left)))
inrange_left = np.where((points2D_left[:, 0] > 0) & (points2D_left[:, 1] > 0) &
(points2D_left[:, 0] < left_img.shape[1] - 1) & (points2D_left[:, 1] < left_img.shape[0] - 1))
points2D_left = points2D_left[inrange_left[0]].round().astype('int')
for i in range(len(points2D_left)):
cv2.circle(left_img, tuple(points2D_left[i]), 2, (0,255,0), -1)
q = Quaternion(matrix=rvec)
# tvec[2] = -.59
result_file = 'final_extrinsic.npz'
with open(result_file, 'w') as f:
f.write("%f %f %f %f %f %f %f" % (q.x, q.y, q.z, q.w, tvec[0], tvec[1], tvec[2]))
cv2.imshow('left_img',cv2.resize(left_img,None,fx=.4,fy=.4))
cv2.waitKey(0)
#cv2.destroyAllWindows()
#=======================================================================================
# calibrate Lidar-> right camera
print('Calibrate LiDAR->right camera===============================================================')
imgp = np.array([points2DRight], dtype=np.float32).squeeze()
objp = np.array([points3D_Lidar], dtype=np.float32).squeeze()
print('imgp->{},objp->{}'.format(np.shape(imgp), np.shape(objp)))
retval, rvec, tvec = cv2.solvePnP(objp, imgp, self.K, self.D, flags=cv2.SOLVEPNP_ITERATIVE)
#success, rvec, tvec, inliers = cv2.solvePnPRansac(objp,imgp, self.K, self.D,flags=cv2.SOLVEPNP_ITERATIVE)
rvec, tvec = cv2.solvePnPRefineLM(objp, imgp, self.K, self.D, rvec, tvec)
rmat, jac = cv2.Rodrigues(rvec)
print("RMSE in pixel = %f" % self.rmse(objp, imgp, self.K, self.D, rvec, tvec))
print("T = ")
print(tvec)
print('Euler angles')
self.Lidar_right_tvec = tvec
self.Lidar_right_rvec = rmat
angles = euler_from_matrix(rmat)
print('euler angles ', [(180.0 / math.pi) * i for i in angles])
print("Quaternion = ")
q = Quaternion(matrix=rmat).transformation_matrix
#tvec[2] = -.59
q[0, 3], q[1, 3], q[2, 3] = tvec[0], tvec[1], tvec[2]
# test calibration LiDAR->Left camera
src = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/right/right_0.png'
src = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/right/right_4.png'
img = cv2.imread(src)
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/cloud_0.npy'
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/cloud_4.npy'
_3DPoints = np.array(np.load(cloud_file, mmap_mode='r'), dtype=np.float32)[:, :3]
# Left image--------------------------------------------------------------------------------------------
objPoints_left = _3DPoints.copy()
Z = self.get_z(q, objPoints_left, self.K)
objPoints_left = objPoints_left[Z > 0]
points2D_left, _ = cv2.projectPoints(objPoints_left, rvec, tvec, self.K_right, self.D_right)
points2D_left = np.squeeze(points2D_left)
print('objPoints_left -> {}, points2D_left -> {}, '.format(np.shape(objPoints_left), np.shape(points2D_left)))
inrange_left = np.where((points2D_left[:, 0] > 0) & (points2D_left[:, 1] > 0) &
(points2D_left[:, 0] < left_img.shape[1] - 1) & (
points2D_left[:, 1] < left_img.shape[0] - 1))
points2D_left = points2D_left[inrange_left[0]].round().astype('int')
for i in range(len(points2D_left)):
cv2.circle(img, tuple(points2D_left[i]), 2, (0, 255, 0), -1)
cv2.imshow('right_img', cv2.resize(img, None, fx=.4, fy=.4))
cv2.waitKey(0)
cv2.destroyAllWindows()
print('=============================================================')
#test stereo calibration based on lidar extrinsics
stere_tvec = np.array([-0.96, 0., 0.12])[:, np.newaxis]
angles = euler_from_matrix(self.R)
stereo_angles = np.array([(180.0 / math.pi) * i for i in angles])
print('Stereo camera calibration extrinsics')
print('angles -> {}'.format(stereo_angles))
print('tvec -> {}'.format(stere_tvec.ravel()))
T_lidar_leftCam = np.vstack((np.hstack((self.Lidar_left_rvec, self.Lidar_left_tvec)), np.array([0, 0, 0, 1])[:,np.newaxis].T))
T_lidar_rightCam = np.vstack((np.hstack((self.Lidar_right_rvec, self.Lidar_right_tvec)), np.array([0, 0, 0, 1])[:,np.newaxis].T))
#T left cam to right cam is T1^-1 * T2
T_leftCam_rightCam = np.dot(T_lidar_rightCam,np.linalg.inv(T_lidar_leftCam))
rvec, tvec = T_leftCam_rightCam[:3, :3], T_leftCam_rightCam[:3, -1]
angles = euler_from_matrix(rvec)
angles = np.array([(180.0 / math.pi) * i for i in angles])
print('')
print('Lidar based camera calibration extrinsics')
print('angles -> {}'.format(angles))
print('tvec -> {}'.format(tvec))
def do_holy_Final_calibration2(self):
def hsv_to_rgb(h, s, v):
if s == 0.0:
return v, v, v
i = int(h * 6.0)
f = (h * 6.0) - i
p = v * (1.0 - s)
q = v * (1.0 - s * f)
t = v * (1.0 - s * (1.0 - f))
i = i % 6
if i == 0:
return v, t, p
if i == 1:
return q, v, p
if i == 2:
return p, v, t
if i == 3:
return p, q, v
if i == 4:
return t, p, v
if i == 5:
return v, p, q
def filterOcclusion(data):
print('data -> {}'.format(np.shape(data)))
# ---create a pandas Dataframe with X,Y,Z
print('Create a DataFrame')
df = pd.DataFrame(data, columns=['X','Y','Z','X3D','Y3X','Z3D','R','G','B'])
# ---sort it ascend by Z
print('Sort by Z')
df = df.sort_values(by=['Z'],kind='quicksort')
print('Data point after sorting------------------------------')
#---For each point create rectangle centered in current point
xGap,yGap = 20, 50
xOffset, yOffset = int(xGap / 2), int(yGap / 2)
def create_rectange(x,y,depth):
bl = [x-xOffset, y+yOffset] #bottom left
tr = [x+xOffset, y-yOffset] #top right
return [bl,tr,depth]
print('Adding rectangles')
#Rectangles = np.array([create_rectange(x=row['X'],y=row['Y'], depth = row['Z']) for index, row in df.iterrows()])
vfunc = np.vectorize(create_rectange)
Rectangles = vfunc(df['X'].values, df['Y'].values, df['Z'].values)
df['Rectangles'] = Rectangles
#Rectangles = np.asarray(Rectangles.tolist())
#print('Rectangles -> {}'.format(np.shape(Rectangles)))
#bl,tr = np.asarray(Rectangles[:,0].tolist()),np.asarray(Rectangles[:,0].tolist())
# 'bl0 -> {}'.format(np.shape(bl), np.shape(tr))
#df['bl0'] = bl[:,0]
#df['bl1'] = bl[:, 1]
#df['tr0'] = tr[:, 0]
#df['tr1'] = tr[:, 1]
# For each point, project it if it does not belong in prev 5 points
t = .5
def lies_inside(bl, tr, p, dist): #bottom_left, top_right, poin, distance_left, distance_right
if (p[0] > bl[0] and p[0] < tr[0] and p[1] < bl[1] and p[1] > tr[1]):
if abs(p[-1]-dist)>t:
return True
else:
return False
else:
return False
def lies_inside_(bl0,bl1, tr0,tr1, p0,p1,p2, dist): #bottom_left, top_right, poin, distance_left, distance_right
if (p0 > bl0 and p0 < tr0 and p1 < bl1 and p1 > tr1):
if abs(p2-dist)>t:
return True
else:
return False
else:
return False
lies_inside_ = np.vectorize(lies_inside_)
occluded = np.zeros_like(Z, dtype=bool)
projected = np.zeros_like(Z, dtype=bool)
df['occluded'] = occluded
df['projected'] = projected
idx = range(len(df))
df['idx'] = idx
df = df.set_index(['idx'])
# for each point check if the prev 5 points belongs to its rectangle -> if yes-> discard it
print('Compute neighbors')
from sklearn.neighbors import NearestNeighbors
X = np.array(df.iloc[:,0:2])
k=10
print('X -> {}'.format(np.shape(X)))
nbrs = NearestNeighbors(n_neighbors=k, algorithm='ball_tree').fit(X)
distances, indices = nbrs.kneighbors(X)
print('distances -> {}, indices->{}, df->{}'.format(np.shape(distances), np.shape(indices), np.shape(df)))
df['nbrs_indices'] = indices[:,1:].tolist()
print(df.head())
import time
start = time.time()
print('Start projection')
def soc_iter(i):
print(i)
# take the neighbours that are already projected and not occluded
nbrs = df.iloc[i, -1]
prev_points = df.iloc[nbrs] # .query('projected == 1 & occluded == 0') #5.82813405991 s
condition = (prev_points.projected == True) & (prev_points.occluded == False)
prev_points = prev_points[condition] # time = 156.481780052 s
# print('nbrs -> {}, prev_points->{}, condition1->{}'.format(np.shape(nbrs), np.shape(prev_points), np.shape(condition)))
if len(prev_points) > 0:
p = np.array(df.iloc[i, 0:3]) # current_point
# time = 156.481780052 s
Rectangles = prev_points['Rectangles']
occlusion = [lies_inside(bl=point[0], tr=point[1], p=p, dist=point[-1]) for point in Rectangles]
# time = 156.481780052 s
#occlusion = lies_inside_(prev_points['bl0'].values, prev_points['bl1'].values, prev_points['tr0'].values, prev_points['tr1'].values, p[0], p[1], p[-1], prev_points['Z'].values)
if np.any(occlusion):
# print('point {} is occluded'.format(p))
df.loc[i, 'occluded'] = True
df.loc[i, 'projected'] = True
soc_iter_vect = np.vectorize(soc_iter)
N = len(df)
m = np.linspace(start=1, stop=N-1, num=N-1, dtype=int)
print('m->{}, N:{}'.format(np.shape(m),N))
soc_iter_vect(m) # uncomment this
'''for i in range(1,2): #len(df)
print i
# take the neighbours that are already projected and not occluded
nbrs = df.iloc[i, -1]
prev_points = df.iloc[nbrs]#.query('projected == 1 & occluded == 0') #5.82813405991 s
condition = (prev_points.projected == True) & (prev_points.occluded == False)
prev_points = prev_points[condition] #time = 156.481780052 s
#print('nbrs -> {}, prev_points->{}, condition1->{}'.format(np.shape(nbrs), np.shape(prev_points), np.shape(condition)))
if len(prev_points)>0:
p = np.array(df.iloc[i, 0:3]) #current_point
# time = 303.82229900
#occlusion = (p[0] > (prev_points.X-xOffset)) & (p[0] < (prev_points.X+xOffset)) & (p[1] < (prev_points.Y+yOffset)) & (p[1] > (prev_points.Y-yOffset)) & (abs(p[-1] - prev_points.Z) > .3)
#time = 156.481780052 s
Rectangles = prev_points['Rectangles']
occlusion = np.array([lies_inside(bl=point[0], tr=point[1], p=p, dist=point[-1]) for point in Rectangles])
if np.any(occlusion):
#print('point {} is occluded'.format(p))
df.loc[i,'occluded'] = True
df.loc[i, 'projected'] = True'''
#soc_iter_vect(1)
end = time.time()
print('the publish took {}'.format(end - start))
print(df.head())
Points = np.array(df[df['occluded']==False]).squeeze()
good_points = Points[:,0:2].astype('int')
distance = Points[:,2]
_3Dpoint = Points[:,3:6]
_3Dcolor = Points[:, 6:9]
MIN_DISTANCE, MAX_DISTANCE = np.min(distance), np.max(distance)
colours = (distance - MIN_DISTANCE) / (MAX_DISTANCE - MIN_DISTANCE)
colours = np.asarray([np.asarray(hsv_to_rgb( c, np.sqrt(1), 1.0)) for c in colours])
cols = 255 * colours
return good_points, cols,_3Dpoint, _3Dcolor
#get data
#use only the center
#self.Lidar_3D = np.array(self.Lidar_3D)[:,-1,:]
#self.Image_2D = np.array(self.Image_2D)[:,-1, :]
#self.Lidar_3D = np.array(self.Lidar_3D)[:, :4, :]
#self.Image_2D = np.array(self.Image_2D)[:, :4, :]
self.Lidar_3D = np.array(self.Lidar_3D)[:, :, :]
self.Image_2D = np.array(self.Image_2D)[:, :, :]
print('self.Lidar_3D ->{}, self.Image_2D->{}'.format(np.shape(self.Lidar_3D), np.shape(self.Image_2D)))
points3D_Lidar = np.array(self.Lidar_3D, dtype=np.float32).reshape(-1, 3)
points2DLeft = np.array(self.Image_2D, dtype=np.float32).reshape(-1, 2)
print('points3D_Lidar->{}, points2DLeft->{}'.format(np.shape(points3D_Lidar), np.shape(points2DLeft)))
#calibrate Lidar-> left camera
print('Calibrate LiDAR->Left camera===============================================================')
imgp = np.array([points2DLeft], dtype=np.float32).squeeze()
objp = np.array([points3D_Lidar], dtype=np.float32).squeeze()
print('imgp->{},objp->{}'.format(np.shape(imgp), np.shape(objp)))
#retval, rvec, tvec = cv2.solvePnP(objp, imgp, self.K, self.D, flags=cv2.SOLVEPNP_ITERATIVE)
retval, rvec, tvec, inliers = cv2.solvePnPRansac(objp,imgp, self.K, self.D,flags=cv2.SOLVEPNP_ITERATIVE)
#rvec, tvec = cv2.solvePnPRefineLM(objp, imgp, self.K, self.D, rvec, tvec)
print('rvec is {}=============='.format(rvec))
print("T = ")
print(tvec)
tvec = np.array([[0.73698884], [1.3237537], [-0.74695895]])
#tvec = np.array([[0.673698884], [1.3237537], [-0.4]])
rvec, jac = cv2.Rodrigues(rvec)
q = Quaternion(matrix=rvec).transformation_matrix
#test calibration LiDAR->Left camera
left_src = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/left/left_0.png'
left_src = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/left/left_4.png'
i = 11
left_src = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/cool/left_{}.png'.format(i)
left_src = '/home/eugeniu/cool/left_100.png'
left_img = cv2.imread(left_src)
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/chess/cloud_0.npy'
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/data/charuco/cloud_4.npy'
cloud_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/cool/cloud_{}.npy'.format(i)
cloud_file = '/home/eugeniu/cool/cloud_100.npy'
_3DPoints = np.array(np.load(cloud_file, mmap_mode='r'), dtype=np.float32)[:, :3]
_3DPoints = np.dot(_3DPoints, Rot_matrix)
print('_3DPoints - > {}'.format(np.shape(_3DPoints)))
distance = np.linalg.norm(_3DPoints, axis=1)[:, np.newaxis]
MIN_DISTANCE, MAX_DISTANCE = np.min(distance), np.max(distance)
colours = (distance - MIN_DISTANCE) / (MAX_DISTANCE - MIN_DISTANCE)
colours = np.asarray([hsv_to_rgb(c[0], np.sqrt(1), 1.0) for c in colours])
cols = 255 * colours
print('distance - > {}, cols ->{}'.format(np.shape(distance), np.shape(cols)))
#Left image--------------------------------------------------------------------------------------------
objPoints_left = _3DPoints.copy()
Z = self.get_z(q, objPoints_left, self.K_left)
objPoints_left = objPoints_left[Z > 0]
points2D_left, _ = cv2.projectPoints(objPoints_left, rvec, tvec, self.K_right, self.D_right)
points2D_left = np.squeeze(points2D_left)
print('objPoints_left -> {}, points2D_left -> {}, '.format(np.shape(objPoints_left), np.shape(points2D_left)))
inrange_left = np.where((points2D_left[:, 0] > 0) & (points2D_left[:, 1] > 0) &
(points2D_left[:, 0] < left_img.shape[1] - 1) & (points2D_left[:, 1] < left_img.shape[0] - 1))
points2D_left = points2D_left[inrange_left[0]].round().astype('int')
colours = cols[inrange_left[0]]
objPoints_left = objPoints_left[inrange_left[0]]
for i in range(len(points2D_left)):
cv2.circle(left_img, tuple(points2D_left[i]), 2, colours[i], -1)
'''Z = distance[inrange_left[0]]
data = np.hstack((points2D_left, Z)) # N x 3 (x,y,distance)
data = np.hstack((data,objPoints_left)) # N x 6
colorImageLeft = cv2.imread(left_src)
colors_left = colorImageLeft[points2D_left[:, 1], points2D_left[:, 0], :]
data = np.hstack((data,colors_left)) # N x 9 (x,y,distance, X,Y,Z,R,G,B)
good_points, cols,_3Dpoint, _3Dcolor = filterOcclusion(data = data)
print('good_points->{}, cols->{}, _3Dpoint->{}, _3Dcolor->{}'.format(np.shape(good_points), np.shape(cols), np.shape(_3Dpoint), np.shape(_3Dcolor)))
for i in range(len(good_points)):
cv2.circle(left_img, tuple(good_points[i]), 2, cols[i], -1)'''
cv2.imshow('left_img',cv2.resize(left_img,None,fx=.4,fy=.4))
cv2.waitKey(0)
#points = _3Dpoint #np.vstack((_3Dpoint, _3Dpoint_))
#color = _3Dcolor #np.vstack((_3Dcolor, _3Dcolor_))
#print('points->{}, color->{}'.format(np.shape(points), np.shape(color)))
#self.write_ply('Lidar_cam_filtered_compareCamera.ply', points, color)
#self.view()
cv2.destroyAllWindows()
def filter_for_video_(self):
def hsv_to_rgb(h, s, v):
if s == 0.0:
return v, v, v
i = int(h * 6.0)
f = (h * 6.0) - i
p = v * (1.0 - s)
q = v * (1.0 - s * f)
t = v * (1.0 - s * (1.0 - f))
i = i % 6
if i == 0:
return v, t, p
if i == 1:
return q, v, p
if i == 2:
return p, v, t
if i == 3:
return p, q, v
if i == 4:
return t, p, v
if i == 5:
return v, p, q
import time
from sklearn.neighbors import NearestNeighbors
#from numba import jit
#init 191.438015938 s
def filterOcclusion(data):
start = time.time()
print('data -> {}'.format(np.shape(data)))
# ---create a pandas Dataframe with X,Y,Z
print('Create a DataFrame')
df = pd.DataFrame(data, columns=['X','Y','Z','X3D','Y3X','Z3D','R','G','B'])
# ---sort it ascend by Z
print('Sort by Z')
df = df.sort_values(by=['Z'],kind='quicksort')
print('Data point after sorting------------------------------')
#---For each point create rectangle centered in current point
xGap,yGap = 70, 150
xGap, yGap = 100, 200
xOffset, yOffset = int(xGap / 2), int(yGap / 2)
def create_rectange(x,y,depth):
bl = [x-xOffset, y+yOffset] #bottom left
tr = [x+xOffset, y-yOffset] #top right
return [bl,tr,depth]
print('Adding rectangles')
#Rectangles = np.array([create_rectange(x=row['X'],y=row['Y'], depth = row['Z']) for index, row in df.iterrows()])
vfunc = np.vectorize(create_rectange)
Rectangles = vfunc(df['X'].values, df['Y'].values, df['Z'].values)
df['Rectangles'] = Rectangles
t = .5
def lies_inside(bl, tr, p, dist): #bottom_left, top_right, poin, distance_left, distance_right
if (p[0] > bl[0] and p[0] < tr[0] and p[1] < bl[1] and p[1] > tr[1]):
if abs(p[-1]-dist)>t:
return True
else:
return False
else:
return False
occluded = np.zeros_like(Z, dtype=bool)
projected = np.zeros_like(Z, dtype=bool)
df['occluded'] = occluded
df['projected'] = projected
idx = range(len(df))
df['idx'] = idx
df = df.set_index(['idx'])
# for each point check if the prev 5 points belongs to its rectangle -> if yes-> discard it
print('Compute neighbors')
X = np.array(df.iloc[:,0:2])
k=15
print('X -> {}'.format(np.shape(X)))
nbrs = NearestNeighbors(n_neighbors=k, algorithm='ball_tree').fit(X)
distances, indices = nbrs.kneighbors(X)
print('distances -> {}, indices->{}, df->{}'.format(np.shape(distances), np.shape(indices), np.shape(df)))
df['nbrs_indices'] = indices[:,1:].tolist()
print(df.head())
print('Start projection')
#@jit(nopython=True)
def soc_iter(i):
#print(i)
# take the neighbours that are already projected and not occluded
nbrs = df.iloc[i, -1]
prev_points = df.iloc[nbrs] # .query('projected == 1 & occluded == 0') #5.82813405991 s
condition = (prev_points.projected == True) & (prev_points.occluded == False)
prev_points = prev_points[condition] # time = 156.481780052 s
# print('nbrs -> {}, prev_points->{}, condition1->{}'.format(np.shape(nbrs), np.shape(prev_points), np.shape(condition)))
if len(prev_points) > 0:
p = np.array(df.iloc[i, 0:3]) # current_point
# time = 156.481780052 s
Rectangles = prev_points['Rectangles']
occlusion = [lies_inside(bl=point[0], tr=point[1], p=p, dist=point[-1]) for point in Rectangles]
# time = 156.481780052 s
#occlusion = lies_inside_(prev_points['bl0'].values, prev_points['bl1'].values, prev_points['tr0'].values, prev_points['tr1'].values, p[0], p[1], p[-1], prev_points['Z'].values)
if np.any(occlusion):
# print('point {} is occluded'.format(p))
df.loc[i, 'occluded'] = True
df.loc[i, 'projected'] = True
#soc_iter_vect = np.vectorize(soc_iter)
N = len(df)
m = np.linspace(start=1, stop=N-1, num=N-1, dtype=int)
print('m->{}, N:{}'.format(np.shape(m),N))
#soc_iter_vect(m) # uncomment this
for i in m:
soc_iter(i)
print(df.head())
Points = np.array(df[df['occluded']==False]).squeeze()
good_points = Points[:,0:2].astype('int')
distance = Points[:,2]
_3Dpoint = Points[:,3:6]
_3Dcolor = Points[:, 6:9]
MIN_DISTANCE, MAX_DISTANCE = np.min(distance), np.max(distance)
MIN_DISTANCE, MAX_DISTANCE = 1.5, 60
colours = (distance - MIN_DISTANCE) / (MAX_DISTANCE - MIN_DISTANCE)
colours = np.asarray([np.asarray(hsv_to_rgb( c, np.sqrt(1), 1.0)) for c in colours])
cols = 255 * colours
end = time.time()
print('the publish took {}'.format(end - start))
return good_points, cols,_3Dpoint, _3Dcolor
def readCalibrationExtrinsic():
self.chess = True
calib_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/solvePnP_extrinsics{}.npz'.format(
'chess' if self.chess else 'charuco')
#calib_file = '/home/eugeniu/catkin_ws/src/testNode/CAMERA_CALIBRATION/combined_extrinsics{}.npz'
with open(calib_file, 'r') as f:
data = f.read().split()
#print('data:{}'.format(data))
qx = float(data[0])
qy = float(data[1])
qz = float(data[2])
qw = float(data[3])
tx = float(data[4])
ty = float(data[5])
tz = float(data[6])
q = Quaternion(qw, qx, qy, qz).transformation_matrix
q[0, 3],q[1, 3],q[2, 3] = tx,ty,tz
tvec = q[:3, 3]
rot_mat = q[:3, :3]
#rvec, _ = cv2.Rodrigues(rot_mat)
rvec = rot_mat
#tvec = np.array([ 0.673738, -0.428458, -0.650393])
#tvec = np.array([0.69, -0.428458, -0.650393])
#tvec = np.array([0.71, -0.428458, -0.650393])
#rvec = np.array([np.deg2rad(90.06), np.deg2rad(-8.5), np.deg2rad(0.71)])
rvec = np.array([np.deg2rad(90.3), np.deg2rad(-8.5), np.deg2rad(0.71)])
rvec = eulerAnglesToRotationMatrix2(rvec)
print('tvec -> {}'.format(tvec))
return rvec, tvec, q
rvec, tvec, q = readCalibrationExtrinsic()
files = glob.glob('/home/eugeniu/myFolder/*png')
currentFile = -1# 27
for currentFile_, fil in enumerate(files):
currentFile += 1
print('current image {}'.format(currentFile))
img_path = '/home/eugeniu/myFolder/left_{}.png'.format(currentFile)
pcl_path = '/home/eugeniu/myFolder/cloud_{}.npy'.format(currentFile)
img = cv2.imread(img_path)
_3DPoints = np.array(np.load(pcl_path, mmap_mode='r'), dtype=np.float32)[:, :3]
objPoints_left = _3DPoints.copy()
Z = self.get_z(q, objPoints_left, self.K)
objPoints_left = objPoints_left[Z > 0]
print('objPoints_left:{}'.format(np.shape(objPoints_left)))
points2D_left, _ = cv2.projectPoints(objPoints_left, rvec, tvec, self.K, self.D)
points2D_left = np.squeeze(points2D_left)
print('objPoints_left -> {}, points2D_left -> {}, '.format(np.shape(objPoints_left),
np.shape(points2D_left)))
inrange_left = np.where((points2D_left[:, 0] > 0) & (points2D_left[:, 1] > 0) &
(points2D_left[:, 0] < img.shape[1] - 1) & (
points2D_left[:, 1] < img.shape[0] - 1))
print('inrange_left : {}'.format(np.shape(inrange_left)))
points2D_left = points2D_left[inrange_left[0]].round().astype('int')
print('points2D_left:{}, '.format(np.shape(points2D_left)))
#for i, point in enumerate(points2D_left):
# cv2.circle(img, (point[0],point[1]), 2, (0,255,0), -1)
#cv2.imshow('img',cv2.resize(img,None,fx=.4,fy=.4))
#cv2.waitKey(0)
# columns=["X", "Y", "Z","intens","ring"]
colors = np.array(np.load(pcl_path, mmap_mode='r'))[:, 4] #
# Color map for the points
colors = colors[inrange_left[0]]
cmap = matplotlib.cm.get_cmap('hsv')
colors = cmap(colors / np.max(colors))
print('colors -> {}, min:{}, max:{}'.format(np.shape(colors), np.min(colors), np.max(colors)))
colorImageLeft = img.copy()
points_left = objPoints_left[inrange_left[0]]
print('points_left -> {}, colorImageLeft->{}'.format(np.shape(points_left), np.shape(colorImageLeft)))
colors_left = colorImageLeft[points2D_left[:, 1], points2D_left[:, 0], :]
print('colors_left -> {}'.format(np.shape(colors_left)))
Z = np.linalg.norm(points_left, axis=1)[:, np.newaxis]
data = np.hstack((points2D_left, Z)) # N x 3 (x,y,distance)
data = np.hstack((data, points_left)) # N x 6
data = np.hstack((data, colors_left)) # N x 9 (x,y,distance, X,Y,Z,R,G,B)
good_points, cols, _3Dpoint, _3Dcolor = filterOcclusion(data=data)
print('good_points->{}, cols->{}, _3Dpoint->{}, _3Dcolor->{}'.format(
np.shape(good_points), np.shape(cols), np.shape(_3Dpoint), np.shape(_3Dcolor)))
for i in range(len(good_points)):
cv2.circle(img, tuple(good_points[i]), 2, cols[i], -1)
cv2.imshow('img ',img)
cv2.waitKey(0)
cv2.destroyAllWindows()
#cv2.imwrite('/home/eugeniu/myFolder/img_synchro_{}.png'.format(currentFile), img)
#with open('/home/eugeniu/myFolder/good_points_{}.npy'.format(currentFile), 'wb') as f:
# np.save(f, good_points)
#with open('/home/eugeniu/myFolder/cols_{}.npy'.format(currentFile), 'wb') as f:
# np.save(f, cols)
#with open('/home/eugeniu/myFolder/_3Dpoint_{}.npy'.format(currentFile), 'wb') as f:
# np.save(f, _3Dpoint)
#with open('/home/eugeniu/myFolder/_3Dcolor_{}.npy'.format(currentFile), 'wb') as f:
# np.save(f, _3Dcolor)
break
def filter_for_video(self):
def hsv_to_rgb(h, s, v):
if s == 0.0:
return v, v, v
i = int(h * 6.0)
f = (h * 6.0) - i
p = v * (1.0 - s)
q = v * (1.0 - s * f)
t = v * (1.0 - s * (1.0 - f))
i = i % 6
if i == 0:
return v, t, p
if i == 1:
return q, v, p
if i == 2:
return p, v, t
if i == 3:
return p, q, v
if i == 4:
return t, p, v
if i == 5:
return v, p, q
import time
from sklearn.neighbors import NearestNeighbors
#from numba import jit
def filterOcclusion(data):
print('data -> {}'.format(np.shape(data)))
start = time.time()
# ---create a pandas Dataframe with X,Y,Z
print('Create a DataFrame')
df = pd.DataFrame(data, columns=['X','Y','Z','X3D','Y3X','Z3D','R','G','B'])
# ---sort it ascend by Z
print('Sort by Z')
df = df.sort_values(by=['Z'],kind='quicksort')
print('Data point after sorting------------------------------')
#---For each point create rectangle centered in current point
xGap,yGap = 70, 150
xGap, yGap = 100, 200
xOffset, yOffset = int(xGap / 2), int(yGap / 2)
def create_rectange(x,y,depth):
bl = [x-xOffset, y+yOffset] #bottom left
tr = [x+xOffset, y-yOffset] #top right
return [bl,tr,depth]
print('Adding rectangles')
#Rectangles = np.array([create_rectange(x=row['X'],y=row['Y'], depth = row['Z']) for index, row in df.iterrows()])
vfunc = np.vectorize(create_rectange)
Rectangles = vfunc(df['X'].values, df['Y'].values, df['Z'].values)
df['Rectangles'] = Rectangles
t = .5
def lies_inside(bl, tr, p, dist): #bottom_left, top_right, poin, distance_left, distance_right
if (p[0] > bl[0] and p[0] < tr[0] and p[1] < bl[1] and p[1] > tr[1]):
if abs(p[-1]-dist)>t:
return True
return False
occluded = np.zeros_like(Z, dtype=bool)
projected = np.zeros_like(Z, dtype=bool)
df['occluded'] = occluded
df['projected'] = projected
idx = range(len(df))
df['idx'] = idx
df = df.set_index(['idx'])
# for each point check if the prev 5 points belongs to its rectangle -> if yes-> discard it
print('Compute neighbors')
X = np.array(df.iloc[:,0:2])
k=15
print('X -> {}'.format(np.shape(X)))
nbrs = NearestNeighbors(n_neighbors=k, algorithm='ball_tree').fit(X)
distances, indices = nbrs.kneighbors(X)
print('distances -> {}, indices->{}, df->{}'.format(np.shape(distances), np.shape(indices), np.shape(df)))
df['nbrs_indices'] = indices[:,1:].tolist()
#print(df.head())
print('Start projection')
#print(df.columns)
#from numba import njit
#
#list_idx = np.array(['X', 'Y', 'Z', 'X3D', 'Y3X', 'Z3D', 'R', 'G', 'B', 'Rectangles','occluded', 'projected', 'nbrs_indices'])
df_numpy = np.array(df.to_numpy()).squeeze() #(45783, 13)
print('df_numpy -> {}, df -> {}, df_numpy type is {}'.format(np.shape(df_numpy), | np.shape(df) | numpy.shape |
"""
SORT: A Simple, Online and Realtime Tracker
Copyright (C) 2016 <NAME> <EMAIL>
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
"""
from __future__ import print_function
import numpy as np
from filterpy.kalman import KalmanFilter
from numba import jit
from scipy.optimize import linear_sum_assignment
@jit(forceobj=True)
def iou(bbox_test, bbox_gt):
"""Computes IOU between two bboxes in the form [x1, y1, x2, y2]
"""
x1, y1 = np.maximum(bbox_test[0:2], bbox_gt[0:2])
x2, y2 = np.minimum(bbox_test[2:4], bbox_gt[2:4])
w = np.maximum(0, x2-x1)
h = np.maximum(0, y2-y1)
area = lambda x: (x[2]-x[0])*(x[3]-x[1])
union = w * h
intersection = area(bbox_test)+area(bbox_gt)-union
return union / intersection
def convert_bbox_to_z(bbox):
"""Convert bbox (x1, y1, x2, y2) to KF.z (x, y, s, r)
x, y is the center of the box
s is the scale/ area
r is the aspect ratio
"""
x1, y1, x2, y2 = bbox[:4]
w, h = (x2 - x1), (y2 - y1)
x, y = (x1 + w/2), (y1 + h/2)
s, r = (w * h), (w / float(h))
return np.array([x, y, s, r]).reshape((4, 1))
def convert_x_to_bbox(x, score=None):
"""Convert KF.x (x, y, s, r) to bbox (x1, y1, x2, y2)
x1, y1 is the top left
x2, y2 is the bottom right
"""
w = np.sqrt(x[2] * x[3])
h = x[2] / w
x1, y1, x2, y2 = (x[0] - w/2), (x[1] - h/2), (x[0] + w/2), (x[1] + h/2)
if score is None:
return np.array((x1, y1, x2, y2)).reshape((1, 4))
else:
return np.array((x1, y1, x2, y2, score)).reshape(1, 5)
class KalmanBBoxTracker(object):
count = 0
def __init__(self, bbox):
"""Init the internel Kalman Filter using bbox
dim_x = 7, Number of state variables for the Kalman filter
dim_z = 4, Number of of measurement inputs
KF.x: init state (x, y, s, r, x', y', s') (dim_x, 1)
x, y is the bbox center
s is the bbox area (w * h)
r is the bbox aspect ratio (w / h)
x' is the velocity/ variance of x
y' is the velocity/ variance of y
s' is the velocity/ variance of s
update(), predict() will update this variable
KF.F: state transition matrix (dim_x, dim_x)
KF.H: measurement function (dim_z, dim_x)
KF.P: covariance matrix (dim_x, dim_x)
update(), predict() will update this variable
KF.R: measurement noise covariance (dim_z, dim_z)
KF.Q: process uncertainty (dim_x, dim_x)
"""
# define internel kalman filter
dim_x, dim_z = 7, 4
self.kf = KalmanFilter(dim_x=dim_x, dim_z=dim_z)
self.kf.x[:4] = convert_bbox_to_z(bbox)
self.kf.F = np.array([[1,0,0,0,1,0,0],
[0,1,0,0,0,1,0],
[0,0,1,0,0,0,1],
[0,0,0,1,0,0,0],
[0,0,0,0,1,0,0],
[0,0,0,0,0,1,0],
[0,0,0,0,0,0,1]])
self.kf.H = np.array([[1,0,0,0,0,0,0],
[0,1,0,0,0,0,0],
[0,0,1,0,0,0,0],
[0,0,0,1,0,0,0]])
self.kf.P[4:, 4:] *= 1000. # set unobservable initial velocities with high uncertainty
self.kf.P *= 10.
self.kf.R[2:, 2:] *= 10.
self.kf.Q[-1, -1] *= 0.01
self.kf.Q[4:, 4:] *= 0.01
self.id = KalmanBBoxTracker.count
KalmanBBoxTracker.count += 1
self.time_since_update = 0
self.history = []
self.hits = 0
self.hit_streak = 0
self.age = 0 # record the tracker preserved time
self.objclass = bbox[6]
self.detect_conf = bbox[4]
def update(self, bbox):
"""Update the state vector with observed bbox"""
self.time_since_update = 0
self.history = []
self.hits += 1
self.hit_streak += 1
self.detect_conf = bbox[4]
self.kf.update(convert_bbox_to_z(bbox))
def predict(self):
"""Advances the state vector and returns the predicted bounding box estimate
KF.x: init state (x, y, s, r, x', y', s')
"""
# area and the area velocity
if self.kf.x[6] + self.kf.x[2] <= 0:
self.kf.x[6] *= 0.0
self.kf.predict()
self.age += 1
if self.time_since_update > 0:
self.hit_streak = 0
self.time_since_update += 1
self.history.append(convert_x_to_bbox(self.kf.x))
return self.history[-1]
def get_state(self):
"""Returns the current bounding box estimate"""
return convert_x_to_bbox(self.kf.x)
def associate_detections_to_trackers(detections, trackers, iou_threshold=0.3):
"""Assigns detections to tracked object with
Apply Hungarian algorithm by linear_assignment from sklearn
Returns (matches, unmatched_detections, unmatched_tackers)
"""
if len(trackers) == 0:
return (np.empty((0, 2), dtype=int),
np.arange(len(detections)),
np.empty((0, 5), dtype=int))
# row: detection, col: trackers
iou_matrix = np.zeros((len(detections), len(trackers)), dtype=np.float32)
for d, det in enumerate(detections):
for t, trk in enumerate(trackers):
iou_matrix[d, t] = iou(det, trk)
# matched_indices = linear_assignment(-iou_matrix)
matched_indices = linear_sum_assignment(-iou_matrix)
matched_indices = | np.asarray(matched_indices) | numpy.asarray |
import os
import argparse
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
prs = argparse.ArgumentParser(formatter_class=argparse.ArgumentDefaultsHelpFormatter,
description="""Plot Traffic Signal Metrics""")
prs.add_argument('-f', nargs='+', required=True, help="Measures files\n")
args = prs.parse_args()
df = pd.read_csv(args.f[0], sep=',')
valores = {}
val = {}
for i, value in enumerate(df['groups']):
groups = df['groups'][i].split('}, ')
for id, group in enumerate(groups):
# print(i, valores, group, eval(group.split(', Reward:')[1].replace('}', '')))
g = group.split(', Neighbours')[0][17:].strip().split(':')[1].strip()
r = eval(group.split(', Reward:')[1].replace('}', ''))
if g in valores:
valores[g]['reward'] += r
val[g].append(r)
valores[g]['times'] += 1
else:
valores[g] = {'reward': r, 'times': 0, 'mean': 0, 'std': 0}
val[g] = [r]
# print(i, valores)
# exit()
newDF = pd.DataFrame.from_dict(valores)
for g in val:
mean = np.mean(val[g])
std = | np.std(val[g]) | numpy.std |
"""
This script calls the Spatial Lag SAR functionality from the PySAL Module
within the ArcGIS environment.
Author(s): <NAME>, <NAME>, <NAME>, <NAME>
"""
import arcpy as ARCPY
import numpy as NUM
import pysal as PYSAL
import os as OS
import sys as SYS
import SSDataObject as SSDO
import SSUtilities as UTILS
import pysal2ArcUtils as AUTILS
FIELDNAMES = ["Predy", "Resid", "Predy_e", "e_Pred"]
FIELDALIAS = ["Predicted {0}", "Residual", "Predicted {0} (Reduced Form)",
"Prediced Error (Reduced Form)"]
MODELTYPES = ["GMM_COMBO", "GMM_HAC", "ML"]
class Lag_PySAL(object):
"""Computes SAR Lag linear regression via GMM/ML using PySAL."""
def __init__(self, ssdo, depVarName, indVarNames, patW,
modelType = "GMM_COMBO",
kernelType = "Uniform", kernelKNN = 2):
#### Set Initial Attributes ####
UTILS.assignClassAttr(self, locals())
#### Validate Model Type ####
if modelType not in MODELTYPES:
ARCPY.AddError("The input model type {0} is not in {1}".format(modelType,
", ".join(MODELTYPES)))
raise SystemExit()
#### Initialize Data ####
self.initialize()
#### Calculate Statistic ####
self.calculate()
def initialize(self):
"""Performs additional validation and populates the SSDataObject."""
ARCPY.SetProgressor("default", ("Starting to perform Spatial Lag "
"regression. Loading features..."))
#### Shorthand Attributes ####
ssdo = self.ssdo
#### MasterField Can Not Be The Dependent Variable ####
if ssdo.masterField == self.depVarName:
ARCPY.AddIDMessage("ERROR", 945, ssdo.masterField,
ARCPY.GetIDMessage(84112))
raise SystemExit()
#### Remove the MasterField from Independent Vars ####
if ssdo.masterField in self.indVarNames:
self.indVarNames.remove(ssdo.masterField)
ARCPY.AddIDMessage("Warning", 736, ssdo.masterField)
#### Remove the Dependent Variable from Independent Vars ####
if self.depVarName in self.indVarNames:
self.indVarNames.remove(self.depVarName)
ARCPY.AddIDMessage("Warning", 850, self.depVarName)
#### Raise Error If No Independent Vars ####
if not len(self.indVarNames):
ARCPY.AddIDMessage("Error", 737)
raise SystemExit()
#### Create Dependent Variable ####
self.allVars = [self.depVarName] + self.indVarNames
self.y = ssdo.fields[self.depVarName].returnDouble()
self.n = ssdo.numObs
self.y.shape = (self.n, 1)
#### Assure that Variance is Larger than Zero ####
yVar = | NUM.var(self.y) | numpy.var |
import abc
import logging
from math import exp, sin
import numpy as np
from ape.intcoords.elem_data import COVALENT_RADII as CR
from ape.intcoords.derivatives import d2q_b, d2q_a, dq_lb, d2q_lb, dq_ld, d2q_ld, d2q_d, dq_oop, d2q_oop
from ape.intcoords.rotate import get_expmap, get_expmap_der, is_linear, calc_rot_vec_diff
from ape.intcoords import nifty, math_utils
class Primitive(metaclass=abc.ABCMeta):
def __init__(self, indices, periodic=False, calc_kwargs=None):
self.indices = list(indices)
self.periodic = periodic
if calc_kwargs is None:
calc_kwargs = ()
self.calc_kwargs = calc_kwargs
self.logger = logging.getLogger("internal_coords")
def log(self, msg, lvl=logging.DEBUG):
self.logger.log(lvl, msg)
@staticmethod
def parallel(u, v, thresh=1e-6):
dot = u.dot(v) / (np.linalg.norm(u) * np.linalg.norm(v))
return (1 - abs(dot)) < thresh
@staticmethod
def _get_cross_vec(coords3d, indices):
m, o, n = indices
# Select initial vector for cross product, similar to
# geomeTRIC. It must NOT be parallel to u and/or v.
x_dash = coords3d[n] - coords3d[m]
x = x_dash / np.linalg.norm(x_dash)
cross_vecs = np.eye(3)
min_ind = np.argmin([np.dot(cv, x) ** 2 for cv in cross_vecs])
return cross_vecs[min_ind]
def set_cross_vec(self, coords3d, indices):
self.cross_vec = self._get_cross_vec(coords3d, self.indices)
self.log(f"Cross vector for {self} set to {self.cross_vec}")
@abc.abstractmethod
def _calculate(*, coords3d, indices, gradient, **kwargs):
pass
@abc.abstractmethod
def _weight(self, atoms, coords3d, indices, f_damping):
pass
def weight(self, atoms, coords3d, f_damping=0.12):
return self._weight(atoms, coords3d, self.indices, f_damping)
@staticmethod
def rho(atoms, coords3d, indices):
i, j = indices
distance = np.linalg.norm(coords3d[i] - coords3d[j])
cov_rad_sum = CR[atoms[i].lower()] + CR[atoms[j].lower()]
return exp(-(distance / cov_rad_sum - 1))
def calculate(self, coords3d, indices=None, gradient=False):
if indices is None:
indices = self.indices
# Gather calc_kwargs
calc_kwargs = {key: getattr(self, key) for key in self.calc_kwargs}
return self._calculate(
coords3d=coords3d,
indices=indices,
gradient=gradient,
**calc_kwargs,
)
def jacobian(self, coords3d, indices=None):
if indices is None:
indices = self.indices
# Gather calc_kwargs
calc_kwargs = {key: getattr(self, key) for key in self.calc_kwargs}
return self._jacobian(
coords3d=coords3d,
indices=indices,
**calc_kwargs,
)
def __str__(self):
return f"{self.__class__.__name__}({self.indices})"
def __repr__(self):
return self.__str__()
class CartesianX(Primitive):
@staticmethod
def _weight(atoms, coords3d, indices, f_damping):
pass
@staticmethod
def _calculate(coords3d, indices, gradient=False, w=1.0):
ind = indices[0]
value = coords3d[ind][0]
if gradient:
row = np.zeros_like(coords3d)
row[ind][0] = w
row = row.flatten()
return value, row
return value
class CartesianY(Primitive):
@staticmethod
def _weight(atoms, coords3d, indices, f_damping):
pass
@staticmethod
def _calculate(coords3d, indices, gradient=False, w=1.0):
ind = indices[0]
value = coords3d[ind][1]
if gradient:
row = np.zeros_like(coords3d)
row[ind][1] = w
row = row.flatten()
return value, row
return value
class CartesianZ(Primitive):
@staticmethod
def _weight(atoms, coords3d, indices, f_damping):
pass
@staticmethod
def _calculate(coords3d, indices, gradient=False, w=1.0):
ind = indices[0]
value = coords3d[ind][2]
if gradient:
row = np.zeros_like(coords3d)
row[ind][2] = w
row = row.flatten()
return value, row
return value
class TranslationX(Primitive):
@staticmethod
def _weight(atoms, coords3d, indices, f_damping):
pass
@staticmethod
def _calculate(coords3d, indices, gradient=False):
indices = np.array(indices)
w = np.ones(len(indices))/len(indices)
value = np.sum(coords3d[indices, 0] * w)
if gradient:
row = np.zeros_like(coords3d)
for i, a in enumerate(indices):
row[a][0] = w[i]
row = row.flatten()
return value, row
return value
class TranslationY(Primitive):
@staticmethod
def _weight(atoms, coords3d, indices, f_damping):
pass
@staticmethod
def _calculate(coords3d, indices, gradient=False):
indices = np.array(indices)
w = np.ones(len(indices))/len(indices)
value = np.sum(coords3d[indices, 1] * w)
if gradient:
row = np.zeros_like(coords3d)
for i, a in enumerate(indices):
row[a][1] = w[i]
row = row.flatten()
return value, row
return value
class TranslationZ(Primitive):
@staticmethod
def _weight(atoms, coords3d, indices, f_damping):
pass
@staticmethod
def _calculate(coords3d, indices, gradient=False):
indices = np.array(indices)
w = np.ones(len(indices))/len(indices)
value = np.sum(coords3d[indices, 2] * w)
if gradient:
row = np.zeros_like(coords3d)
for i, a in enumerate(indices):
row[a][2] = w[i]
row = row.flatten()
return value, row
return value
class Rotator(object):
def __init__(self, a, x0):
self.a = list(tuple(sorted(a)))
x0 = x0.reshape(-1, 3)
self.x0 = x0.copy()
self.stored_valxyz = np.zeros_like(x0)
self.stored_value = None
# A second set of xyz coordinates used only when computing
# differences in rotation coordinates
self.stored_valxyz2 = np.zeros_like(x0)
self.stored_value2 = None
self.stored_derxyz = np.zeros_like(x0)
self.stored_deriv = None
self.stored_deriv2xyz = np.zeros_like(x0)
self.stored_deriv2 = None
self.stored_norm = 0.0
# Extra variables to account for the case of linear molecules
# The reference axis used for computing dummy atom position
self.e0 = None
# Dot-squared measures alignment of molecule long axis with reference axis.
# If molecule becomes parallel with reference axis, coordinates must be reset.
self.stored_dot2 = 0.0
# Flag that records linearity of molecule
self.linear = False
def reset(self, x0):
x0 = x0.reshape(-1, 3)
self.x0 = x0.copy()
self.stored_valxyz = np.zeros_like(x0)
self.stored_value = None
self.stored_valxyz2 = np.zeros_like(x0)
self.stored_value2 = None
self.stored_derxyz = np.zeros_like(x0)
self.stored_deriv = None
self.stored_deriv2xyz = np.zeros_like(x0)
self.stored_deriv2 = None
self.stored_norm = 0.0
self.e0 = None
self.stored_dot2 = 0.0
self.linear = False
def __eq__(self, other):
if type(self) is not type(other): return False
eq = set(self.a) == set(other.a)
if eq and np.sum((self.x0-other.x0)**2) > 1e-6:
logger.warning("Warning: Rotator same atoms, different reference positions\n")
return eq
def __repr__(self):
return "Rotator %s" % commadash(self.a)
def __ne__(self, other):
return not self.__eq__(other)
@property
def w(self):
sel = self.x0[self.a,:]
sel -= np.mean(sel, axis=0)
rg = np.sqrt(np.mean(np.sum(sel ** 2, axis=1)))
return rg
def calc_e0(self):
"""
Compute the reference axis for adding dummy atoms.
Only used in the case of linear molecules.
We first find the Cartesian axis that is "most perpendicular" to the molecular axis.
Next we take the cross product with the molecular axis to create a perpendicular vector.
Finally, this perpendicular vector is normalized to make a unit vector.
"""
ysel = self.x0[self.a, :]
vy = ysel[-1]-ysel[0]
ev = vy / np.linalg.norm(vy)
# Cartesian axes.
ex = np.array([1.0,0.0,0.0])
ey = np.array([0.0,1.0,0.0])
ez = np.array([0.0,0.0,1.0])
self.e0 = np.cross(vy, [ex, ey, ez][np.argmin([np.dot(i, ev)**2 for i in [ex, ey, ez]])])
self.e0 /= np.linalg.norm(self.e0)
def value(self, xyz, store=True):
xyz = xyz.reshape(-1, 3)
if np.max(np.abs(xyz-self.stored_valxyz)) < 1e-12:
return self.stored_value
else:
xsel = xyz[self.a, :]
ysel = self.x0[self.a, :]
xmean = np.mean(xsel,axis=0)
ymean = np.mean(ysel,axis=0)
if not self.linear and is_linear(xsel, ysel):
# print "Setting linear flag for", self
self.linear = True
if self.linear:
# Handle linear molecules.
vx = xsel[-1]-xsel[0]
vy = ysel[-1]-ysel[0]
# Calculate reference axis (if needed)
if self.e0 is None: self.calc_e0()
#log.debug(vx)
ev = vx / np.linalg.norm(vx)
# Measure alignment of molecular axis with reference axis
self.stored_dot2 = np.dot(ev, self.e0)**2
# Dummy atom is located one Bohr from the molecular center, direction
# given by cross-product of the molecular axis with the reference axis
xdum = np.cross(vx, self.e0)
ydum = np.cross(vy, self.e0)
exdum = xdum / np.linalg.norm(xdum)
eydum = ydum / np.linalg.norm(ydum)
xsel = | np.vstack((xsel, exdum+xmean)) | numpy.vstack |
# -*- coding: utf-8 -*-
"""
Created on Mon Jan 30 20:43:05 2017
@author: michael
"""
import parameters as params
import numpy as np
from scipy import special
import gaussian_quadrature as gq
def fill_z_mat_orig(node_coords, num_elem, elem_nodes):
z = np.zeros((num_elem, num_elem), dtype=complex)
for m in range(0, num_elem):
xm = (node_coords[elem_nodes[m][0]][0] + node_coords[elem_nodes[m][1]][0])/2
ym = (node_coords[elem_nodes[m][0]][1] + node_coords[elem_nodes[m][1]][1])/2
for n in range(0, num_elem):
if m == n:
wm = np.sqrt( np.power((node_coords[elem_nodes[m][0]][0] - node_coords[elem_nodes[m][1]][0]), 2) + np.power((node_coords[elem_nodes[m][0]][1] + node_coords[elem_nodes[m][1]][1]), 2) )
z[m][n] = ( params.k0*params.eta0*(wm)/4 )*( 1 - (1j*2/params.pi)*(np.log(params.gam*params.k0*wm/4) - 1 ) )
else:
xn = ((node_coords[elem_nodes[n][0]][0]) + (node_coords[elem_nodes[n][1]][0]))/2
yn = ((node_coords[elem_nodes[n][0]][1]) + (node_coords[elem_nodes[n][1]][1]))/2
r = np.sqrt( np.power((xm - xn), 2) + np.power((ym - yn), 2) )
xx = params.k0*r
wn = np.sqrt( np.power((node_coords[elem_nodes[n][0]][0] - node_coords[elem_nodes[n][1]][0]), 2) + np.power((node_coords[elem_nodes[n][0]][1] + node_coords[elem_nodes[n][1]][1]), 2) )
z[m][n] = (params.k0*params.eta0/4)*wn*(np.sqrt(2/(params.pi*xx))*np.exp(-1j*(xx-(params.pi/4))))
return -z
def fill_z_mat(node_coords, num_elem, elem_nodes, n_gaus=params.gaus_default):
z = np.zeros((num_elem, num_elem), dtype=complex)
gaus = gq.getGaussianQuadrature(n_gaus)
const = params.k0*params.eta0/4
for m in range(0, num_elem):
xm = (node_coords[elem_nodes[m][0]][0] + node_coords[elem_nodes[m][1]][0])/2
ym = (node_coords[elem_nodes[m][0]][1] + node_coords[elem_nodes[m][1]][1])/2
for n in range(0, num_elem):
if m == n:
wm = np.sqrt( np.power((node_coords[elem_nodes[m][0]][0] - node_coords[elem_nodes[m][1]][0]), 2) + np.power((node_coords[elem_nodes[m][0]][1] + node_coords[elem_nodes[m][1]][1]), 2) )
z[m][n] = const*( 1 - (1j*2/params.pi)*(np.log(params.gam*params.k0*wm/4) - 1 ) )
else:
start_node_x = node_coords[elem_nodes[n][0]][0]
start_node_y = node_coords[elem_nodes[n][0]][1]
end_node_x = node_coords[elem_nodes[n][1]][0]
end_node_y = node_coords[elem_nodes[n][1]][1]
vec_x = end_node_x - start_node_x
vec_y = end_node_y - start_node_y
wn = np.sqrt( np.power((start_node_x - end_node_x), 2) + np.power((start_node_y - end_node_y), 2) )
for k in range(0, n_gaus):
xn = start_node_x + vec_x*gaus[k][0]
yn = start_node_y + vec_y*gaus[k][0]
r = np.sqrt( np.power((xm - xn), 2) + np.power((ym - yn), 2) )
xx = params.k0*r
z[m][n] = z[m][n] + const*wn*special.hankel2(0, xx)
return -z
def create_e_inc(node_coords, num_elem, elem_nodes):
b_vec = np.zeros((num_elem, 1), dtype=complex)
for m in range(0, num_elem):
x = (node_coords[elem_nodes[m][0]][0] + node_coords[elem_nodes[m][1]][0])/2
y = (node_coords[elem_nodes[m][0]][1] + node_coords[elem_nodes[m][1]][1])/2
b_vec[m][0] = np.exp(1j*params.k0*(x*np.cos(params.phi_inc) + y*np.sin(params.phi_inc)))
return b_vec.reshape(num_elem, 1)
def calculate_scat(curr, node_coords, num_elem, elem_nodes, n_gaus=params.gaus_default):
e_scat = np.zeros((params.num_fieldpoints, 1), dtype=complex)
const = params.k0*params.eta0/4
gaus = gq.getGaussianQuadrature(n_gaus)
for obs in range(0, params.num_fieldpoints):
x_obs = params.rad_fieldpoints*np.cos(params.phi_fieldpoints[obs])
y_obs = params.rad_fieldpoints*np.sin(params.phi_fieldpoints[obs])
for n in range(0, num_elem):
xn = (node_coords[elem_nodes[n][0]][0] + node_coords[elem_nodes[n][1]][0])/2
yn = (node_coords[elem_nodes[n][0]][1] + node_coords[elem_nodes[n][1]][1])/2
r = np.sqrt( np.power((x_obs - xn), 2) + np.power((y_obs - yn), 2) )
xx = params.k0*r
wn = np.sqrt( np.power((node_coords[elem_nodes[n][0]][0] - node_coords[elem_nodes[n][1]][0]), 2) + np.power((node_coords[elem_nodes[n][0]][1] + node_coords[elem_nodes[n][1]][1]), 2) )
# z = (params.k0*params.eta0/4)*wn*(np.sqrt(2/(params.pi*xx))*np.exp(-1j*(xx-(params.pi/4))))
z = const*wn*special.hankel2(0, xx)
# start_node_x = node_coords[elem_nodes[n][0]][0]
# start_node_y = node_coords[elem_nodes[n][0]][1]
#
# end_node_x = node_coords[elem_nodes[n][1]][0]
# end_node_y = node_coords[elem_nodes[n][1]][1]
#
# vec_x = end_node_x - start_node_x
# vec_y = end_node_y - start_node_y
#
# wn = np.sqrt( np.power((start_node_x - end_node_x), 2) + np.power((start_node_y - end_node_y), 2) )
#
# for k in range(0, n_gaus):
# xn = start_node_x + vec_x*gaus[k][0]
# yn = start_node_y + vec_y*gaus[k][0]
#
# r = np.sqrt( np.power((x_obs - xn), 2) + np.power((y_obs - yn), 2) )
# xx = params.k0*r
#
# z = const*wn*special.hankel2(0, xx)
e_scat[obs][0] = e_scat[obs][0] + z*curr[n][0]
return e_scat
def calculate_db_scat(scat):
return 20*np.log10(np.sqrt(2*np.pi*params.rad_fieldpoints)*np.abs(scat)) # Not sure if this should be 10 or 20
def calculate_mom_different_quads(node_coords, num_elem, elem_nodes):
data = | np.ndarray((params.num_quads, 1, params.num_fieldpoints, 1), dtype=complex) | numpy.ndarray |
from scipy import integrate
import numpy as np
from quaternion_euler_utility import euler_quat, quat_euler, deriv_quat, quat_rot_mat
from numpy.linalg import norm
from mpl_toolkits.mplot3d import Axes3D
import matplotlib
from matplotlib import pyplot as plt
from scipy.spatial.transform import Rotation
"""""
QUADROTOR ENVIRONMENT
DEVELOPED BY:
<NAME>
PROGRAMA DE PÓS GRADUAÇÃO EM ENGENHARIA MECÂNICA, UNIVERSIDADE FEDERAL DO ABC
SP - SANTO ANDRÉ - BRASIL
FURTHER DOCUMENTATION ON README.MD
"""""
# matplotlib.use("pgf")
# matplotlib.rcParams.update({
# "pgf.texsystem": "pdflatex",
# 'font.family': 'serif',
# 'text.usetex': True,
# 'pgf.rcfonts': False,
# 'pgf.preamble':[
# '\DeclareUnicodeCharacter{2212}{-}']
# })
## SIMULATION BOUNDING BOXES ##
BB_POS = 5
BB_VEL = 10
BB_CONTROL = 9
BB_ANG = np.pi/2
# QUADROTOR MASS AND GRAVITY VALUE
M, G = 1.03, 9.82
# AIR DENSITY
RHO = 1.2041
#DRAG COEFFICIENT
C_D = 1.1
# ELETRIC MOTOR THRUST AND MOMENT
K_F = 1.435e-5
K_M = 2.4086e-7
I_R = 5e-5
T2WR = 2
# INERTIA MATRIX
J = np.array([[16.83e-3, 0, 0],
[0, 16.83e-3, 0],
[0, 0, 28.34e-3]])
# ELETRIC MOTOR DISTANCE TO CG
D = 0.26
#PROJECTED AREA IN X_b, Y_b, Z_b
BEAM_THICKNESS = 0.05
A_X = BEAM_THICKNESS*2*D
A_Y = BEAM_THICKNESS*2*D
A_Z = BEAM_THICKNESS*2*D*2
A = np.array([[A_X,A_Y,A_Z]]).T
## REWARD PARAMETERS ##
SOLVED_REWARD = 20
BROKEN_REWARD = -20
SHAPING_WEIGHT = 5
SHAPING_INTERNAL_WEIGHTS = [15, 4, 1]
# CONTROL REWARD PENALITIES #
P_C = 0.003
P_C_D = 0
## TARGET STEADY STATE ERROR ##
TR = [0.005, 0.01, 0.1]
TR_P = [3, 2, 1]
## ROBUST CONTROL PARAMETERS
class robust_control():
def __init__(self):
self.D_KF = 0.1
self.D_KM = 0.1
self.D_M = 0.3
self.D_IR = 0.1
self.D_J = np.ones(3) * 0.1
self.reset()
self.gust_std = [[5], [5], [2]]
self.gust_period = 500 # integration steps
self.i_gust = 0
self.gust = np.zeros([3, 1])
def reset(self):
self.episode_kf = np.random.random(4) * self.D_KF
self.episode_m = np.random.normal(0, self.D_M, 1)
self.episode_ir = np.random.random(4) * self.D_IR
self.episode_J = np.eye(3)*np.random.normal(np.zeros(3), self.D_J, [3])
def wind(self, i):
index = (i % self.gust_period) - 1
if index % self.gust_period == 0:
self.last_gust = self.gust
self.gust = np.random.normal(np.zeros([3, 1]), self.gust_std, [3, 1])
self.linear_wind_change = np.linspace(self.last_gust, self.gust, self.gust_period)
return self.linear_wind_change[index]
class quad():
def __init__(self, t_step, n, training = True, euler=0, direct_control=1, T=1, clipped = True):
""""
inputs:
t_step: integration time step
n: max timesteps
euler: flag to set the states return in euler angles, if off returns quaternions
deep learning:
deep learning flag: If on, changes the way the env. outputs data, optimizing it to deep learning use.
T: Number of past history of states/actions used as inputs in the neural network
debug: If on, prints a readable reward funcion, step by step, for a simple reward weight debugging.
"""
self.clipped = clipped
if training:
self.ppo_training = True
else:
self.ppo_training = False
self.mass = M
self.gravity = G
self.i = 0
self.T = T #Initial Steps
self.bb_cond = np.array([BB_VEL,
BB_VEL,
BB_VEL,
BB_ANG, BB_ANG, 3/4*np.pi,
BB_VEL*2, BB_VEL*2, BB_VEL*2]) #Bounding Box Conditions Array
if not self.ppo_training:
self.bb_cond = self.bb_cond*1
#Quadrotor states dimension
self.state_size = 13
#Quadrotor action dimension
self.action_size = 4
#Env done Flag
self.done = True
#Env Maximum Steps
self.n = n+self.T
self.t_step = t_step
#Neutral Action (used in reset and absolute action penalty)
if direct_control:
self.zero_control = np.ones(4)*(2/T2WR - 1)
else:
self.zero_control = np.array([M*G, 0, 0, 0])
self.direct_control_flag = direct_control
self.ang_vel = np.zeros(3)
self.prev_ang = np.zeros(3)
self.J_mat = J
#Absolute sum of control efforts over the episode
self.abs_sum = 0
self.d_xx = np.linspace(0, D, 10)
self.d_yy = np.linspace(0, D, 10)
self.d_zz = np.linspace(0, D, 10)
self.robust_parameters = robust_control()
self.robust_control = False
ev_cd = 'Training' if self.ppo_training else 'Eval'
ct_cd = ' with robust environment' if self.robust_control else ''
print('Environment Condition: ' + ev_cd + ct_cd)
def seed(self, seed):
""""
Set random seeds for reproducibility
"""
np.random.seed(seed)
def f2w(self,f,m):
"""""
Translates F (Thrust) and M (Body x, y and z moments) into eletric motor angular velocity (rad/s)
input:
f - thrust
m - body momentum in np.array([[mx, my, mz]]).T
outputs:
F - Proppeler Thrust - engine 1 to 4
w - Proppeler angular velocity - engine 1 to 4
F_new - clipped thrust (if control surpasses engine maximum)
M_new - clipped momentum (same as above)
"""""
x = np.array([[K_F, K_F, K_F, K_F],
[-D*K_F, 0, D*K_F, 0],
[0, D*K_F, 0, -D*K_F],
[-K_M, +K_M, -K_M, +K_M]])
y = np.array([f, m[0,0], m[1,0], m[2,0]])
u = np.linalg.solve(x, y)
if self.clipped:
u = np.clip(u, 0, T2WR*M*G/4/K_F)
w_1 = np.sqrt(u[0])
w_2 = np.sqrt(u[1])
w_3 = np.sqrt(u[2])
w_4 = np.sqrt(u[3])
else:
modules = np.zeros(4)
for k in range(4):
modules[k] = -1 if u[k] < 0 else 1
w_1 = np.sqrt(np.abs(u[0]))*modules[0]
w_2 = np.sqrt(np.abs(u[1]))*modules[1]
w_3 = np.sqrt(np.abs(u[2]))*modules[2]
w_4 = np.sqrt(np.abs(u[3]))*modules[3]
w = np.array([[w_1,w_2,w_3,w_4]]).T
if self.robust_control:
u -= u*self.robust_parameters.episode_kf
FM_new = np.dot(x, u)
F_new = FM_new[0]
M_new = FM_new[1:4]
step_effort = (u*K_F/(T2WR*M*G/4)*2)-1
return step_effort, w, F_new, M_new
def f2F(self, f_action):
"""""
Translates Proppeler thrust to body trhust and body angular momentum.
input:
f_action - proppeler thrust written as np.array([f1, f2, f3, f4])
the proppeler thrust if normalized in [-1, 1] domain, where -1 is 0 thrust and 1 is maximum thrust
output:
w - proppeler angular velocity
F_new - body thrust
M_new - body angular momentum
"""""
f = (f_action + 1) * T2WR * M * G / 8
w = np.array([[np.sqrt(f[0]/K_F)],
[np.sqrt(f[1]/K_F)],
[np.sqrt(f[2]/K_F)],
[np.sqrt(f[3]/K_F)]])
if self.robust_control:
f = f - self.robust_parameters.episode_kf * f
F_new = np.sum(f)
M_new = np.array([[(f[2]-f[0])*D],
[(f[1]-f[3])*D],
[(-f[0]+f[1]-f[2]+f[3])*K_M/K_F]])
return w, F_new, M_new
def drone_eq(self, t, x, action):
""""
Main differential equation, not used directly by the user, rather used in the step function integrator.
Dynamics based in:
MODELAGEM DINÂMICA E CONTROLE DE UM VEÍCULO AÉREO NÃO TRIPULADO DO TIPO QUADRIRROTOR
by <NAME>
BRASIL, SP-SANTO ANDRÉ, UFABC - 2019
Incorporates:
Drag Forces, Gyroscopic Forces
In indirect mode: Force clipping (preventing motor shutoff and saturates over Thrust to Weight Ratio)
In direct mode: maps [-1,1] to forces [0,T2WR*G*M/4]
"""
if self.direct_control_flag:
self.w, f_in, m_action = self.f2F(action)
else:
f_in = action[0]
m_action = np.array([action[1::]]).T
#BODY INERTIAL VELOCITY
vel_x = x[1]
vel_y = x[3]
vel_z = x[5]
#QUATERNIONS
q0 = x[6]
q1 = x[7]
q2 = x[8]
q3 = x[9]
#BODY ANGULAR VELOCITY
w_xx = x[10]
w_yy = x[11]
w_zz = x[12]
#QUATERNION NORMALIZATION (JUST IN CASE)
q = np.array([[q0, q1, q2, q3]]).T
q = q/np.linalg.norm(q)
# DRAG FORCES ESTIMATION (BASED ON BODY VELOCITIES)
self.mat_rot = quat_rot_mat(q)
v_inertial = np.array([[vel_x, vel_y, vel_z]]).T
if self.robust_control:
wind = self.robust_parameters.wind(self.i)
v_inertial += wind
v_body = np.dot(self.mat_rot.T, v_inertial)
f_drag = -0.5*RHO*C_D*np.multiply(A,np.multiply(abs(v_body),v_body))
# DRAG MOMENTS ESTIMATION (BASED ON BODY ANGULAR VELOCITIES)
#Discretization over 10 steps (linear velocity varies over the body)
m_x = 0
m_y = 0
m_z = 0
for xx,yy,zz in zip(self.d_xx, self.d_yy, self.d_zz):
m_x += -RHO*C_D*BEAM_THICKNESS*D/10*(abs(xx*w_xx)*(xx*w_xx))*xx
m_y += -RHO*C_D*BEAM_THICKNESS*D/10*(abs(yy*w_yy)*(yy*w_yy))*yy
m_z += -2*RHO*C_D*BEAM_THICKNESS*D/10*(abs(zz*w_zz)*(zz*w_zz))*zz
m_drag = np.array([[m_x],
[m_y],
[m_z]])
#GYROSCOPIC EFFECT ESTIMATION (BASED ON ELETRIC MOTOR ANGULAR VELOCITY)
if self.robust_control:
ir = I_R*(np.ones(4)+self.robust_parameters.episode_ir)
omega_r = (-self.w[0]*ir[0]+self.w[1]*ir[1]-self.w[2]*ir[2]+self.w[3]*ir[3])[0]
else:
omega_r = (-self.w[0]+self.w[1]-self.w[2]+self.w[3])[0]*I_R
m_gyro = np.array([[-w_xx*omega_r],
[+w_yy*omega_r],
[0]])
#BODY FORCES
self.f_in = np.array([[0, 0, f_in]]).T
self.f_body = self.f_in+f_drag
#BODY FORCES ROTATION TO INERTIAL
self.f_inertial = np.dot(self.mat_rot, self.f_body)
#INERTIAL ACCELERATIONS
if self.robust_control:
quad_m = M * (1 + self.robust_parameters.episode_m)
else:
quad_m = M
accel_x = self.f_inertial[0, 0]/quad_m
accel_y = self.f_inertial[1, 0]/quad_m
accel_z = self.f_inertial[2, 0]/quad_m-G
self.accel = np.array([[accel_x, accel_y, accel_z]]).T
# self.accelerometer_read = self.f_body/quad_m
self.accelerometer_read = self.mat_rot.T @ (self.accel.flatten() + np.array([0, 0, -G]))
#BODY MOMENTUM
W = np.array([[w_xx],
[w_yy],
[w_zz]])
m_in = m_action + m_gyro + m_drag - np.cross(W.flatten(), np.dot(J, W).flatten()).reshape((3,1))
#INERTIAL ANGULAR ACCELERATION
if self.robust_control:
self.inv_j = np.linalg.inv(J + J*self.robust_parameters.episode_J)
else:
self.inv_j = np.linalg.inv(J)
accel_ang = np.dot(self.inv_j, m_in).flatten()
accel_w_xx = accel_ang[0]
accel_w_yy = accel_ang[1]
accel_w_zz = accel_ang[2]
#QUATERNION ANGULAR VELOCITY (INERTIAL)
self.V_q = deriv_quat(W, q).flatten()
dq0=self.V_q[0]
dq1=self.V_q[1]
dq2=self.V_q[2]
dq3=self.V_q[3]
# RESULTS ORDER:
# 0 x, 1 vx, 2 y, 3 vy, 4 z, 5 vz, 6 q0, 7 q1, 8 q2, 9 q3, 10 w_xx, 11 w_yy, 12 w_zz
out = np.array([vel_x, accel_x,
vel_y, accel_y,
vel_z, accel_z,
dq0, dq1, dq2, dq3,
accel_w_xx, accel_w_yy, accel_w_zz])
return out
def reset(self, det_state = None):
"""""
inputs:_, self.w, f_in, m_action = self.f2w(f_in, m_action)
det_state:
if == 0 randomized initial state
else det_state is the actual initial state, depending on the euler flag
if euler flag is on:
[x, dx, y, dy, z, dz, phi, theta, psi, w_xx, w_yy, w_zz]
if euler flag is off:
[x, dx, y, dy, z, dz, q_0, q_1, q_2, q_3, w_xx, w_yy, w_zz]
outputs:
previous_state: system's initial state
"""""
state = []
action = []
self.action_hist = []
self.robust_parameters.reset()
self.solved = 0
self.done = False
self.i = 0
self.prev_shaping = None
self.previous_state = np.zeros(self.state_size)
self.abs_sum = 0
if det_state is not None:
self.previous_state = det_state
q = np.array([self.previous_state[6:10]]).T
self.ang = quat_euler(q)
else:
self.ang = np.random.rand(3)-0.5
Q_in = euler_quat(self.ang)
self.previous_state[0:5:2] = np.clip((np.random.normal([0, 0, 0], 2)), -BB_POS/2, BB_POS/2)
self.previous_state[1:6:2] = np.clip((np.random.normal([0, 0, 0], 2)), -BB_VEL/2, BB_VEL/2)
self.previous_state[6:10] = Q_in.T
self.previous_state[10:13] = np.clip((np.random.normal([0, 0, 0], 2)), -BB_VEL*1.5, BB_POS*1.5)
for i in range(self.T):
self.action = self.zero_control
self.action_hist.append(self.action)
state_t, reward, done = self.step(self.action)
state.append(state_t.flatten())
action.append(self.zero_control)
return np.array(state), np.array(action)
def step(self, action):
"""""
inputs:
action: action to be applied on the system
outputs:
state: system's state in t+t_step actuated by the action
done: False, else the system has breached any bounding box, exceeded maximum timesteps, or reached goal.
"""""
self.i += 1
if self.direct_control_flag:
self.action = np.clip(action,-1,1)
u = self.action
self.clipped_action = self.action
self.step_effort = self.action
else:
self.action = action
self.step_effort, self.w, f_in, m_action = self.f2w(action[0], np.array([action[1::]]).T)
self.clipped_action = np.append([f_in], m_action)
u = self.clipped_action
self.action_hist.append(self.clipped_action)
self.y = (integrate.solve_ivp(self.drone_eq, (0, self.t_step), self.previous_state, args=(u, ))).y
self.state = np.transpose(self.y[:, -1])
self.quat_state = np.array([np.concatenate((self.state[0:10], self.V_q))])
q = np.array([self.state[6:10]]).T
q = q/np.linalg.norm(q)
self.ang = quat_euler(q)
self.ang_vel = (self.ang - self.prev_ang)/self.t_step
self.prev_ang = self.ang
self.previous_state = self.state
self.done_condition()
self.reward_function()
self.control_effort()
return self.state, self.reward, self.done
def done_condition(self):
"""""
Checks if bounding boxes done condition have been met
"""""
cond_x = np.concatenate((self.state[1:6:2], self.ang, self.state[-3:]))
for x, c in zip(np.abs(cond_x), self.bb_cond):
if x >= c:
self.done = True
def reward_function(self, debug=0):
"""""
Reward Function: Working with PPO great results.
Shaping with some ideas based on Continuous Lunar Lander v.2 gym environment:
https://gym.openai.com/envs/LunarLanderContinuous-v2/
"""""
self.reward = 0
velocity = self.state[1:6:2]
euler_angles = self.ang
psi = self.ang[2]
body_ang_vel = self.state[-3:]
action = self.action
shaping = -SHAPING_WEIGHT/np.sum(SHAPING_INTERNAL_WEIGHTS)*(SHAPING_INTERNAL_WEIGHTS[0]*norm(velocity/BB_VEL)+
SHAPING_INTERNAL_WEIGHTS[1]*norm(psi/4)+
SHAPING_INTERNAL_WEIGHTS[2]*norm(euler_angles[0:2]/BB_ANG))
#CASCADING REWARDS
r_state = np.concatenate((velocity, [psi]))
for TR_i, TR_Pi in zip(TR, TR_P):
if norm(r_state) < norm(np.ones(len(r_state))*TR_i):
shaping += TR_Pi
if norm(euler_angles[0:2]) < norm(np.ones(2)*TR_i*4):
shaping += TR_Pi
break
if self.prev_shaping is not None:
self.reward = shaping - self.prev_shaping
self.prev_shaping = shaping
#ABSOLUTE CONTROL PENALTY
## TOTAL REWARD SHAPING ##
abs_control = -np.sum(np.square(action - self.zero_control)) * P_C
self.reward += + abs_control
#SOLUTION ACHIEVED?
self.target_state = 9*(TR[0]**2)
self.current_state = np.sum(np.square(np.concatenate((velocity, euler_angles, body_ang_vel))))
if self.current_state < self.target_state:
self.reward += SOLVED_REWARD
self.solved = 1
if self.ppo_training:
self.done = True
elif self.i >= self.n:
self.reward = self.reward
self.solved = 0
self.done=True
elif self.done:
self.reward += BROKEN_REWARD
self.solved = 0
def control_effort(self):
instant_effort = np.sqrt(np.sum(np.square(self.step_effort-np.array([0*M*G, 0, 0, 0]))))
self.abs_sum += instant_effort
class sensor():
"""Sensor class - simulates onboard sensors, given standard deviation and bias.
Aimed to simulate kallman filters or to execute robust control, etc.
Self explanatory, adds standard deviation noise and bias to quadrotor real state.
"""
def __init__(self, env,
accel_std = 0.1, accel_bias_drift = 0.0005,
gyro_std = 0.035, gyro_bias_drift = 0.00015,
magnet_std = 15, magnet_bias_drift = 0.075,
gps_std_p = 1.71, gps_std_v=0.5):
self.std = [accel_std, gyro_std, magnet_std, gps_std_p, gps_std_v]
self.b_d = [accel_bias_drift, gyro_bias_drift, magnet_bias_drift]
self.quad = env
self.error = True
self.bias_reset()
def bias_reset(self):
self.a_std = self.std[0]*self.error
self.a_b_d = (np.random.random()-0.5)*2*self.b_d[0]*self.error
self.g_std = self.std[1]*self.error
self.g_b_d = (np.random.random()-0.5)*2*self.b_d[1]*self.error
self.m_std = self.std[2]*self.error
self.m_b_d = (np.random.random()-0.5)*2*self.b_d[2]*self.error
self.gps_std_p = self.std[3]*self.error
self.gps_std_v = self.std[4]*self.error
self.R = np.eye(3)
def accel(self):
self.a_b_accel = self.a_b_accel + self.a_b_d*self.quad.t_step
read_error = np.random.normal(self.a_b_accel, self.a_std, 3)
read_accel_body = self.quad.accelerometer_read.flatten()
return read_accel_body+read_error
def accel_grav(self, norm=True):
gravity_vec = np.array([0, 0, -9.81])
self.a_b_grav = self.a_b_grav + self.a_b_d*self.quad.t_step
#Gravity vector as read from body sensor
gravity_body = np.dot(self.quad.mat_rot.T, gravity_vec)+ np.random.normal(np.random.random(3)*self.a_b_grav, self.a_std, 3)
if norm:
ax = gravity_body[0]
ay = gravity_body[1]
az = gravity_body[2]
if ax !=0 and ay != 0 and az != 0:
# Normalise accelerometer measurement
recipNorm = 1/(math.sqrt(ax * ax + ay * ay + az * az))
ax *= recipNorm
ay *= recipNorm
az *= recipNorm
gravity_body = np.array([[ax, ay, az]], dtype='float32')
return gravity_body
def mag_gauss(self, norm=True):
magnet_vec = np.array([-65.269, 165.115, -144.205])
self.m_b = self.m_b + self.m_b_d*self.quad.t_step
magnet_body = np.dot(self.quad.mat_rot.T, magnet_vec) + np.random.normal(np.random.random(3)*self.m_b, self.m_std, 3)
mx = magnet_body[0]
my = magnet_body[1]
mz = magnet_body[2]
if norm:
recipNorm = 1/math.sqrt(mx * mx + my * my + mz * mz)
mx *= recipNorm
my *= recipNorm
mz *= recipNorm
magnet_body = np.array([mx, my, mz])
return magnet_body
def gyro(self):
self.g_b = self.g_b + self.g_b_d*self.quad.t_step
read_error = np.random.normal(self.g_b, self.g_std, 3)
read_gyro = self.quad.state[-3:].flatten()
return np.array([read_error+read_gyro], dtype='float32').T
def reset(self):
self.a_b_grav = 0
self.a_b_accel = 0
self.m_b = 0
self.g_b = 0
self.acceleration_t0 = np.zeros(3)
self.position_t0 = self.quad.state[0:5:2]
self.velocity_t0 = self.quad.state[1:6:2]
self.quaternion_t0 = self.quad.state[6:10]
self.bias_reset()
def gps(self):
read_error_pos = np.random.normal(0, self.gps_std_p, 3)
read_error_vel = np.random.normal(0, self.gps_std_v, 3)
gps_pos = self.quad.state[0:5:2].flatten()
gps_vel = self.quad.state[1:6:2].flatten()
return read_error_pos+gps_pos, read_error_vel+gps_vel
def triad(self):
gravity_vec = np.array([0, 0, -G])
magnet_vec = np.array([-65.269, 165.115,-144.205]) #mGauss
#Magnetic Vector of Santo André - Brasil in MiliGauss
#https://www.ngdc.noaa.gov/geomag/calculators/magcalc.shtml#igrfwmm
#Gravity vector as read from body sensor
induced_acceleration = self.quad.f_in.flatten()/M - (self.R @ np.array([[0, 0, -G]]).T).flatten()
gravity_body = self.accel() - induced_acceleration
#Magnetic Field vector as read from body sensor
magnet_body = self.quad.mat_rot.T @ (np.random.normal(magnet_vec, self.m_std))
#Accel vector is more accurate
#Body Coordinates
gravity_body = gravity_body / np.linalg.norm(gravity_body)
magnet_body = magnet_body / np.linalg.norm(magnet_body)
t1b = gravity_body/np.linalg.norm(gravity_body)
t2b = np.cross(gravity_body, magnet_body)
t2b = t2b/np.linalg.norm(t2b)
t3b = np.cross(t1b, t2b)
t3b = t3b/np.linalg.norm(t3b)
tb = np.vstack((t1b, t2b, t3b)).T
#Inertial Coordinates
gravity_vec = gravity_vec/np.linalg.norm(gravity_vec)
magnet_vec = magnet_vec / np.linalg.norm(magnet_vec)
t1i = gravity_vec/np.linalg.norm(gravity_vec)
t2i = np.cross(gravity_vec, magnet_vec)
t2i = t2i/np.linalg.norm(t2i)
t3i = | np.cross(t1i, t2i) | numpy.cross |
import numpy as np
import matplotlib.pylab as plt
import scipy
import scipy.linalg
import sys
def lu_decomposition(A):
m, n = A.shape
LU = np.copy(A)
pivots = np.empty(n, dtype=int)
# initialise the pivot row and column
h = 0
k = 0
while h < m and k < n:
# Find the k-th pivot:
pivots[k] = np.argmax(LU[h:, k]) + h
if LU[pivots[k], k] == 0:
# No pivot in this column, pass to next column
k = k+1
else:
# swap rows
LU[[h, pivots[k]], :] = LU[[pivots[k], h], :]
# Do for all rows below pivot:
for i in range(h+1, m):
f = LU[i, k] / LU[h, k]
# Store f as the new L column values
LU[i, k] = f
# Do for all remaining elements in current row:
for j in range(k + 1, n):
LU[i, j] = LU[i, j] - LU[h, j] * f
# Increase pivot row and column
h = h + 1
k = k + 1
return LU, pivots
def random_matrix(n):
R = np.random.rand(n, n)
A = np.zeros((n, n))
triu = | np.triu_indices(n) | numpy.triu_indices |
import os
import math
import numpy as np
import matplotlib.pyplot as plt
from scipy import interpolate
from django.shortcuts import render
from django.conf import settings
def get_res(D_o: float):
for i in range(1,7):
plt.figure(i)
plt.cla()
plt.clf()
teta_HO=[]
input_teta_txt=open(settings.STATICFILES_DIRS[1]/'input_teta.txt','r+')
for num in input_teta_txt.readlines():
teta_HO.append(float(num))
# D_o=0.324
t=0.0205
D_in=D_o-(2*t)
A_out=math.pi*(D_o**2)/4
A_in=math.pi*(D_in**2)/4
Area=A_out-A_in
I=math.pi*(D_o**4-D_in**4)/64
ro_s=7850
ro_c=494
ro_w=1025
m_s=Area*ro_s
m_c=A_in*ro_c
m_bouy=A_out*ro_w
m_subm=m_s+m_c-m_bouy
g=9.81
Depth=1800
k=300000
E=207000000000
delta_Z=1600
Z_A=delta_Z-(D_o/2)
size_teta=len(teta_HO) # teta_HO should be positive values.
# creating list with teta size
teta_HO_rad=[0]*size_teta
H_T=[0]*size_teta
X_TDP_cat=[0]*size_teta
S_TDP_cat=[0]*size_teta
landa=[0]*size_teta
K_BLM=[0]*size_teta
cur_BLM_0=[0]*size_teta
kesi_f=[0]*size_teta
s_f=[0]*size_teta
S_TDP_BLM=[0]*size_teta
X_TDP_BLM=[0]*size_teta
x=np.arange(-3500,9601)/10
size_x=len(x)
kesi=np.array([[0.0]*size_teta]*size_x)
cur_BLM=np.array([[0.0]*size_teta]*size_x)
mom_BLM=np.array([[0.0]*size_teta]*size_x)
mom_cat=np.array([[0.0]*size_teta]*size_x)
s=np.array([[0.0]*size_teta]*size_x)
mom_fin=np.array([[0.0]*size_teta]*size_x)
Eff_T=np.array([[0.0]*size_teta]*size_x)
z=np.array([[0.0]*size_teta]*size_x)
h=np.array([[0.0]*size_teta]*size_x)
Ext_Force=np.array([[0.0]*size_teta]*size_x)
Int_Force=np.array([[0.0]*size_teta]*size_x)
Wall_T=np.array([[0.0]*size_teta]*size_x)
x_from_ho=np.array([[0.0]*size_teta]*size_x)
z_from_ho= | np.array([[0.0]*size_teta]*size_x) | numpy.array |
"""
setinit:
this routine creates local directories and makes topo, qinit, and aux DEMs
to be used by setrun.py
If you have other files, modify this and/or your setrun.py accordingly.
"""
import numpy as np
import dclaw.topotools as gt
import os
#import pylab
#import pdb
cdir = os.path.abspath(os.environ['PWD'])
#---create local directories for data if they do not exist----------
indatadir=os.path.join(cdir,'init_data')
topodir = os.path.join(cdir,indatadir,'topo')
auxdir = os.path.join(cdir,indatadir,'aux')
qinitdir = os.path.join(cdir,indatadir,'qinit')
if not os.path.isdir(indatadir):
execstr = 'mkdir '+indatadir
os.system(execstr)
if not os.path.isdir(topodir):
execstr = 'mkdir '+topodir
os.system(execstr)
if not os.path.isdir(auxdir):
execstr = 'mkdir '+auxdir
os.system(execstr)
if not os.path.isdir(qinitdir):
execstr = 'mkdir '+qinitdir
os.system(execstr)
#------------------------------------------------------------------------
#---------------- functions for flume geometry to build DEMs ------------
def zero(X,Y):
yind1 = np.where((Y[:,0]>=-0.5)&(Y[:,0]<=0.0))[0]
yind2 = np.where((Y[:,0]>=2.0)&(Y[:,0]<=2.5))[0]
xind = np.where((X[0,:]>=-15.0)&(X[0,:]<=90.0))[0]
Z = np.zeros(np.shape(X))
return Z
def wallzero(X,Y):
yind1 = np.where((Y[:,0]>=-0.5)&(Y[:,0]<=0.0))[0]
yind2 = np.where((Y[:,0]>=2.0)&(Y[:,0]<=2.5))[0]
xind = np.where((X[0,:]>=-15.0)&(X[0,:]<=82.5))[0]
xhopperind = np.where((X[0,:]>=-15.0)&(X[0,:]<=0.0))[0]
Z = np.zeros(np.shape(X))
Z[np.ix_(yind1,xind)] = 1.6
Z[np.ix_(yind2,xind)] = 1.6
Z[np.ix_(yind1,xhopperind)] = 2.5
Z[np.ix_(yind2,xhopperind)] = 2.5
return Z
def zero_backstop(X,Y):
yind1 = np.where((Y[:,0]>=-0.5)&(Y[:,0]<=0.0))[0]
yind2 = np.where((Y[:,0]>=2.0)&(Y[:,0]<=2.5))[0]
xind = np.where((X[0,:]>=-15.0)&(X[0,:]<=90.0))[0]
xbackstopind = np.where(X[0,:]<=-4.0)[0]
ybackstopind = np.where((Y[:,0]>=-0.5)&(Y[:,0]<=2.5))[0]
Z = np.zeros(np.shape(X))
Z[np.ix_(ybackstopind,xbackstopind)] = 2.5
return Z
def wallzero_backstop(X,Y):
yind1 = np.where((Y[:,0]>=-0.5)&(Y[:,0]<=0.0))[0]
yind2 = np.where((Y[:,0]>=2.0)&(Y[:,0]<=2.5))[0]
xind = np.where((X[0,:]>=-15.0)&(X[0,:]<=82.5))[0]
xhopperind = np.where((X[0,:]>=-15.0)&(X[0,:]<=0.0))[0]
Z = np.zeros(np.shape(X))
xbackstopind = np.where(X[0,:]<=-4.0)[0]
ybackstopind = np.where((Y[:,0]>=-0.5)&(Y[:,0]<=2.5))[0]
Z[np.ix_(yind1,xind)] = 1.6
Z[np.ix_(yind2,xind)] = 1.6
Z[np.ix_(yind1,xhopperind)] = 2.5
Z[np.ix_(yind2,xhopperind)] = 2.5
Z[np.ix_(ybackstopind,xbackstopind)] = 2.5
return Z
def flume_eta(X,Y):
hopperlen = 4.7
hmax = 1.9
hoppertop = 3.3
topangle = 17.0*np.pi/180.0
flumeangle = 31.0*np.pi/180.0
x0 = -hopperlen
x2 = -hmax*np.cos(0.5*np.pi - flumeangle)
x1 = x2 - hoppertop*np.cos(flumeangle-topangle)
x3 = 0.0
y2 = hmax*np.sin(0.5*np.pi - flumeangle)
y1 = y2 - hoppertop*np.sin(flumeangle-topangle)
slope0 = y1/(x1-x0)
slope1 = (y2-y1)/(x2-x1)
slope2 = -y2/(x3-x2)
yind = np.where((Y[:,0]<=2.0)&(Y[:,0]>=0.0))[0]
x0ind = np.where((X[0,:]>=x0)&(X[0,:]<x1))[0]
x1ind = np.where((X[0,:]>=x1)&(X[0,:]<x2))[0]
x2ind = np.where((X[0,:]>=x2)&(X[0,:]<x3))[0]
#pdb.set_trace()
Z=np.zeros(np.shape(X))
Z[np.ix_(yind,x0ind)] = (X[np.ix_(yind,x0ind)]-x0)*slope0
Z[np.ix_(yind,x1ind)] = y1+(X[np.ix_(yind,x1ind)]-x1)*slope1
Z[np.ix_(yind,x2ind)] = -(x3-X[np.ix_(yind,x2ind)])*slope2
return Z
def flume_eta_res(X,Y):
hopperlen = 4.7
hmax = 1.9
hoppertop = 3.3
topangle = 17.0*np.pi/180.0
flumeangle = 31.0*np.pi/180.0
x0 = -hopperlen
x2 = -hmax*np.cos(0.5*np.pi - flumeangle)
x1 = x2 - hoppertop*np.cos(flumeangle-topangle)
x3 = 0.0
y2 = hmax*np.sin(0.5*np.pi - flumeangle)
y1 = y2 - hoppertop*np.sin(flumeangle-topangle)
xm1 = x1 - y1*np.tan(0.5*np.pi - flumeangle)
slope0 = y1/(x1-xm1)
slope1 = (y2-y1)/(x2-x1)
slope2 = -y2/(x3-x2)
yind = np.where((Y[:,0]<=2.0)&(Y[:,0]>=0.0))[0]
xm1ind = np.where((X[0,:]>=xm1)&(X[0,:]<x1))[0]
x1ind = np.where((X[0,:]>=x1)&(X[0,:]<x2))[0]
x2ind = np.where((X[0,:]>=x2)&(X[0,:]<x3))[0]
#pdb.set_trace()
Z=np.zeros(np.shape(X))
Z[np.ix_(yind,xm1ind)] = (X[np.ix_(yind,xm1ind)]-xm1)*slope0
Z[np.ix_(yind,x1ind)] = y1+(X[np.ix_(yind,x1ind)]-x1)*slope1
Z[np.ix_(yind,x2ind)] = -(x3-X[np.ix_(yind,x2ind)])*slope2
return Z
def flume_eta_res_half(X,Y):
hopperlen = 4.7
hmax = 1.9
hoppertop = 3.3
topangle = 17.0*np.pi/180.0
flumeangle = 31.0*np.pi/180.0
x0 = -hopperlen
x2 = -hmax*np.cos(0.5*np.pi - flumeangle)
x1 = x2 - hoppertop*np.cos(flumeangle-topangle)
x3 = 0.0
y2 = hmax*np.sin(0.5*np.pi - flumeangle)
y1 = y2 - hoppertop*np.sin(flumeangle-topangle)
xm1 = x1 - y1*np.tan(0.5*np.pi - flumeangle)
xmhalf = 0.5*(x0 + xm1)
slope0 = y1/(x1-xm1)
slopehalf = y1/(x1-xmhalf)
slope1 = (y2-y1)/(x2-x1)
slope2 = -y2/(x3-x2)
yind = np.where((Y[:,0]<=2.0)&(Y[:,0]>=0.0))[0]
xmhalfind = np.where((X[0,:]> xmhalf)&(X[0,:]<x1))[0]
x1ind = np.where((X[0,:]>=x1)&(X[0,:]<x2))[0]
x2ind = np.where((X[0,:]>=x2)&(X[0,:]<x3))[0]
#pdb.set_trace()
Z=np.zeros( | np.shape(X) | numpy.shape |
"""
Module for neural analysis
"""
import numpy as np
from typing import Any, Callable, Dict, List, NamedTuple, Optional, Tuple
def get_isi(spk_ts_list: list):
"""
Get inter-analysis interval of spikes
Parameters
----------
spk_ts_list : list
Returns
-------
isi : class object
class object for inter-spike intervals
"""
isi = np.array([], dtype=np.float64)
for spk in spk_ts_list:
isi = np.append(isi, np.diff(spk))
isi = ISI(isi) # return the class object
return isi
def get_peth(evt_ts_list: list, spk_ts_list: list,
pre_evt_buffer=None, duration=None,
bin_size=None,
nb_bins=None
):
"""
Get peri-event histogram & firing rates
Parameters
----------
evt_ts_list : list
Timestamps for behavioral events (e.g., syllable onset/offsets)
spk_ts_list : list
Spike timestamps
pre_evt_buffer : int, default=None
Size of buffer window prior to the first event (in ms)
duration : int, optional
Duration of the peth (in ms). Truncate the
bin_size : int, default=None
Time bin size
nb_bins : int, default=None
Number of bins
Returns
-------
peth : np.ndarray
Peri-event time histograms
time_bin : np.ndarray
Time bin vector
parameter : dict
Parameters for draw peth
Notes
-----
If pre_evt_buffer, bin_size, nb_bins not specified,
take values from analysis ..analysis.parameters
"""
from ..analysis.parameters import peth_parm
import copy
import math
parameter = peth_parm.copy()
if pre_evt_buffer is None:
pre_evt_buffer = parameter['buffer']
if bin_size is None:
bin_size = parameter['bin_size']
if nb_bins is None:
nb_bins = parameter['nb_bins']
time_bin = np.arange(0, nb_bins, bin_size) - pre_evt_buffer
peth = np.zeros((len(evt_ts_list), nb_bins)) # nb of trials x nb of time bins
for trial_ind, (evt_ts, spk_ts) in enumerate(zip(evt_ts_list, spk_ts_list)):
spk_ts_new = copy.deepcopy(spk_ts)
if not isinstance(evt_ts, np.float64):
# evt_ts = np.asarray(list(map(float, evt_ts))) + pre_evt_buffer
# spk_ts_new -= evt_ts[0]
evt_ts = np.asarray(list(map(float, evt_ts)))
spk_ts_new -= evt_ts[0]
spk_ts_new += pre_evt_buffer
else:
spk_ts_new -= evt_ts
spk_ts_new += pre_evt_buffer
for spk in spk_ts_new:
ind = math.ceil(spk / bin_size)
# print("spk = {}, bin index = {}".format(spk, ind)) # for debugging
if ind < 0: raise Exception("Index out of bound")
peth[trial_ind, ind] += 1
# Truncate the array leaving out only the portion of our interest
if duration:
ind = np.where(((0 - pre_evt_buffer) <= time_bin) & (time_bin < duration))[0]
peth = peth[:, ind[0]:ind[-1]+1]
time_bin = time_bin[ind[0]:ind[-1]+1]
return peth, time_bin, parameter
def get_pcc(fr_array: np.ndarray) -> dict:
"""
Get pairwise cross-correlation
Parameters
----------
fr_array : np.ndarray
(trial x time_bin)
Returns
-------
pcc_dict : dict
"""
pcc_dict = {}
pcc_arr = np.array([])
for ind1, fr1 in enumerate(fr_array):
for ind2, fr2 in enumerate(fr_array):
if ind2 > ind1:
if np.linalg.norm((fr1 - fr1.mean()), ord=1) * np.linalg.norm((fr2 - fr2.mean()), ord=1):
if not np.isnan(np.corrcoef(fr1, fr2)[0, 1]):
pcc_arr = np.append(pcc_arr, np.corrcoef(fr1, fr2)[0, 1]) # get correlation coefficient
pcc_dict['array'] = pcc_arr
pcc_dict['mean'] = round(pcc_arr.mean(), 3)
return pcc_dict
def jitter_spk_ts(spk_ts_list, shuffle_limit, reproducible=True):
"""
Add a random temporal jitter to the spike
Parameters
----------
reproducible : bool
Make the results reproducible by setting the seed as equal to index
"""
spk_ts_jittered_list = []
for ind, spk_ts in enumerate(spk_ts_list):
np.random.seed()
if reproducible: # randomization seed
seed = ind
np.random.seed(seed) # make random jitter reproducible
else:
seed = np.random.randint(len(spk_ts_list), size=1)
np.random.seed(seed) # make random jitter reproducible
nb_spk = spk_ts.shape[0]
jitter = np.random.uniform(-shuffle_limit, shuffle_limit, nb_spk)
spk_ts_jittered_list.append(spk_ts + jitter)
return spk_ts_jittered_list
def pcc_shuffle_test(ClassObject, PethInfo, plot_hist=False, alpha=0.05):
"""
Run statistical test to see if baseline pairwise cross-correlation obtained by spike time shuffling is significant
Parameters
----------
ClassObject : class object (e.g., NoteInfo, MotifInfo)
PethInfo : peth info class object
plot_hist : bool
Plot histogram of bootstrapped pcc values (False by default)
Returns
-------
p_sig : dict
True if the pcc is significantly above the baseline
"""
from ..analysis.parameters import peth_shuffle
from collections import defaultdict
from functools import partial
import scipy.stats as stats
import matplotlib.pyplot as plt
pcc_shuffle = defaultdict(partial(np.ndarray, 0))
for i in range(peth_shuffle['shuffle_iter']):
ClassObject.jitter_spk_ts(peth_shuffle['shuffle_limit'])
pi_shuffle = ClassObject.get_note_peth(shuffle=True) # peth object
pi_shuffle.get_fr() # get firing rates
pi_shuffle.get_pcc() # get pcc
for context, pcc in pi_shuffle.pcc.items():
pcc_shuffle[context] = np.append(pcc_shuffle[context], pcc['mean'])
# One-sample t-test (one-sided)
p_val = {}
p_sig = {}
for context in pcc_shuffle.keys():
(_, p_val[context]) = stats.ttest_1samp(a=pcc_shuffle[context], popmean=PethInfo.pcc[context]['mean'],
nan_policy='omit', alternative='less') # one-tailed t-test
for context, value in p_val.items():
p_sig[context] = value < alpha
# Plot histogram
if plot_hist:
from ..utils.draw import remove_right_top
fig, axes = plt.subplots(1, 2, figsize=(6, 3))
plt.suptitle('PCC shuffle distribution', y=.98, fontsize=10)
for axis, context in zip(axes, pcc_shuffle.keys()):
axis.set_title(context)
axis.hist(pcc_shuffle[context], color='k')
axis.set_xlim([-0.1, 0.6])
axis.set_xlabel('PCC'), axis.set_ylabel('Count')
if p_sig[context]:
axis.axvline(x=PethInfo.pcc[context]['mean'], color='r', linewidth=1, ls='--')
else:
axis.axvline(x=PethInfo.pcc[context]['mean'], color='k', linewidth=1, ls='--')
remove_right_top(axis)
plt.tight_layout()
plt.show()
return p_sig
class ClusterInfo:
def __init__(self, path, channel_nb, unit_nb, format='rhd', *name, update=False, time_unit='ms'):
"""
Load information about cluster
Parameters
----------
path : path
path that contains recording files for the cluster
channel_nb : int
number of the channel that recorded the cluster
unit_nb : int
number id of the cluster (needed because multiple neurons could have been recorded in the same session & channel)
format : str
'rhd' by default (Intan)
name : name of the cluster
e.g., ('096-g70r40-Predeafening-D07(20191106)-S03-Ch17-Cluster01')
update : bool
If not exists, create a .npz cache file in the same folder so that it doesn't read from the raw data every time the class is called.
time_unit : str
'ms' by default
"""
from ..analysis.load import load_song
self.path = path
if channel_nb: # if a neuron was recorded
if len(str(channel_nb)) == 1:
self.channel_nb = 'Ch0' + str(channel_nb)
elif len(str(channel_nb)) == 2:
self.channel_nb = 'Ch' + str(channel_nb)
else:
self.channel_nb = 'Ch'
self.unit_nb = unit_nb
self.format = format
if name:
self.name = name[0]
else:
self.name = self.path
self._print_name()
# Load events
file_name = self.path / "ClusterInfo_{}_Cluster{}.npy".format(self.channel_nb, self.unit_nb)
if update or not file_name.exists(): # if .npy doesn't exist or want to update the file
song_info = load_song(self.path)
# Save cluster_info as a numpy object
np.save(file_name, song_info)
else:
song_info = np.load(file_name, allow_pickle=True).item()
# Set the dictionary values to class attributes
for key in song_info:
setattr(self, key, song_info[key])
# Load spike
if channel_nb and unit_nb:
self._load_spk(time_unit)
def __repr__(self): # print attributes
return str([key for key in self.__dict__.keys()])
def _print_name(self) -> None:
print('')
print('Load cluster {self.name}'.format(self=self))
def list_files(self, ext: str):
from ..utils.functions import list_files
return list_files(self.path, ext)
def _load_spk(self, time_unit, delimiter='\t') -> None:
"""
Load spike information
Parameters
----------
time_unit : str
time unit (e.g., 'ms')
delimiter : str
delimiter of the cluster file (tab (\t) by default)
Returns
-------
sets spk_wf, spk_ts, nb_spk as attributes
"""
spk_txt_file = list(self.path.glob('*' + self.channel_nb + '(merged).txt'))
if not spk_txt_file:
print("spk text file doesn't exist !")
return
spk_txt_file = spk_txt_file[0]
spk_info = np.loadtxt(spk_txt_file, delimiter=delimiter, skiprows=1) # skip header
# Select only the unit (there could be multiple isolated units in the same file)
if self.unit_nb: # if the unit number is specified
spk_info = spk_info[spk_info[:, 1] == self.unit_nb, :]
spk_ts = spk_info[:, 2] # analysis time stamps
spk_wf = spk_info[:, 3:] # analysis waveform
nb_spk = spk_wf.shape[0] # total number of spikes
self.spk_wf = spk_wf # individual waveforms
self.nb_spk = nb_spk # the number of spikes
# Units are in second by default, but convert to millisecond with the argument
if time_unit == 'ms':
spk_ts *= 1E3
# Output analysis timestamps per file in a list
spk_list = []
for file_start, file_end in zip(self.file_start, self.file_end):
spk_list.append(spk_ts[np.where((spk_ts >= file_start) & (spk_ts <= file_end))])
self.spk_ts = spk_list # analysis timestamps in ms
# print("spk_ts, spk_wf, nb_spk attributes added")
def analyze_waveform(self,
align_wf=True,
interpolate=True, interp_factor=None
):
"""
Perform waveform analysis
Parameters
----------
align_wf : bool
align all spike waveforms relative to the max location
interpolate : bool
Set to true if waveform interpolation is needed
interp_factor : int
Factor by which to increase the sampling frequency of the waveform
e.g., 100 if you want to increase the data points by 100 fold
"""
from ..analysis.functions import align_waveform, get_half_width
from ..analysis.parameters import sample_rate
if align_wf:
self.spk_wf = align_waveform(self.spk_wf)
def _get_spk_profile(wf_ts, avg_wf, interpolate=interpolate):
spk_height = np.abs(np.max(avg_wf) - np.min(avg_wf)) # in microseconds
if interpolate:
spk_width = abs(((np.argmax(avg_wf) - np.argmin(avg_wf)) + 1)) * (
(1 / sample_rate[self.format]) / interp_factor) * 1E6 # in microseconds
else:
spk_width = abs(((np.argmax(avg_wf) - np.argmin(avg_wf)) + 1)) * (
1 / sample_rate[self.format]) * 1E6 # in microseconds
deflection_range, half_width = get_half_width(wf_ts, avg_wf) # get the half width from the peak deflection
return spk_height, spk_width, half_width, deflection_range
if not interp_factor:
from ..analysis.parameters import interp_factor
interp_factor = interp_factor
self.avg_wf = np.nanmean(self.spk_wf, axis=0)
self.wf_ts = np.arange(0, self.avg_wf.shape[0]) / sample_rate[self.format] * 1E3 # x-axis in ms
if interpolate: # interpolate the waveform to increase sampling frequency
from scipy import interpolate
f = interpolate.interp1d(self.wf_ts, self.avg_wf)
wf_ts_interp = np.arange(0, self.wf_ts[-1], ((self.wf_ts[1] - self.wf_ts[0]) * (1 / interp_factor)))
assert (np.diff(wf_ts_interp)[0] * interp_factor) == np.diff(self.wf_ts)[0]
avg_wf_interp = f(wf_ts_interp) # use interpolation function returned by `interp1d`
# Replace the original value with interpolated ones
self.wf_ts_interp = wf_ts_interp
self.avg_wf_interp = avg_wf_interp
spk_height, spk_width, half_width, deflection_range = _get_spk_profile(wf_ts_interp, avg_wf_interp)
else:
spk_height, spk_width, half_width, deflection_range = _get_spk_profile(self.wf_ts, self.avg_wf)
self.spk_height = round(spk_height, 3) # in microvolts
self.spk_width = round(spk_width, 3) # in microseconds
self.half_width = half_width
self.deflection_range = deflection_range # the range where half width was calculated
# print("avg_wf, spk_height (uv), spk_width (us), wf_ts (ms) added")
def get_conditional_spk(self) -> dict:
"""Get spike timestamps from different contexts"""
conditional_spk = {}
conditional_spk['U'] = [spk_ts for spk_ts, context in zip(self.spk_ts, self.contexts) if context == 'U']
conditional_spk['D'] = [spk_ts for spk_ts, context in zip(self.spk_ts, self.contexts) if context == 'D']
return conditional_spk
def get_correlogram(self, ref_spk_list, target_spk_list, normalize=False) -> dict:
"""Get auto- or cross-correlogram"""
from ..analysis.parameters import spk_corr_parm
import math
correlogram = {}
for social_context in set(self.contexts):
# Compute spk correlogram
corr_temp = np.zeros(len(spk_corr_parm['time_bin']))
for ref_spks, target_spks, context in zip(ref_spk_list, target_spk_list, self.contexts):
if context == social_context:
for ref_spk in ref_spks:
for target_spk in target_spks:
diff = target_spk - ref_spk # time difference between two spikes
if (diff) and (diff <= spk_corr_parm['lag'] and diff >= -spk_corr_parm['lag']):
if diff < 0:
ind = np.where(spk_corr_parm['time_bin'] <= -math.ceil(abs(diff)))[0][-1]
elif diff > 0:
ind = np.where(spk_corr_parm['time_bin'] >= math.ceil(diff))[0][0]
# print("diff = {}, bin index = {}".format(diff, spk_corr_parm['time_bin'][ind])) # for debugging
corr_temp[ind] += 1
# Make sure the array is symmetrical
first_half = np.fliplr([corr_temp[:int((spk_corr_parm['lag'] / spk_corr_parm['bin_size']))]])[0]
second_half = corr_temp[int((spk_corr_parm['lag'] / spk_corr_parm['bin_size'])) + 1:]
assert np.sum(first_half - second_half) == 0
# Normalize correlogram by the total sum (convert to probability density )
if normalize:
corr_temp /= np.sum(correlogram)
correlogram[social_context] = corr_temp
correlogram['parameter'] = spk_corr_parm # store parameters in the dictionary
return correlogram
def jitter_spk_ts(self, shuffle_limit, reproducible=True):
"""
Add a random temporal jitter to the spike
Parameters
----------
shuffle_limit : int
shuffling limit (in ms)
e.g., If set to 5, any integer values between -5 to 5 drawn from uniform distribution will be added to the spike timestamp
reproducible : bool
make the results reproducible by setting the seed as equal to index
"""
spk_ts_jittered_list = []
for ind, spk_ts in enumerate(self.spk_ts):
np.random.seed()
if reproducible: # randomization seed
seed = ind
np.random.seed(seed) # make random jitter reproducible
else:
seed = np.random.randint(len(self.spk_ts), size=1)
np.random.seed(seed) # make random jitter reproducible
nb_spk = spk_ts.shape[0]
jitter = np.random.uniform(-shuffle_limit, shuffle_limit, nb_spk)
spk_ts_jittered_list.append(spk_ts + jitter)
self.spk_ts_jittered = spk_ts_jittered_list
def get_jittered_corr(self) -> dict:
"""Get spike correlogram from time-jittered spikes"""
from ..analysis.parameters import corr_shuffle
from collections import defaultdict
correlogram_jitter = defaultdict(list)
for iter in range(corr_shuffle['shuffle_iter']):
self.jitter_spk_ts(corr_shuffle['shuffle_limit'])
corr_temp = self.get_correlogram(self.spk_ts_jittered, self.spk_ts_jittered)
# Combine correlogram from two contexts
for key, value in corr_temp.items():
if key != 'parameter':
try:
correlogram_jitter[key].append(value)
except:
correlogram_jitter[key] = value
# Convert to array
for key, value in correlogram_jitter.items():
correlogram_jitter[key] = (np.array(value))
return correlogram_jitter
def get_isi(self, add_premotor_spk=False):
"""
Get inter-spike interval
Parameters
----------
add_premotor_spk : bool
Add spikes from the premotor window for calculation
"""
isi_dict = {}
list_zip = zip(self.onsets, self.offsets, self.spk_ts)
if not add_premotor_spk:
# Include spikes from the pre-motif buffer for calculation
# Pre-motor spikes are included in spk_list by default
spk_list = []
for onset, offset, spks in list_zip:
onset = np.asarray(list(map(float, onset)))
offset = np.asarray(list(map(float, offset)))
spk_list.append(spks[np.where((spks >= onset[0]) & (spks <= offset[-1]))])
for context1 in set(self.contexts):
if not add_premotor_spk:
spk_list_context = [spk_ts for spk_ts, context2 in zip(spk_list, self.contexts) if context2 == context1]
else:
spk_list_context = [spk_ts for spk_ts, context2 in zip(self.spk_ts, self.contexts) if
context2 == context1]
isi_dict[context1] = get_isi(spk_list_context)
return isi_dict
@property
def nb_files(self) -> dict:
"""
Return the number of files per context
Returns
-------
nb_files : dict
Number of files per context ('U', 'D', 'All')
"""
nb_files = {}
nb_files['U'] = len([context for context in self.contexts if context == 'U'])
nb_files['D'] = len([context for context in self.contexts if context == 'D'])
nb_files['All'] = nb_files['U'] + nb_files['D']
return nb_files
def nb_bouts(self, song_note: str) -> dict:
"""
Return the number of bouts per context
Parameters
----------
song_note : str
song motif syllables
Returns
-------
nb_bouts : dict
"""
from ..analysis.functions import get_nb_bouts
nb_bouts = {}
syllable_list = [syllable for syllable, context in zip(self.syllables, self.contexts) if context == 'U']
syllables = ''.join(syllable_list)
nb_bouts['U'] = get_nb_bouts(song_note, syllables)
syllable_list = [syllable for syllable, context in zip(self.syllables, self.contexts) if context == 'D']
syllables = ''.join(syllable_list)
nb_bouts['D'] = get_nb_bouts(song_note, syllables)
nb_bouts['All'] = nb_bouts['U'] + nb_bouts['D']
return nb_bouts
def nb_motifs(self, motif: str) -> dict:
"""
Return the number of motifs per context
Parameters
----------
motf : str
Song motif (e.g., 'abcd')
Returns
-------
nb_motifs : dict
"""
from ..utils.functions import find_str
nb_motifs = {}
syllable_list = [syllable for syllable, context in zip(self.syllables, self.contexts) if context == 'U']
syllables = ''.join(syllable_list)
nb_motifs['U'] = len(find_str(syllables, motif))
syllable_list = [syllable for syllable, context in zip(self.syllables, self.contexts) if context == 'D']
syllables = ''.join(syllable_list)
nb_motifs['D'] = len(find_str(syllables, motif))
nb_motifs['All'] = nb_motifs['U'] + nb_motifs['D']
return nb_motifs
def get_note_info(self, target_note,
pre_buffer=0, post_buffer=0
):
"""
Obtain a class object (NoteInfo) for individual note
spikes will be collected from note onset (+- pre_buffer) to offset (+- post_buffer)
Parameters
----------
target_note : str
Get information from this note
pre_buffer : int
Amount of time buffer relative to the event onset (e.g., syllable onset)
post_buffer : int
Amount of time buffer relative to the event offset (e.g., syllable onset)
Returns
-------
NoteInfo : class object
"""
from ..utils.functions import find_str
syllables = ''.join(self.syllables)
onsets = np.hstack(self.onsets)
offsets = np.hstack(self.offsets)
durations = np.hstack(self.durations)
contexts = ''
for i in range(len(self.contexts)): # concatenate contexts
contexts += self.contexts[i] * len(self.syllables[i])
ind = np.array(find_str(syllables, target_note)) # get note indices
if not ind.any(): # skil if the note does not exist
return
note_onsets = np.asarray(list(map(float, onsets[ind])))
note_offsets = np.asarray(list(map(float, offsets[ind])))
note_durations = np.asarray(list(map(float, durations[ind])))
note_contexts = ''.join(np.asarray(list(contexts))[ind])
# Get the note that immeidately follows
next_notes = ''
for i in ind:
next_notes += syllables[i + 1]
# Get spike info
spk_ts = np.hstack(self.spk_ts)
note_spk_ts_list = []
for onset, offset in zip(note_onsets, note_offsets):
note_spk_ts_list.append(
spk_ts[np.where((spk_ts >= onset - pre_buffer) & (spk_ts <= offset + post_buffer))])
# Organize data into a dictionary
note_info = {
'note': target_note,
'next_notes' : next_notes,
'onsets': note_onsets,
'offsets': note_offsets,
'durations': note_durations,
'contexts': note_contexts,
'median_dur': np.median(note_durations, axis=0),
'spk_ts': note_spk_ts_list,
'path': self.path, # directory where the data exists
'pre_buffer' : pre_buffer,
'post_buffer' : post_buffer
}
return NoteInfo(note_info) # return note info
@property
def open_folder(self) -> None:
"""Open the data folder"""
from ..utils.functions import open_folder
open_folder(self.path)
class NoteInfo:
"""
Class for storing information about a single note syllable and its associated spikes
"""
def __init__(self, note_dict):
# Set the dictionary values to class attributes
for key in note_dict:
setattr(self, key, note_dict[key])
# Perform PLW (piecewise linear warping)
self.spk_ts_warp = self._piecewise_linear_warping()
def __repr__(self):
return str([key for key in self.__dict__.keys()])
def select_index(self, index) -> None:
"""
Select only the notes with the matching index
Parameters
----------
index : np.array or list
Note indices to keep
"""
if isinstance(index, list):
index = np.array(index)
self.contexts = ''.join(np.array(list(self.contexts))[index])
self.onsets, self.offsets, self.durations, self.spk_ts, self.spk_ts_warp \
= self.onsets[index], self.offsets[index], self.durations[index], self.spk_ts[index], self.spk_ts_warp[index]
def select_context(self, target_context : str,
keep_median_duration=True
) -> None:
"""
Select one context
Parameters
----------
target_context : str
'U' or 'D'
keep_median_duration : bool
Normally medial note duration is calculated using all syllables regardless of the context
one may prefer to use this median to reduce variability when calculating pcc
if set False, new median duration will be calculated using the selected notes
"""
zipped_list = \
list(zip(self.contexts, self.next_notes, self.onsets, self.offsets, self.durations, self.spk_ts, self.spk_ts_warp))
zipped_list = list(filter(lambda x: x[0] == target_context, zipped_list)) # filter context
unzipped_object = zip(*zipped_list)
self.contexts, self.next_notes, self.onsets, self.offsets, self.durations, self.spk_ts, self.spk_ts_warp = \
list(unzipped_object)
self.contexts = ''.join(self.contexts)
self.next_notes = ''.join(self.next_notes)
self.onsets = np.array(self.onsets)
self.offsets = np.array(self.offsets)
self.durations = np.array(self.durations)
self.spk_ts = np.array(self.spk_ts)
self.spk_ts_warp = np.array(self.spk_ts_warp)
if not keep_median_duration:
self.median_dur = np.median(self.median_dur, axis=0)
def get_entropy(self, normalize=True, mode='spectral'):
"""
Calculate syllable entropy from all renditions and get the average
Two versions : spectro-temporal entropy & spectral entropy
"""
from ..analysis.parameters import nb_note_crit
from ..analysis.functions import get_spectral_entropy, get_spectrogram
from ..utils.functions import find_str
entropy_mean = {}
entropy_var = {}
audio = AudioData(self.path)
for context in ['U', 'D']:
se_mean_arr = np.array([], dtype=np.float32)
se_var_arr = np.array([], dtype=np.float32)
ind = np.array(find_str(self.contexts, context))
if ind.shape[0] >= nb_note_crit:
for (start, end) in zip(self.onsets[ind], self.offsets[ind]):
timestamp, data = audio.extract([start, end]) # audio object
_, spect, _ = get_spectrogram(timestamp, data, audio.sample_rate)
se = get_spectral_entropy(spect, normalize=normalize, mode=mode)
if isinstance(se, dict):
se_mean_arr = np.append(se_mean_arr, se['mean']) # spectral entropy averaged over time bins per rendition
se_var_arr = np.append(se_var_arr, se['var']) # spectral entropy variance per rendition
else:
se_mean_arr = np.append(se_mean_arr, se) # spectral entropy time-resolved
entropy_mean[context] = round(se_mean_arr.mean(), 3)
entropy_var[context] = round(se_var_arr.mean(), 5)
if mode == 'spectro_temporal':
return entropy_mean, entropy_var
else: # spectral entropy (does not have entropy variance)
return entropy_mean
def _piecewise_linear_warping(self):
"""Perform piecewise linear warping per note"""
import copy
note_spk_ts_warp_list = []
for onset, duration, spk_ts in zip(self.onsets, self.durations, self.spk_ts):
spk_ts_new = copy.deepcopy(spk_ts)
ratio = self.median_dur / duration
origin = 0
spk_ts_temp, ind = spk_ts[spk_ts >= onset], np.where(spk_ts >= onset)
spk_ts_temp = ((ratio * ((spk_ts_temp - onset))) + origin) + onset
np.put(spk_ts_new, ind, spk_ts_temp) # replace original spk timestamps with warped timestamps
note_spk_ts_warp_list.append(spk_ts_new)
return note_spk_ts_warp_list
def get_note_peth(self, time_warp=True, shuffle=False, pre_evt_buffer=None, duration=None,
bin_size=None,
nb_bins=None
):
"""
Get peri-event time histograms for single syllable
Parameters
----------
time_warp : perform piecewise linear transform
shuffle : add jitter to spike timestamps
duration : duration of the peth
bin_size : size of single bin (in ms) (take values from peth_parm by default)
nb_bins : number of time bins (take values from peth_parm by default)
Returns
-------
PethInfo : class object
"""
peth_dict = {}
if shuffle:
peth, time_bin, peth_parm = \
get_peth(self.onsets, self.spk_ts_jittered,
pre_evt_buffer=pre_evt_buffer, duration=duration,
bin_size=bin_size,
nb_bins=nb_bins
)
else:
if time_warp: # peth calculated from time-warped spikes by default
# peth, time_bin = get_note_peth(self.onsets, self.spk_ts_warp, self.median_durations.sum()) # truncated version to fit the motif duration
peth, time_bin, peth_parm = \
get_peth(self.onsets, self.spk_ts_warp,
pre_evt_buffer=pre_evt_buffer, duration=duration,
bin_size = bin_size,
nb_bins = nb_bins
)
else:
peth, time_bin, peth_parm = \
get_peth(self.onsets, self.spk_ts,
pre_evt_buffer=pre_evt_buffer, duration=duration,
bin_size=bin_size,
nb_bins=nb_bins
)
peth_dict['peth'] = peth
peth_dict['time_bin'] = time_bin
peth_dict['parameters'] = peth_parm
peth_dict['contexts'] = self.contexts
peth_dict['median_duration'] = self.median_dur
return PethInfo(peth_dict) # return peth class object for further analysis
def jitter_spk_ts(self, shuffle_limit):
"""
Add a random temporal jitter to the spike
This version limit the jittered timestamp within the motif window
"""
from ..analysis.parameters import pre_motor_win_size
spk_ts_jittered_list = []
list_zip = zip(self.onsets, self.offsets, self.spk_ts)
for ind, (onset, offset, spk_ts) in enumerate(list_zip):
# Find motif onset & offset
onset = float(onset) - pre_motor_win_size # start from the premotor window
jittered_spk = np.array([], dtype=np.float32)
for spk_ind, spk in enumerate(spk_ts):
while True:
jitter = np.random.uniform(-shuffle_limit, shuffle_limit, 1)
new_spk = spk + jitter
if onset < new_spk < offset:
jittered_spk = np.append(jittered_spk, spk + jitter)
break
spk_ts_jittered_list.append(jittered_spk)
self.spk_ts_jittered = spk_ts_jittered_list
@property
def nb_note(self) -> dict:
"""Return number of notes per context"""
from ..utils.functions import find_str
nb_note = {}
for context in ['U', 'D']:
nb_note[context] = len(find_str(self.contexts, context))
return nb_note
@property
def mean_fr(self) -> dict:
"""Return mean firing rates for the note (includes pre-motor window) per context"""
from ..analysis.parameters import nb_note_crit, pre_motor_win_size
from ..utils.functions import find_str
note_spk = {}
note_fr = {}
for context1 in ['U', 'D']:
if self.nb_note[context1] >= nb_note_crit:
note_spk[context1] = \
sum([len(spk) for context2, spk in zip(self.contexts, self.spk_ts) if context2 == context1])
note_fr[context1] = \
round(note_spk[context1] / ((self.durations[find_str(self.contexts, context1)] + pre_motor_win_size).sum() / 1E3), 3)
else:
note_fr[context1] = np.nan
return note_fr
# @property
# def open_folder(self) -> None:
# """Open the data folder"""
# from ..utils.functions import open_folder
#
# open_folder(self.path)
class MotifInfo(ClusterInfo):
"""
Class object for motif information
child class of ClusterInfo
"""
def __init__(self, path, channel_nb, unit_nb, motif, format='rhd', *name, update=False):
super().__init__(path, channel_nb, unit_nb, format, *name, update=False)
self.motif = motif
if name:
self.name = name[0]
else:
self.name = str(self.path)
# Load motif info
file_name = self.path / "MotifInfo_{}_Cluster{}.npy".format(self.channel_nb, self.unit_nb)
if update or not file_name.exists(): # if .npy doesn't exist or want to update the file
motif_info = self._load_motif()
# Save info dict as a numpy object
np.save(file_name, motif_info)
else:
motif_info = np.load(file_name, allow_pickle=True).item()
# Set the dictionary values to class attributes
for key in motif_info:
setattr(self, key, motif_info[key])
# Delete un-used attributes
self._delete_attr()
def _delete_attr(self):
"""Delete un-used attributes/methods inheritied from the parent class """
delattr(self, 'spk_wf')
delattr(self, 'nb_spk')
delattr(self, 'file_start')
delattr(self, 'file_end')
def _load_motif(self):
"""Load motif info"""
from ..analysis.parameters import peth_parm
from ..utils.functions import find_str
# Store values here
file_list = []
spk_list = []
onset_list = []
offset_list = []
syllable_list = []
duration_list = []
context_list = []
list_zip = zip(self.files, self.spk_ts, self.onsets, self.offsets, self.syllables, self.contexts)
for file, spks, onsets, offsets, syllables, context in list_zip:
print('Loading... ' + file)
onsets = onsets.tolist()
offsets = offsets.tolist()
# Find motifs
motif_ind = find_str(syllables, self.motif)
# Get syllable, analysis time stamps
for ind in motif_ind:
# start (first syllable) and stop (last syllable) index of a motif
start_ind = ind
stop_ind = ind + len(self.motif) - 1
motif_onset = float(onsets[start_ind])
motif_offset = float(offsets[stop_ind])
# Includes pre-motor spikes
motif_spk = spks[np.where((spks >= motif_onset - peth_parm['buffer']) & (spks <= motif_offset))]
onsets_in_motif = onsets[start_ind:stop_ind + 1] # list of motif onset timestamps
offsets_in_motif = offsets[start_ind:stop_ind + 1] # list of motif offset timestamps
file_list.append(file)
spk_list.append(motif_spk)
duration_list.append(motif_offset - motif_onset)
onset_list.append(onsets_in_motif)
offset_list.append(offsets_in_motif)
syllable_list.append(syllables[start_ind:stop_ind + 1])
context_list.append(context)
# Organize event-related info into a single dictionary object
motif_info = {
'files': file_list,
'spk_ts': spk_list,
'onsets': onset_list,
'offsets': offset_list,
'durations': duration_list, # this is motif durations
'syllables': syllable_list,
'contexts': context_list,
'parameter': peth_parm
}
# Set the dictionary values to class attributes
for key in motif_info:
setattr(self, key, motif_info[key])
# Get duration
note_duration_list, median_duration_list = self.get_note_duration()
self.note_durations = note_duration_list
self.median_durations = median_duration_list
motif_info['note_durations'] = note_duration_list
motif_info['median_durations'] = median_duration_list
# Get PLW (piecewise linear warping)
spk_ts_warp_list = self.piecewise_linear_warping()
# self.spk_ts_warp = spk_ts_warp_list
motif_info['spk_ts_warp'] = spk_ts_warp_list
return motif_info
def select_context(self, target_context : str,
keep_median_duration=True
) -> None:
"""
Select one context
Parameters
----------
target_context : str
'U' or 'D'
keep_median_duration : bool
Normally medial note duration is calculated using all syllables regardless of the context.
One may prefer to use this median to reduce variability when calculating pcc.
IF set False, new median duration will be calculated using the selected notes.
"""
zipped_list = \
list(zip(self.contexts, self.files, self.onsets, self.offsets, self.durations, self.spk_ts, self.spk_ts_warp, self.note_durations))
zipped_list = list(filter(lambda x: x[0] == target_context, zipped_list)) # filter context
unzipped_object = zip(*zipped_list)
self.contexts, self.files, self.onsets, self.offsets, self.durations, self.spk_ts, self.spk_ts_warp, self.note_durations = \
list(unzipped_object)
if not keep_median_duration:
_, self.median_durations = self.get_note_duration()
def get_note_duration(self):
"""
Calculate note & gap duration per motif
"""
note_durations = np.empty((len(self), len(self.motif) * 2 - 1))
list_zip = zip(self.onsets, self.offsets)
for motif_ind, (onset, offset) in enumerate(list_zip):
# Convert from string to array of floats
onset = np.asarray(list(map(float, onset)))
offset = np.asarray(list(map(float, offset)))
# Calculate note & interval duration
timestamp = [[onset, offset] for onset, offset in zip(onset, offset)]
timestamp = sum(timestamp, [])
for i in range(len(timestamp) - 1):
note_durations[motif_ind, i] = timestamp[i + 1] - timestamp[i]
# Get median duration
median_durations = np.median(note_durations, axis=0)
return note_durations, median_durations
def piecewise_linear_warping(self):
"""
Performs piecewise linear warping on raw analysis timestamps
Based on each median note and gap durations
"""
import copy
from ..utils.functions import extract_ind
spk_ts_warped_list = []
list_zip = zip(self.note_durations, self.onsets, self.offsets, self.spk_ts)
for motif_ind, (durations, onset, offset, spk_ts) in enumerate(list_zip): # per motif
onset = np.asarray(list(map(float, onset)))
offset = np.asarray(list(map(float, offset)))
# Make a deep copy of spk_ts so as to make it modification won't affect the original
spk_ts_new = copy.deepcopy(spk_ts)
# Calculate note & interval duration
timestamp = [[onset, offset] for onset, offset in zip(onset, offset)]
timestamp = sum(timestamp, [])
for i in range(0, len(self.median_durations)):
ratio = self.median_durations[i] / durations[i]
diff = timestamp[i] - timestamp[0]
if i == 0:
origin = 0
else:
origin = sum(self.median_durations[:i])
# Add spikes from motif
ind, spk_ts_temp = extract_ind(spk_ts, [timestamp[i], timestamp[i + 1]])
spk_ts_temp = ((ratio * ((spk_ts_temp - timestamp[0]) - diff)) + origin) + timestamp[0]
# spk_ts_new = np.append(spk_ts_new, spk_ts_temp)
np.put(spk_ts_new, ind, spk_ts_temp) # replace original spk timestamps with warped timestamps
spk_ts_warped_list.append(spk_ts_new)
return spk_ts_warped_list
def get_mean_fr(self, add_pre_motor=False):
"""
Calculate mean firing rates during motif
Parameters
----------
add_pre_motor : bool
Set True if you want to include spikes from the pre-motor window for calculating firing rates
(False by default)
"""
from ..analysis.parameters import peth_parm
fr_dict = {}
motif_spk_list = []
list_zip = zip(self.onsets, self.offsets, self.spk_ts)
# Make sure spikes from the pre-motif buffer is not included in calculation
for onset, offset, spks in list_zip:
onset = np.asarray(list(map(float, onset)))
offset = np.asarray(list(map(float, offset)))
if add_pre_motor:
motif_spk_list.append(spks[np.where((spks >= (onset[0] - peth_parm['buffer'])) & (spks <= offset[-1]))])
else:
motif_spk_list.append(spks[np.where((spks >= onset[0]) & (spks <= offset[-1]))])
for context1 in set(self.contexts):
nb_spk = sum([len(spk) for spk, context2 in zip(motif_spk_list, self.contexts) if context2 == context1])
if add_pre_motor:
total_duration = sum([duration + peth_parm['buffer'] for duration, context2 in zip(self.durations, self.contexts) if context2 == context1])
else:
total_duration = sum([duration for duration, context2 in zip(self.durations, self.contexts) if context2 == context1])
mean_fr = nb_spk / (total_duration / 1E3)
fr_dict[context1] = round(mean_fr, 3)
# print("mean_fr added")
self.mean_fr = fr_dict
def jitter_spk_ts(self, shuffle_limit: int, **kwargs):
"""
Add a random temporal jitter to the spike
This version limit the jittered timestamp within the motif window
"""
from ..analysis.parameters import pre_motor_win_size
spk_ts_jittered_list = []
list_zip = zip(self.onsets, self.offsets, self.spk_ts)
for ind, (onset, offset, spk_ts) in enumerate(list_zip):
# Find motif onset & offset
onset = float(onset[0]) - pre_motor_win_size # start from the premotor window
offset = float(offset[-1])
jittered_spk = np.array([], dtype=np.float32)
for spk_ind, spk in enumerate(spk_ts):
while True:
jitter = np.random.uniform(-shuffle_limit, shuffle_limit, 1)
new_spk = spk + jitter
if onset < new_spk < offset:
jittered_spk = np.append(jittered_spk, spk + jitter)
break
spk_ts_jittered_list.append(jittered_spk)
self.spk_ts_jittered = spk_ts_jittered_list
def get_peth(self, time_warp=True, shuffle=False):
"""
Get peri-event time histogram & raster during song motif
Parameters
----------
time_warp : bool
perform piecewise linear transform
shuffle : bool
add jitter to spike timestamps
Returns
-------
PethInfo : class object
"""
peth_dict = {}
if shuffle: # Get peth with shuffled (jittered) spikes
peth, time_bin, peth_parm = get_peth(self.onsets, self.spk_ts_jittered)
else:
if time_warp: # peth calculated from time-warped spikes by default
# peth, time_bin = get_note_peth(self.onsets, self.spk_ts_warp, self.median_durations.sum()) # truncated version to fit the motif duration
peth, time_bin, peth_parm = get_peth(self.onsets, self.spk_ts_warp)
else:
peth, time_bin, peth_parm = get_peth(self.onsets, self.spk_ts)
peth_parm.pop('time_bin'); peth_parm.pop('nb_bins')
peth_dict['peth'] = peth
peth_dict['time_bin'] = time_bin
peth_dict['parameters'] = peth_parm
peth_dict['contexts'] = self.contexts
peth_dict['median_duration'] = self.median_durations.sum()
return PethInfo(peth_dict) # return peth class object for further analysis
def __len__(self):
return len(self.files)
def __repr__(self): # print attributes
return str([key for key in self.__dict__.keys()])
@property
def open_folder(self):
"""Open the data folder"""
from ..utils.functions import open_folder
open_folder(self.path)
def _print_name(self):
print('')
print('Load motif {self.name}'.format(self=self))
class PethInfo():
def __init__(self, peth_dict: dict):
"""
Class object for peri-event time histogram (PETH)
Parameters
----------
peth_dict : dict
"peth" : array (nb of trials (motifs) x time bins), numbers indicate analysis counts in that bin
"contexts" : list of strings, social contexts
"""
# Set the dictionary values to class attributes
for key in peth_dict:
setattr(self, key, peth_dict[key])
# Get conditional peth, fr, spike counts
peth_dict = {}
peth_dict['All'] = self.peth
for context in set(self.contexts):
if type(self.contexts) == str:
self.contexts = list(self.contexts)
ind = np.array(self.contexts) == context
peth_dict[context] = self.peth[ind, :]
self.peth = peth_dict
def get_fr(self, gaussian_std=None, smoothing=True):
"""
Get trials-by-trial firing rates by default
Parameters
----------
gaussian_std : int
gaussian smoothing parameter. If not specified, read from analysis.parameters
smoothing : bool
performs gaussian smoothing on the firing rates
"""
# if duration:
# ind = (((0 - peth_parm['buffer']) <= time_bin) & (time_bin <= duration))
# peth = peth[:, ind]
# time_bin = time_bin[ind]
from ..analysis.parameters import peth_parm, gauss_std, nb_note_crit
from scipy.ndimage import gaussian_filter1d
if not gaussian_std: # if not specified, get the value fromm analysis.parameters
gaussian_std = gauss_std
# Get trial-by-trial firing rates
fr_dict = {}
for k, v in self.peth.items(): # loop through different conditions in peth dict
if v.shape[0] >= nb_note_crit:
fr = v / (peth_parm['bin_size'] / 1E3) # in Hz
if smoothing: # Gaussian smoothing
fr = gaussian_filter1d(fr, gaussian_std)
# Truncate values outside the range
ind = (((0 - peth_parm['buffer']) <= self.time_bin) & (self.time_bin <= self.median_duration))
fr = fr[:, ind]
fr_dict[k] = fr
self.fr = fr_dict
self.time_bin = self.time_bin[ind]
# Get mean firing rates
mean_fr_dict = {}
for context, fr in self.fr.items():
fr = np.mean(fr, axis=0)
mean_fr_dict[context] = fr
if smoothing:
mean_fr_dict['gauss_std'] = gauss_std
self.mean_fr = mean_fr_dict
def get_pcc(self):
"""Get pairwise cross-correlation"""
from ..analysis.parameters import nb_note_crit
pcc_dict = {}
for k, v in self.fr.items(): # loop through different conditions in peth dict
if k != 'All':
if v.shape[0] >= nb_note_crit:
pcc = get_pcc(v)
pcc_dict[k] = pcc
self.pcc = pcc_dict
def get_fr_cv(self):
"""Get coefficient of variation (CV) of firing rates"""
if not self.mean_fr:
self.get_fr()
fr_cv = {}
for context, fr in self.mean_fr.items(): # loop through different conditions in peth dict
if context in ['U', 'D']:
fr_cv[context] = round(fr.std(axis=0) / fr.mean(axis=0), 3)
return fr_cv
def get_sparseness(self, bin_size=None):
"""
Get sparseness index
Parameters
----------
bin_size : int
By default, it uses the same time bin size used in peth calculation (in ms)
Returns
-------
sparseness : dict
"""
from ..analysis.parameters import gauss_std, nb_note_crit
import math
mean_fr = dict()
sparseness = dict()
if bin_size != None and bin_size != self.parameters['bin_size']:
for context, peth in self.peth.items():
if context == 'All': continue
new_peth = np.empty([peth.shape[0], 0])
nb_bins = math.ceil(peth.shape[1] / bin_size)
bin_ind = 0
start_ind = 0
end_ind = 0 + bin_size
while bin_ind < nb_bins:
if end_ind > peth.shape[1]:
end_ind = peth.shape[1]
# print(start_ind, end_ind)
peth_bin = peth[:, start_ind: end_ind].sum(axis=1).reshape(peth.shape[0], 1)
new_peth = np.append(new_peth, peth_bin, axis=1)
start_ind += bin_size
end_ind += bin_size
bin_ind += 1
fr = new_peth / (bin_size / 1E3) # in Hz
mean_fr[context] = np.mean(fr, axis=0)
else:
mean_fr = self.mean_fr
# Calculate sparseness
for context, fr in mean_fr.items():
if context not in ['U', 'D']: continue
norm_fr = fr / np.sum(fr)
sparseness[context] = round(1 + (np.nansum(norm_fr * np.log10(norm_fr)) / np.log10(len(norm_fr))), 3)
return sparseness
def get_spk_count(self):
"""
Calculate the number of spikes within a specified time window
"""
from ..analysis.parameters import peth_parm, spk_count_parm
win_size = spk_count_parm['win_size']
spk_count_dict = {}
fano_factor_dict = {}
spk_count_cv_dict = {}
for k, v in self.peth.items(): # loop through different conditions in peth dict
spk_arr = np.empty((v.shape[0], 0), int) # (renditions x time bins)
if k != 'All': # skip all trials
win_inc = 0
for i in range(v.shape[1] - win_size):
count = v[:, i: win_size + win_inc].sum(axis=1)
# print(f"from {i} to {win_size + win_inc}, count = {count}")
spk_arr = np.append(spk_arr, np.array([count]).transpose(), axis=1)
win_inc += 1
# Truncate values outside the range
ind = (((0 - peth_parm['buffer']) <= self.time_bin) & (self.time_bin <= self.median_duration))
spk_arr = spk_arr[:, :ind.shape[0]]
spk_count = spk_arr.sum(axis=0)
fano_factor = spk_arr.var(axis=0) / spk_arr.mean(
axis=0) # per time window (across renditions) (renditions x time window)
spk_count_cv = spk_count.std(axis=0) / spk_count.mean(axis=0) # cv across time (single value)
# store values in a dictionary
spk_count_dict[k] = spk_count
fano_factor_dict[k] = fano_factor
spk_count_cv_dict[k] = round(spk_count_cv, 3)
self.spk_count = spk_count_dict
self.fano_factor = fano_factor_dict
self.spk_count_cv = spk_count_cv_dict
def __repr__(self): # print attributes
return str([key for key in self.__dict__.keys()])
class BoutInfo(ClusterInfo):
"""
Get song & spike information for a song bout
Child class of ClusterInfo
"""
def __init__(self, path, channel_nb, unit_nb, song_note, format='rhd', *name, update=False):
super().__init__(path, channel_nb, unit_nb, format, *name, update=False)
self.song_note = song_note
if name:
self.name = name[0]
else:
self.name = str(self.path)
# Load bout info
file_name = self.path / "BoutInfo_{}_Cluster{}.npy".format(self.channel_nb, self.unit_nb)
if update or not file_name.exists(): # if .npy doesn't exist or want to update the file
bout_info = self._load_bouts()
# Save info dict as a numpy object
np.save(file_name, bout_info)
else:
bout_info = np.load(file_name, allow_pickle=True).item()
# Set the dictionary values to class attributes
for key in bout_info:
setattr(self, key, bout_info[key])
def _print_name(self):
print('')
print('Load bout {self.name}'.format(self=self))
def __len__(self):
return len(self.files)
def _load_bouts(self):
# Store values here
from ..utils.functions import find_str
file_list = []
spk_list = []
onset_list = []
offset_list = []
syllable_list = []
duration_list = []
context_list = []
list_zip = zip(self.files, self.spk_ts, self.onsets, self.offsets, self.syllables, self.contexts)
for file, spks, onsets, offsets, syllables, context in list_zip:
bout_ind = find_str(syllables, '*')
for ind in range(len(bout_ind)):
if ind == 0:
start_ind = 0
else:
start_ind = bout_ind[ind - 1] + 1
stop_ind = bout_ind[ind] - 1
# breakpoint()
bout_onset = float(onsets[start_ind])
bout_offset = float(offsets[stop_ind])
bout_spk = spks[np.where((spks >= bout_onset) & (spks <= bout_offset))]
onsets_in_bout = onsets[start_ind:stop_ind + 1] # list of bout onset timestamps
offsets_in_bout = offsets[start_ind:stop_ind + 1] # list of bout offset timestamps
file_list.append(file)
spk_list.append(bout_spk)
duration_list.append(bout_offset - bout_onset)
onset_list.append(onsets_in_bout)
offset_list.append(offsets_in_bout)
syllable_list.append(syllables[start_ind:stop_ind + 1])
context_list.append(context)
# Organize event-related info into a single dictionary object
bout_info = {
'files': file_list,
'spk_ts': spk_list,
'onsets': onset_list,
'offsets': offset_list,
'durations': duration_list, # this is bout durations
'syllables': syllable_list,
'contexts': context_list,
}
return bout_info
def plot(self):
#TODO: this function needs revision
from ..analysis.parameters import bout_buffer, freq_range, bout_color
from ..utils import save
from ..utils.draw import remove_right_top
import matplotlib.colors as colors
import matplotlib.pyplot as plt
import numpy as np
from ..database.load import ProjectLoader, DBInfo
from scipy import stats
import warnings
warnings.filterwarnings('ignore')
# Parameters
save_fig = False
update = False
dir_name = 'RasterBouts'
fig_ext = '.png' # .png or .pdf
font_size = 12 # figure font size
rec_yloc = 0.05
rect_height = 0.2
text_yloc = 1 # text height
nb_row = 13
nb_col = 1
tick_length = 1
tick_width = 1
# Load database
db = ProjectLoader().load_db()
# SQL statementwa
# query = "SELECT * FROM cluster"
# query = "SELECT * FROM cluster WHERE ephysOK"
query = "SELECT * FROM cluster WHERE id = 12"
db.execute(query)
# Loop through db
for row in db.cur.fetchall():
# Load cluster info from db
cluster_db = DBInfo(row)
name, path = cluster_db.load_cluster_db()
unit_nb = int(cluster_db.unit[-2:])
channel_nb = int(cluster_db.channel[-2:])
format = cluster_db.format
ci = ClusterInfo(path, channel_nb, unit_nb, format, name, update=update) # cluster object
bi = BoutInfo(path, channel_nb, unit_nb, cluster_db.songNote, format, name, update=update) # bout object
list_zip = zip(bi.files, bi.spk_ts, bi.onsets, bi.offsets, bi.syllables, bi.contexts)
for bout_ind, (file, spks, onsets, offsets, syllables, context) in enumerate(list_zip):
# Convert from string to array of floats
onsets = np.asarray(list(map(float, onsets)))
offsets = np.asarray(list(map(float, offsets)))
spks = spks - onsets[0]
# bout start and end
start = onsets[0] - bout_buffer
end = offsets[-1] + bout_buffer
duration = offsets[-1] - onsets[0]
# Get spectrogram
audio = AudioData(path, update=update).extract([start, end]) # audio object
audio.spectrogram()
audio.spect_time = audio.spect_time - audio.spect_time[0] - bout_buffer
# Plot figure
fig = plt.figure(figsize=(8, 7))
fig.tight_layout()
fig_name = f"{file} - Bout # {bout_ind}"
print("Processing... " + fig_name)
fig.suptitle(fig_name, y=0.95)
# Plot spectrogram
ax_spect = plt.subplot2grid((nb_row, nb_col), (2, 0), rowspan=2, colspan=1)
ax_spect.pcolormesh(audio.spect_time, audio.spect_freq, audio.spect, # data
cmap='hot_r',
norm=colors.SymLogNorm(linthresh=0.05,
linscale=0.03,
vmin=0.5,
vmax=100
))
remove_right_top(ax_spect)
ax_spect.set_ylim(freq_range[0], freq_range[1])
ax_spect.set_ylabel('Frequency (Hz)', fontsize=font_size)
plt.yticks(freq_range, [str(freq_range[0]), str(freq_range[1])])
plt.setp(ax_spect.get_xticklabels(), visible=False)
plt.xlim([audio.spect_time[0] - 100, audio.spect_time[-1] + 100])
# Plot syllable duration
ax_syl = plt.subplot2grid((nb_row, nb_col), (1, 0), rowspan=1, colspan=1, sharex=ax_spect)
note_dur = offsets - onsets # syllable duration
onsets -= onsets[0] # start from 0
offsets = onsets + note_dur
# Mark syllables
for i, syl in enumerate(syllables):
rectangle = plt.Rectangle((onsets[i], rec_yloc), note_dur[i], rect_height,
linewidth=1, alpha=0.5, edgecolor='k', facecolor=bout_color[syl])
ax_syl.add_patch(rectangle)
ax_syl.text((onsets[i] + (offsets[i] - onsets[i]) / 2), text_yloc, syl, size=font_size)
ax_syl.axis('off')
# Plot song amplitude
audio.data = stats.zscore(audio.data)
audio.timestamp = audio.timestamp - audio.timestamp[0] - bout_buffer
ax_amp = plt.subplot2grid((nb_row, nb_col), (4, 0), rowspan=2, colspan=1, sharex=ax_spect)
ax_amp.plot(audio.timestamp, audio.data, 'k', lw=0.1)
ax_amp.axis('off')
# Plot rasters
ax_raster = plt.subplot2grid((nb_row, nb_col), (6, 0), rowspan=2, colspan=1, sharex=ax_spect)
# spks2 = spks - start -peth_parm['buffer'] -peth_parm['buffer']
ax_raster.eventplot(spks, colors='k', lineoffsets=0.5,
linelengths=tick_length, linewidths=tick_width, orientation='horizontal')
ax_raster.axis('off')
# Plot raw neural data
nd = NeuralData(path, channel_nb, format, update=update).extract([start, end]) # raw neural data
nd.timestamp = nd.timestamp - nd.timestamp[0] - bout_buffer
ax_nd = plt.subplot2grid((nb_row, nb_col), (8, 0), rowspan=2, colspan=1, sharex=ax_spect)
ax_nd.plot(nd.timestamp, nd.data, 'k', lw=0.5)
# Add a scale bar
plt.plot([ax_nd.get_xlim()[0] + 50, ax_nd.get_xlim()[0] + 50],
[-250, 250], 'k', lw=3) # for amplitude
plt.text(ax_nd.get_xlim()[0] - (bout_buffer / 2), -200, '500 µV', rotation=90)
plt.subplots_adjust(wspace=0, hspace=0)
remove_right_top(ax_nd)
ax_nd.spines['left'].set_visible(False)
plt.yticks([], [])
ax_nd.set_xlabel('Time (ms)')
# Save results
if save_fig:
save_path = save.make_dir(ProjectLoader().path / 'Analysis', 'RasterBouts')
save.save_fig(fig, save_path, fig_name, fig_ext=fig_ext)
else:
plt.show()
print('Done!')
class BaselineInfo(ClusterInfo):
def __init__(self, path, channel_nb, unit_nb, format='rhd', *name, update=False):
super().__init__(path, channel_nb, unit_nb, format, *name, update=False)
from ..analysis.parameters import baseline
from ..utils.functions import find_str
if name:
self.name = name[0]
else:
self.name = str(self.path)
# Load baseline info
file_name = self.path / "BaselineInfo_{}_Cluster{}.npy".format(self.channel_nb, self.unit_nb)
if update or not file_name.exists(): # if .npy doesn't exist or want to update the file
# Store values in here
file_list = []
spk_list = []
nb_spk_list = []
duration_list = []
context_list = []
baseline_info = {}
list_zip = zip(self.files, self.spk_ts, self.file_start, self.onsets, self.offsets, self.syllables,
self.contexts)
for file, spks, file_start, onsets, offsets, syllables, context in list_zip:
bout_ind_list = find_str(syllables, '*')
bout_ind_list.insert(0, -1) # start from the first index
for bout_ind in bout_ind_list:
# print(bout_ind)
if bout_ind == len(syllables) - 1: # skip if * indicates the end syllable
continue
baseline_onset = float(onsets[bout_ind + 1]) - baseline['time_buffer'] - baseline['time_win']
if bout_ind > 0 and baseline_onset < float(offsets[
bout_ind - 1]): # skip if the baseline starts before the offset of the previous syllable
continue
if baseline_onset < file_start:
baseline_onset = file_start
baseline_offset = float(onsets[bout_ind + 1]) - baseline['time_buffer']
if baseline_offset - baseline_onset < 0: # skip if there's not enough baseline period at the start of a file
continue
if baseline_onset > baseline_offset:
print('start time ={} to end time = {}'.format(baseline_onset, baseline_offset))
baseline_spk = spks[np.where((spks >= baseline_onset) & (spks <= baseline_offset))]
file_list.append(file)
spk_list.append(baseline_spk)
nb_spk_list.append(len(baseline_spk))
duration_list.append(
(baseline_offset - baseline_onset)) # convert to seconds for calculating in Hz
context_list.append(context)
baseline_info = {
'files': file_list,
'spk_ts': spk_list,
'nb_spk': nb_spk_list,
'durations': duration_list,
'contexts': context_list,
'parameter': baseline
}
# Save baseline_info as a numpy object
np.save(file_name, baseline_info)
else:
baseline_info = np.load(file_name, allow_pickle=True).item()
# Set the dictionary values to class attributes
for key in baseline_info:
setattr(self, key, baseline_info[key])
def _print_name(self):
print('')
print('Load baseline {self.name}'.format(self=self))
def get_correlogram(self, ref_spk_list, target_spk_list, normalize=False):
"""
Override the parent method
Combine correlogram from undir and dir since no contextual differentiation is needed in baseline
"""
from ..analysis.parameters import spk_corr_parm
correlogram_all = super().get_correlogram(ref_spk_list, target_spk_list, normalize=False)
correlogram = np.zeros(len(spk_corr_parm['time_bin']))
# Combine correlogram from two contexts
for key, value in correlogram_all.items():
if key in ['U', 'D']:
correlogram += value
return correlogram # return class object for further analysis
def get_jittered_corr(self) -> np.ndarray:
"""Get spike correlogram from time-jittered spikes"""
from ..analysis.parameters import corr_shuffle
correlogram_jitter = []
for iter in range(corr_shuffle['shuffle_iter']):
self.jitter_spk_ts(corr_shuffle['shuffle_limit'])
corr_temp = self.get_correlogram(self.spk_ts_jittered, self.spk_ts_jittered)
correlogram_jitter.append(corr_temp)
return np.array(correlogram_jitter)
def get_isi(self):
"""Get inter-spike interval"""
return get_isi(self.spk_ts)
@property
def mean_fr(self):
"""Mean firing rates"""
nb_spk = sum([len(spk_ts) for spk_ts in self.spk_ts])
total_duration = sum(self.durations)
mean_fr = nb_spk / (total_duration / 1E3)
return round(mean_fr, 3)
def __repr__(self): # print attributes
return str([key for key in self.__dict__.keys()])
class AudioData:
"""
Create an object that has concatenated audio signal and its timestamps
Get all data by default; specify time range if needed
"""
def __init__(self, path, format='.wav', update=False):
from ..analysis.load import load_audio
self.path = path
self.format = format
file_name = self.path / "AudioData.npy"
if update or not file_name.exists(): # if .npy doesn't exist or want to update the file
audio_info = load_audio(self.path, self.format)
else:
audio_info = np.load(file_name, allow_pickle=True).item()
# Set the dictionary values to class attributes
for key in audio_info:
setattr(self, key, audio_info[key])
def __repr__(self): # print attributes
return str([key for key in self.__dict__.keys()])
@property
def open_folder(self):
"""Open the data folder"""
from ..utils.functions import open_folder
open_folder(self.path)
def extract(self, time_range: list):
"""
Extracts data from the specified range
Parameters
----------
time_range : list
"""
start = time_range[0]
end = time_range[-1]
ind = np.where((self.timestamp >= start) & (self.timestamp <= end))
return self.timestamp[ind], self.data[ind]
def spectrogram(self, timestamp, data, freq_range=[300, 8000]):
"""Calculate spectrogram"""
from ..utils.spect import spectrogram
spect, spect_freq, _ = spectrogram(data, self.sample_rate, freq_range=freq_range)
spect_time = np.linspace(timestamp[0], timestamp[-1], spect.shape[1]) # timestamp for spectrogram
return spect_time, spect, spect_freq
def get_spectral_entropy(self, spect, normalize=True, mode=None):
"""
Calculate spectral entropy
Parameters
----------
normalize : bool
Get normalized spectral entropy
mode : {'spectral', ''spectro_temporal'}
Returns
-------
array of spectral entropy
"""
from ..analysis.functions import get_spectral_entropy
return get_spectral_entropy(spect, normalize=normalize, mode=mode)
class NeuralData:
def __init__(self, path, channel_nb, format='rhd', update=False):
self.path = path
self.channel_nb = str(channel_nb).zfill(2)
self.format = format # format of the file (e.g., rhd), this info should be in the database
file_name = self.path / f"NeuralData_Ch{self.channel_nb}.npy"
if update or not file_name.exists(): # if .npy doesn't exist or want to update the file
data_info = self.load_neural_data()
# Save event_info as a numpy object
else:
data_info = np.load(file_name, allow_pickle=True).item()
# Set the dictionary values to class attributes
for key in data_info:
setattr(self, key, data_info[key])
def __repr__(self): # print attributes
return str([key for key in self.__dict__.keys()])
def load_neural_data(self):
"""
Load and concatenate all neural data files (e.g., .rhd) in the input dir (path)
"""
from ..analysis.load import read_rhd
from ..analysis.parameters import sample_rate
print("")
print("Load neural data")
# List .rhd files
files = list(self.path.glob(f'*.{self.format}'))
# Initialize
timestamp_concat = np.array([], dtype=np.float64)
amplifier_data_concat = np.array([], dtype=np.float64)
# Store values in these lists
file_list = []
if self.format == 'cbin':
# if the neural data is in .cbin format, read from .mat files that has contains concatenated data
# currently does not have files to extract data from .cbin files in python
import scipy.io
mat_file = list(self.path.glob(f'*Ch{self.channel_nb}(merged).mat'))[0]
timestamp_concat = scipy.io.loadmat(mat_file)['t_amplifier'][0].astype(np.float64)
amplifier_data_concat = scipy.io.loadmat(mat_file)['amplifier_data'][0].astype(np.float64)
else:
# Loop through Intan .rhd files
for file in files:
# Load data file
print('Loading... ' + file.stem)
file_list.append(file.name)
intan = read_rhd(file) # note that the timestamp is in second
# Concatenate timestamps
intan['t_amplifier'] -= intan['t_amplifier'][0] # start from t = 0
if timestamp_concat.size == 0:
timestamp_concat = np.append(timestamp_concat, intan['t_amplifier'])
else:
intan['t_amplifier'] += (timestamp_concat[-1] + (1 / sample_rate[self.format]))
timestamp_concat = np.append(timestamp_concat, intan['t_amplifier'])
# Concatenate neural data
for ind, ch in enumerate(intan['amplifier_channels']):
if int(self.channel_nb) == int(ch['native_channel_name'][-2:]):
amplifier_data_concat = np.append(amplifier_data_concat, intan['amplifier_data'][ind, :])
timestamp_concat *= 1E3 # convert to microsecond
# Organize data into a dictionary
data_info = {
'files': file_list,
'timestamp': timestamp_concat,
'data': amplifier_data_concat,
'sample_rate': sample_rate[self.format]
}
file_name = self.path / f"NeuralData_Ch{self.channel_nb}.npy"
np.save(file_name, data_info)
return data_info
def extract(self, time_range: list):
"""
Extracts data from the specified range
Parameters
----------
time_range : list
list of time stamps [start, end]
Returns
-------
timestamp : arr
data : arr
"""
start = time_range[0]
end = time_range[-1]
ind = np.where((self.timestamp >= start) & (self.timestamp <= end))
return self.timestamp[ind], self.data[ind]
@property
def open_folder(self):
"""Open the data folder"""
from ..utils.functions import open_folder
open_folder(self.path)
class Correlogram():
"""
Class for correlogram analysis
"""
def __init__(self, correlogram):
from ..analysis.parameters import spk_corr_parm, burst_hz
corr_center = round(correlogram.shape[0] / 2) + 1 # center of the correlogram
self.data = correlogram
self.time_bin = np.arange(-spk_corr_parm['lag'],
spk_corr_parm['lag'] + spk_corr_parm['bin_size'],
spk_corr_parm['bin_size'])
if self.data.sum():
self.peak_ind = np.min(
np.abs(np.argwhere(correlogram == np.amax(correlogram)) - corr_center)) + corr_center # index of the peak
self.peak_latency = self.time_bin[self.peak_ind] - 1
self.peak_value = self.data[self.peak_ind]
burst_range = np.arange(corr_center - (1000 / burst_hz) - 1, corr_center + (1000 / burst_hz),
dtype='int') # burst range in the correlogram
self.burst_index = round(self.data[burst_range].sum() / self.data.sum(), 3)
else:
self.peak_ind = self.peak_latency = self.peak_value = self.burst_index = np.nan
def __repr__(self): # print attributes
return str([key for key in self.__dict__.keys()])
def category(self, correlogram_jitter: np.ndarray) -> str:
"""
Get bursting category of a neuron based on autocorrelogram
Parameters
----------
correlogram_jitter : np.ndarray
Random time-jittered correlogram for baseline setting
Returns
-------
Category of a neuron ('Bursting' or 'Nonbursting')
"""
from ..analysis.parameters import corr_burst_crit
corr_mean = correlogram_jitter.mean(axis=0)
if corr_mean.sum():
corr_std = correlogram_jitter.std(axis=0)
upper_lim = corr_mean + (corr_std * 2)
lower_lim = corr_mean - (corr_std * 2)
self.baseline = upper_lim
# Check peak significance
if self.peak_value > upper_lim[self.peak_ind] and self.peak_latency <= corr_burst_crit:
self.category = 'Bursting'
else:
self.category = 'NonBursting'
else:
self.baseline = self.category = np.array(np.nan)
return self.category
def plot_corr(self, ax, time_bin, correlogram,
title, xlabel=None, ylabel=None,
font_size=10,
peak_line_width=0.8,
normalize=False,
peak_line=True,
baseline=True):
"""
Plot correlogram
Parameters
----------
ax : axis object
axis to plot the figure
time_bin : np.ndarray
correlogram : np.ndarray
title : str
font_size : int
title font size
normalize : bool
normalize the correlogram
"""
import matplotlib.pyplot as plt
from ..utils.draw import remove_right_top
from ..utils.functions import myround
if correlogram.sum():
ax.bar(time_bin, correlogram, color='k', rasterized=True)
ymax = max([self.baseline.max(), correlogram.max()])
round(ymax / 10) * 10
ax.set_ylim(0, ymax)
plt.yticks([0, ax.get_ylim()[1]], [str(0), str(int(ymax))])
ax.set_title(title, size=font_size)
ax.set_xlabel(xlabel)
if normalize:
ax.set_ylabel(ylabel)
else:
ax.set_ylabel(ylabel)
remove_right_top(ax)
if peak_line and not np.isnan(self.peak_ind):
# peak_time_ind = np.where(self.time_bin == self.peak_latency)
ax.axvline(x=self.time_bin[self.peak_ind], color='r', linewidth=peak_line_width, ls='--')
if baseline and not np.isnan(self.baseline.mean()):
ax.plot(self.time_bin, self.baseline, 'm', lw=0.5, ls='--')
else:
ax.axis('off')
ax.set_title(title, size=font_size)
class BurstingInfo:
def __init__(self, ClassInfo, *input_context):
from ..analysis.parameters import burst_hz
# ClassInfo can be BaselineInfo, MotifInfo etc
if input_context: # select data based on social context
spk_list = [spk_ts for spk_ts, context in zip(ClassInfo.spk_ts, ClassInfo.contexts) if
context == input_context[0]]
duration_list = [duration for duration, context in zip(ClassInfo.durations, ClassInfo.contexts) if
context == input_context[0]]
self.context = input_context
else:
spk_list = ClassInfo.spk_ts
duration_list = ClassInfo.durations
# Bursting analysis
burst_spk_list = []
burst_duration_arr = []
nb_bursts = []
nb_burst_spk_list = []
for ind, spks in enumerate(spk_list):
# spk = bi.spk_ts[8]
isi = np.diff(spks) # inter-spike interval
inst_fr = 1E3 / np.diff(spks) # instantaneous firing rates (Hz)
bursts = np.where(inst_fr >= burst_hz)[0] # burst index
# Skip if no bursting detected
if not bursts.size:
continue
# Get the number of bursts
temp = np.diff(bursts)[np.where(np.diff(bursts) == 1)].size # check if the spikes occur in bursting
nb_bursts = np.append(nb_bursts, bursts.size - temp)
# Get burst onset
temp = np.where(np.diff(bursts) == 1)[0]
spk_ind = temp + 1
# Remove consecutive spikes in a burst and just get burst onset
burst_onset_ind = bursts
for i, ind in enumerate(temp):
burst_spk_ind = spk_ind[spk_ind.size - 1 - i]
burst_onset_ind = np.delete(burst_onset_ind, burst_spk_ind)
# Get burst offset index
burst_offset_ind = np.array([], dtype=np.int)
for i in range(bursts.size - 1):
if bursts[i + 1] - bursts[i] > 1: # if not successive spikes
burst_offset_ind = np.append(burst_offset_ind, bursts[i] + 1)
# Need to add the subsequent spike time stamp since it is not included (burst is the difference between successive spike time stamps)
burst_offset_ind = np.append(burst_offset_ind, bursts[bursts.size - 1] + 1)
burst_onset = spks[burst_onset_ind]
burst_offset = spks[burst_offset_ind]
burst_spk_list.append(spks[burst_onset_ind[0]: burst_offset_ind[0] + 1])
burst_duration_arr = | np.append(burst_duration_arr, burst_offset - burst_onset) | numpy.append |
from __future__ import print_function
import itertools
import math
import os
import random
import shutil
import tempfile
import unittest
import uuid
import numpy as np
import tensorflow as tf
import coremltools
import coremltools.models.datatypes as datatypes
from coremltools.models import _MLMODEL_FULL_PRECISION, _MLMODEL_HALF_PRECISION
from coremltools.models import neural_network as neural_network
from coremltools.models.utils import macos_version
from coremltools.models.neural_network import flexible_shape_utils
np.random.seed(10)
MIN_MACOS_VERSION_REQUIRED = (10, 13)
LAYERS_10_15_MACOS_VERSION = (10, 15)
def _get_unary_model_spec(x, mode, alpha=1.0):
input_dim = x.shape
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', datatypes.Array(*input_dim))]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_unary(name='unary', input_name='data',
output_name='output', mode=mode, alpha=alpha)
return builder.spec
class CorrectnessTest(unittest.TestCase):
def runTest(self):
pass
def _compare_shapes(self, np_preds, coreml_preds):
return np.squeeze(np_preds).shape == np.squeeze(coreml_preds).shape
def _compare_nd_shapes(self, np_preds, coreml_preds, shape=()):
if shape:
return coreml_preds.shape == shape
else:
return coreml_preds.shape == np_preds.shape
def _compare_predictions(self, np_preds, coreml_preds, delta=.01):
np_preds = np_preds.flatten()
coreml_preds = coreml_preds.flatten()
for i in range(len(np_preds)):
max_den = max(1.0, np_preds[i], coreml_preds[i])
if np.abs(
np_preds[i] / max_den - coreml_preds[i] / max_den) > delta:
return False
return True
@staticmethod
def _compare_moments(model, inputs, expected, use_cpu_only=True, num_moments=10):
"""
This utility function is used for validate random distributions layers.
It validates the first 10 moments of prediction and expected values.
"""
def get_moment(data, k):
return np.mean(np.power(data - np.mean(data), k))
if isinstance(model, str):
model = coremltools.models.MLModel(model)
model = coremltools.models.MLModel(model, useCPUOnly=use_cpu_only)
prediction = model.predict(inputs, useCPUOnly=use_cpu_only)
for output_name in expected:
np_preds = expected[output_name]
coreml_preds = prediction[output_name]
np_moments = [get_moment(np_preds.flatten(), k) for k in range(num_moments)]
coreml_moments = [get_moment(coreml_preds.flatten(), k) for k in range(num_moments)]
np.testing.assert_almost_equal(np_moments, coreml_moments, decimal=2)
# override expected values to allow element-wise compares
for output_name in expected:
expected[output_name] = prediction[output_name]
def _test_model(self,
model,
input,
expected,
model_precision=_MLMODEL_FULL_PRECISION,
useCPUOnly=False,
output_name_shape_dict={},
validate_shapes_only=False):
model_dir = None
# if we're given a path to a model
if isinstance(model, str):
model = coremltools.models.MLModel(model)
# If we're passed in a specification, save out the model
# and then load it back up
elif isinstance(model, coremltools.proto.Model_pb2.Model):
model_dir = tempfile.mkdtemp()
model_name = str(uuid.uuid4()) + '.mlmodel'
model_path = os.path.join(model_dir, model_name)
coremltools.utils.save_spec(model, model_path)
model = coremltools.models.MLModel(model, useCPUOnly=useCPUOnly)
# If we want to test the half precision case
if model_precision == _MLMODEL_HALF_PRECISION:
model = coremltools.utils.convert_neural_network_weights_to_fp16(
model)
prediction = model.predict(input, useCPUOnly=useCPUOnly)
for output_name in expected:
if self.__class__.__name__ == "SimpleTest":
assert (self._compare_shapes(expected[output_name],
prediction[output_name]))
else:
if output_name in output_name_shape_dict:
output_shape = output_name_shape_dict[output_name]
else:
output_shape = []
if len(output_shape) == 0 and len(expected[output_name].shape) == 0:
output_shape = (1,)
assert (self._compare_nd_shapes(expected[output_name],
prediction[output_name],
output_shape))
if not validate_shapes_only:
assert (self._compare_predictions(expected[output_name],
prediction[output_name]))
# Remove the temporary directory if we created one
if model_dir and os.path.exists(model_dir):
shutil.rmtree(model_dir)
@unittest.skipIf(macos_version() < MIN_MACOS_VERSION_REQUIRED,
'macOS 10.13+ is required. Skipping tests.')
class SimpleTest(CorrectnessTest):
def test_tiny_upsample_linear_mode(self):
input_dim = (1, 1, 3) # (C,H,W)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_upsample(name='upsample',
scaling_factor_h=2, scaling_factor_w=3,
input_name='data', output_name='output',
mode='BILINEAR')
input = {
'data': np.reshape(np.array([1.0, 2.0, 3.0]), (1, 1, 3))
}
expected = {
'output': np.array(
[[1, 1.333, 1.666, 2, 2.333, 2.666, 3, 3, 3],
[1, 1.333, 1.6666, 2, 2.33333, 2.6666, 3, 3, 3]
])
}
self._test_model(builder.spec, input, expected)
def test_LRN(self):
input_dim = (1, 3, 3)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', datatypes.Array(*input_dim))]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_lrn(name='lrn', input_name='data', output_name='output',
alpha=2, beta=3, local_size=1, k=8)
input = {
'data': np.ones((1, 3, 3))
}
expected = {
'output': 1e-3 * np.ones((1, 3, 3))
}
self._test_model(builder.spec, input, expected)
def test_MVN(self):
input_dim = (2, 2, 2)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', datatypes.Array(*input_dim))]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_mvn(name='mvn', input_name='data', output_name='output',
across_channels=False, normalize_variance=False)
input = {
'data': np.reshape(np.arange(8, dtype=np.float32), (2, 2, 2))
}
expected = {
'output': np.reshape(np.arange(8) - np.array(
[1.5, 1.5, 1.5, 1.5, 5.5, 5.5, 5.5, 5.5]), (2, 2, 2))
}
self._test_model(builder.spec, input, expected)
def test_L2_normalize(self):
input_dim = (1, 2, 2)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', datatypes.Array(*input_dim))]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_l2_normalize(name='mvn', input_name='data',
output_name='output')
input = {
'data': np.reshape(np.arange(4, dtype=np.float32), (1, 2, 2))
}
expected = {
'output': np.reshape(np.arange(4, dtype=np.float32),
(1, 2, 2)) / np.sqrt(14)
}
self._test_model(builder.spec, input, expected)
def test_unary_sqrt(self):
x = np.reshape(np.arange(1, 5, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': np.sqrt(x)}
spec = _get_unary_model_spec(x, 'sqrt')
self._test_model(spec, input, expected)
def test_unary_rsqrt(self):
x = np.reshape(np.arange(1, 5, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': 1 / np.sqrt(x)}
spec = _get_unary_model_spec(x, 'rsqrt')
self._test_model(spec, input, expected)
def test_unary_inverse(self):
x = np.reshape(np.arange(1, 5, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': 1 / x}
spec = _get_unary_model_spec(x, 'inverse')
self._test_model(spec, input, expected)
def test_unary_power(self):
x = np.reshape(np.arange(1, 5, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': x ** 3}
spec = _get_unary_model_spec(x, 'power', 3)
self._test_model(spec, input, expected)
def test_unary_exp(self):
x = np.reshape(np.arange(1, 5, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': np.exp(x)}
spec = _get_unary_model_spec(x, 'exp')
self._test_model(spec, input, expected)
def test_unary_log(self):
x = np.reshape(np.arange(1, 5, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': np.log(x)}
spec = _get_unary_model_spec(x, 'log')
self._test_model(spec, input, expected)
def test_unary_abs(self):
x = np.reshape(np.arange(1, 5, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': np.abs(x)}
spec = _get_unary_model_spec(x, 'abs')
self._test_model(spec, input, expected)
def test_unary_threshold(self):
x = np.reshape(np.arange(1, 5, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': np.maximum(x, 2)}
spec = _get_unary_model_spec(x, 'threshold', 2)
self._test_model(spec, input, expected)
def test_split(self):
input_dim = (9, 2, 2)
x = np.random.rand(*input_dim)
input_features = [('data', datatypes.Array(*input_dim))]
output_names = []
output_features = []
for i in range(3):
out = 'out_' + str(i)
output_names.append(out)
output_features.append((out, None))
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_split(name='split', input_name='data',
output_names=output_names)
input = {'data': x}
expected = {
'out_0': x[0: 3, :, :],
'out_1': x[3: 6, :, :],
'out_2': x[6: 9, :, :]
}
self._test_model(builder.spec, input, expected)
def test_scale_constant(self):
input_dim = (1, 2, 2)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_scale(name='scale', W=5, b=45, has_bias=True,
input_name='data', output_name='output')
x = np.reshape(np.arange(4, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': 5 * x + 45}
self._test_model(builder.spec, input, expected)
def test_scale_matrix(self):
input_dim = (1, 2, 2)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
W = np.reshape(np.arange(5, 9), (1, 2, 2))
builder.add_scale(name='scale', W=W, b=None, has_bias=False,
input_name='data', output_name='output',
shape_scale=[1, 2, 2])
x = np.reshape(np.arange(4, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': W * x}
self._test_model(builder.spec, input, expected)
def test_bias_constant(self):
input_dim = (1, 2, 2)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_bias(name='bias', b=45, input_name='data',
output_name='output')
x = np.reshape(np.arange(4, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': x + 45}
self._test_model(builder.spec, input, expected)
def test_bias_matrix(self):
input_dim = (1, 2, 2)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
b = np.reshape(np.arange(5, 9), (1, 2, 2))
builder.add_bias(name='bias', b=b, input_name='data',
output_name='output',
shape_bias=[1, 2, 2])
x = np.reshape(np.arange(4, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': x + b}
self._test_model(builder.spec, input, expected)
def test_load_constant(self, model_precision=_MLMODEL_FULL_PRECISION):
input_dim = (1, 2, 2)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
b = np.reshape(np.arange(5, 9), (1, 2, 2))
builder.add_load_constant(name='load_constant', output_name='bias',
constant_value=b, shape=[1, 2, 2])
builder.add_elementwise(name='add', input_names=['data', 'bias'],
output_name='output', mode='ADD')
x = np.reshape(np.arange(4, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': x + b}
self._test_model(builder.spec, input, expected, model_precision)
def test_load_constant_half_precision(self):
self.test_load_constant(model_precision=_MLMODEL_HALF_PRECISION)
def test_min(self):
input_dim = (1, 2, 2)
input_features = [('data_0', datatypes.Array(*input_dim)),
('data_1', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_elementwise(name='min', input_names=['data_0', 'data_1'],
output_name='output', mode='MIN')
x1 = np.reshape(np.arange(4, dtype=np.float32), (1, 2, 2))
x2 = np.reshape(np.arange(2, 6, dtype=np.float32), (1, 2, 2))
input = {'data_0': x1, 'data_1': x2}
expected = {'output': np.minimum(x1, x2)}
self._test_model(builder.spec, input, expected)
def test_conv_same_padding(self):
input_dim = (10, 15, 15)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
W = np.random.rand(3, 3, 10, 20)
builder.add_convolution(name='conv', kernel_channels=10,
output_channels=20,
height=3, width=3, stride_height=2,
stride_width=2,
border_mode='same', groups=1,
W=W, b=None, has_bias=False,
input_name='data', output_name='output',
same_padding_asymmetry_mode='TOP_LEFT_HEAVY')
x = np.random.rand(*input_dim)
input = {'data': x}
expected = {'output': np.random.rand(20, 8, 8)}
self._test_model(
builder.spec, input, expected, validate_shapes_only=True)
def test_deconv_valid_padding(self):
input_dim = (10, 15, 15)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
W = np.random.rand(3, 3, 10, 20)
builder.add_convolution(name='deconv', kernel_channels=10,
output_channels=20,
height=3, width=3, stride_height=2,
stride_width=2,
border_mode='valid', groups=1,
W=W, b=None, has_bias=False,
is_deconv=True,
input_name='data', output_name='output',
padding_top=2, padding_bottom=3,
padding_left=2, padding_right=3)
x = np.random.rand(*input_dim)
input = {'data': x}
expected = {'output': np.random.rand(20, 26, 26)}
self._test_model(
builder.spec, input, expected, validate_shapes_only=True)
def test_deconv_non_unit_groups(self):
input_dim = (16, 15, 15)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features)
W = np.random.rand(3, 3, 16, 5)
builder.add_convolution(name='deconv', kernel_channels=16,
output_channels=20,
height=3, width=3, stride_height=2,
stride_width=2,
border_mode='valid', groups=4,
W=W, b=None, has_bias=False,
is_deconv=True,
input_name='data', output_name='output',
padding_top=2, padding_bottom=3,
padding_left=2, padding_right=3)
x = np.random.rand(*input_dim)
input = {'data': x}
expected = {'output': np.random.rand(20, 26, 26)}
self._test_model(
builder.spec, input, expected, validate_shapes_only=True)
def test_linear_activation(self):
input_dim = (10, 15, 15)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_activation(name='activation',
non_linearity='LINEAR',
input_name='data',
output_name='output', params=[34.0, 67.0])
x = np.random.rand(*input_dim)
input = {'data': x}
expected = {'output': 34.0 * x + 67.0}
self._test_model(builder.spec, input, expected)
def test_padding_constant(self):
input_dim = (1, 2, 3)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features)
builder.add_padding(name='pad',
left=1, right=0, top=2, bottom=0,
value=-1,
input_name='data',
output_name='output')
x = np.reshape(np.array([[1, 2, 3], [4, 5, 6]]), (1, 2, 3)).astype(
np.float32)
input = {'data': x}
y = np.reshape(
np.array([[-1, -1, -1, -1], [-1, -1, -1, -1], [-1, 1, 2, 3],
[-1, 4, 5, 6]]), (1, 4, 4)).astype(np.float32)
expected = {'output': y}
self._test_model(builder.spec, input, expected)
def test_padding_replication(self):
input_dim = (1, 2, 3)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_padding(name='pad',
left=1, top=2,
input_name='data',
output_name='output', padding_type='replication')
x = np.reshape(np.array([[1, 2, 3], [4, 5, 6]]), (1, 2, 3)).astype(
np.float32)
input = {'data': x}
y = np.reshape(np.array([[1, 1, 2, 3], [1, 1, 2, 3], [1, 1, 2, 3],
[4, 4, 5, 6]]), (1, 4, 4)).astype(np.float32)
expected = {'output': y}
self._test_model(builder.spec, input, expected)
def test_reshape_target_shape_3(self):
input_dim = (1, 2, 5) # (C,H,W)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_reshape(name='reshape', input_name='data',
output_name='output', target_shape=(10, 1, 1),
mode=0)
x = np.random.rand(*input_dim)
input = {'data': x}
expected = {'output': np.reshape(x, (10, 1, 1))}
self._test_model(builder.spec, input, expected)
def test_reshape_target_shape_4(self):
input_dim = (1, 2, 5) # (C,H,W)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_reshape(name='reshape', input_name='data',
output_name='output', target_shape=(1, 10, 1, 1),
mode=0)
x = np.random.rand(*input_dim)
input = {'data': x}
expected = {'output': np.reshape(x, (1, 10, 1, 1))}
self._test_model(builder.spec, input, expected)
def test_bias_matrix_cpu(self):
input_dim = (1, 2, 2)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
b = np.reshape(np.arange(5, 9), (1, 2, 2))
builder.add_bias(name='bias', b=b, input_name='data',
output_name='output',
shape_bias=[1, 2, 2])
x = np.reshape(np.arange(4, dtype=np.float32), (1, 2, 2))
input = {'data': x}
expected = {'output': x + b}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_linear_activation_cpu(self):
input_dim = (10, 15, 15)
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features,
output_features)
builder.add_activation(name='activation',
non_linearity='LINEAR',
input_name='data',
output_name='output', params=[34.0, 67.0])
x = np.random.rand(*input_dim)
input = {'data': x}
expected = {'output': 34.0 * x + 67.0}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
@unittest.skipIf(macos_version() < LAYERS_10_15_MACOS_VERSION,
'macOS 10.15+ required. Skipping tests.')
class NewLayersSimpleTest(CorrectnessTest):
def test_shape_flexibility_range(self):
input_features = [('data', datatypes.Array(*(3,4)))]
builder = neural_network.NeuralNetworkBuilder(input_features,
[('output', None)], disable_rank5_shape_mapping=True)
builder.add_sin(name='sin', input_name='data', output_name='output')
spec = builder.spec
flexible_shape_utils.set_multiarray_ndshape_range(spec, feature_name='data',
lower_bounds=[1,1], upper_bounds=[-1,5])
shapes = [(3,4), (1,5), (60,5), (22,4), (5,3)]
for s in shapes:
x = np.random.rand(*s)
expected = {'output': np.sin(x)}
self._test_model(spec, {'data': x}, expected, useCPUOnly=True)
@unittest.skip('TO FIX')
def test_shape_flexibility_enumeration(self):
input_features = [('data', datatypes.Array(*(3,4,6)))]
builder = neural_network.NeuralNetworkBuilder(input_features,
[('output', None)], disable_rank5_shape_mapping=True)
builder.add_sin(name='sin', input_name='data', output_name='output')
spec = builder.spec
shapes = [(1, 5, 7), (60, 5, 2), (22, 4, 9), (5, 3, 56)]
flexible_shape_utils.add_multiarray_ndshape_enumeration(spec, feature_name='data', enumerated_shapes=shapes)
shapes.append((3,4,6))
for s in shapes:
x = np.random.rand(*s)
expected = {'output': np.sin(x)}
self._test_model(spec, {'data': x}, expected, useCPUOnly=True)
def test_transpose_cpu(self):
for rank in range(1, 6):
axes = np.random.permutation(rank)
axes = [axis - rank if np.random.choice([True, False]) else axis for axis in axes]
input_shape = np.random.randint(low=2, high=6, size=rank)
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_transpose(name='TransposeND',
axes=axes,
input_name='data',
output_name='output')
x = np.random.rand(*input_shape)
input = {'data': x}
expected = {'output': np.transpose(x, axes)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_batched_mat_mul_cpu(self):
a_shapes = [(10,), (4, 10), (10,), (10,), (2, 3), (1, 3, 4),
(1, 3, 1, 2, 3), (2, 3, 1, 3, 4)]
b_shapes = [(10,), (10,), (10, 3), (2, 10, 3), (3, 4), (3, 2, 4, 5),
(1, 4, 3, 2), (2, 1, 2, 4, 5)]
out_shapes = [(1, 1), (4, 1), (1, 3), (2, 1, 3), (2, 4), (3, 2, 3, 5),
(1, 3, 4, 2, 2), (2, 3, 2, 3, 5)]
for a_shape, b_shape, outShape in zip(a_shapes, b_shapes, out_shapes):
input_shapes = [a_shape, b_shape]
input_features = [
('A', datatypes.Array(*input_shapes[0])),
('B', datatypes.Array(*input_shapes[1]))
]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_batched_mat_mul(name='batched_mat_mul',
input_names=['A', 'B'],
output_name='output',
transpose_a=False,
transpose_b=False)
a = np.random.rand(*input_shapes[0])
b = np.random.rand(*input_shapes[1])
input = {'A': a, 'B': b}
expected = {'output': np.array(np.matmul(a, b))}
shape_dict = {'output': outShape}
self._test_model(builder.spec, input, expected, useCPUOnly=True,
output_name_shape_dict=shape_dict)
def test_batched_mat_mul_with_transposes_cpu(self):
for transpose_a, transpose_b in itertools.product([True, False],
[True, False]):
a_shape = (3, 4)
b_shape = (4, 5)
a_shape = a_shape[::-1] if transpose_a else a_shape
b_shape = b_shape[::-1] if transpose_b else b_shape
input_shapes = [a_shape, b_shape]
input_features = [
('A', datatypes.Array(*input_shapes[0])),
('B', datatypes.Array(*input_shapes[1]))
]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True
)
builder.add_batched_mat_mul(
name='BatchedMatMul', input_names=['A', 'B'],
output_name='output', transpose_a=transpose_a,
transpose_b=transpose_b
)
a = np.random.rand(*input_shapes[0])
b = np.random.rand(*input_shapes[1])
inputs = {'A': a, 'B': b}
a = a.T if transpose_a else a
b = b.T if transpose_b else b
expected = {'output': np.matmul(a, b)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_batched_mat_mul_single_input_cpu(
self, model_precision=_MLMODEL_FULL_PRECISION):
X1 = 11
X2 = 23
W = np.random.rand(X1, X2)
bias = np.random.rand(X2)
input_shapes = [(X1,), (5, X1), (2, 3, X1), (4, 1, X1), (12, 5, 8, X1),
(2, 3, 1, 5, X1)]
for input_shape in input_shapes:
x = np.random.rand(*input_shape)
np_out = np.matmul(x, W) + bias
expected = {'output': np_out}
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_batched_mat_mul(name='batched_mat_mul',
input_names=['data'],
output_name='output',
weight_matrix_rows=X1,
weight_matrix_columns=X2,
W=W, bias=bias)
inputs = {'data': x}
self._test_model(
builder.spec, inputs, expected,
model_precision=model_precision, useCPUOnly=True)
def test_batched_mat_mul_single_input_half_precision_cpu(self):
self.test_batched_mat_mul_single_input_cpu(
model_precision=_MLMODEL_HALF_PRECISION)
def test_embedding_nd_cpu(
self, model_precision=_MLMODEL_FULL_PRECISION, use_cpu_only=True):
vocab_size = 10
embedding_size = 19
W = np.random.rand(embedding_size, vocab_size)
input_shapes = [(5, 1), (2, 3, 1), (4, 1, 1), (12, 5, 8, 1),
(2, 3, 1, 5, 1)]
for input_shape in input_shapes:
x = np.random.randint(vocab_size, size=input_shape)
np_out = np.take(np.transpose(W), np.squeeze(x, axis=-1), axis=0)
expected = {'output': np_out}
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_embedding_nd(name='embedding_nd',
input_name='data',
output_name='output',
vocab_size=vocab_size,
embedding_size=embedding_size,
W=W)
input = {'data': x.astype(np.float32)}
self._test_model(
builder.spec, input, expected,
model_precision=model_precision, useCPUOnly=use_cpu_only)
def test_embedding_nd_half_precision_cpu(self):
self.test_embedding_nd_cpu(
model_precision=_MLMODEL_HALF_PRECISION, use_cpu_only=True)
def test_embedding_nd_GPU(self):
self.test_embedding_nd_cpu(
model_precision=_MLMODEL_FULL_PRECISION, use_cpu_only=False)
def test_embedding_nd_half_precision_GPU(self):
self.test_embedding_nd_cpu(
model_precision=_MLMODEL_HALF_PRECISION, use_cpu_only=False)
def test_softmax_nd_cpu(self):
for rank in range(1, 6):
for axis in range(-rank, rank):
input_shape = np.random.randint(low=2, high=5, size=rank)
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_softmax_nd(name='softmax_nd', input_name='data',
output_name='output', axis=axis)
x = np.random.rand(*input_shape)
input = {'data': x}
y = np.exp(x - np.max(x, axis=axis, keepdims=True))
y = y / np.sum(y, axis=axis, keepdims=True)
expected = {'output': y}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_concat_nd_cpu(self):
for rank in range(1, 6):
for axis in range(-rank, rank):
n_inputs = np.random.choice(range(2, 5))
output_shape = np.random.randint(low=2, high=5, size=rank)
output_shape[axis] = 0
input_shapes = []
input_features = []
input_names = []
for _ in range(n_inputs):
input_shapes.append(np.copy(output_shape))
input_shapes[-1][axis] = np.random.choice(range(2, 8))
output_shape[axis] += input_shapes[-1][axis]
for i, input_dim in enumerate(input_shapes):
input_name = 'input_%s' % str(i)
input_names.append(input_name)
input_features.append((input_name, datatypes.Array(*input_dim)))
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_concat_nd(name='concat_nd', input_names=input_names,
output_name='output', axis=axis)
input_tensors = []
for input_dim in input_shapes:
input_tensors.append(np.random.rand(*input_dim))
input = dict(zip(input_names, input_tensors))
expected = {'output': np.concatenate(input_tensors, axis)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_fill_like_cpu(self):
for rank in range(1, 6):
target_shape = np.random.randint(low=2, high=6, size=rank)
value = float(np.random.rand())
input_features = [('tensor', datatypes.Array(*target_shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
builder.add_fill_like(name='fill_like', input_name='tensor',
output_name='output', value=value)
tensor = np.random.rand(*target_shape)
input = {'tensor': tensor}
expected = {'output': np.zeros(target_shape) + value}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_fill_static_cpu(self):
for rank in range(1, 6):
shape = np.random.randint(low=2, high=8, size=rank)
input_features = [('data', datatypes.Array(*shape))]
value = float(np.random.rand())
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
builder.add_fill_static(name='fill_static', output_name='tmp',
output_shape=list(shape), value=value)
builder.add_elementwise('add_layer', ['data', 'tmp'], 'output', mode='ADD')
data = np.random.rand(*shape)
input = {'data': data}
expected = {'output': data + value}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_fill_dynamic_cpu(self):
for rank in range(1, 6):
input_shape = np.random.randint(low=2, high=8, size=rank)
value = float(np.random.rand())
input_features = [('shape', datatypes.Array(len(input_shape)))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
builder.add_fill_dynamic(name='fill_dynamic', input_name='shape',
output_name='output', value=value)
input = {'shape': np.array(input_shape, dtype='float')}
expected = {'output': np.zeros(input_shape) + value}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_broadcast_to_like_cpu(self):
for rank in range(1, 6):
input_shape = np.random.randint(low=2, high=8, size=rank)
mask = [np.random.choice([True, False, False]) for _ in range(rank)]
input_shape = np.where(mask, 1, input_shape)
target_rank = np.random.randint(low=rank, high=6)
target_shape = [np.random.randint(low=2, high=8) if (-i > rank or input_shape[i] == 1)
else input_shape[i] for i in range(-1, -target_rank - 1, -1)][::-1]
input_features = [('data', datatypes.Array(*input_shape)),
('tensor', datatypes.Array(*target_shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
builder.add_broadcast_to_like(name='broadcast_to_like',
input_names=['data', 'tensor'],
output_name='output')
data = np.random.rand(*input_shape)
tensor = np.random.rand(*target_shape)
inputs = {'data': data, 'tensor': tensor}
expected = {'output': np.broadcast_to(data, target_shape)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_broadcast_to_static_cpu(self):
for rank in range(1, 6):
input_shape = np.random.randint(low=2, high=8, size=rank)
mask = [np.random.choice([True, False, False]) for _ in range(rank)]
input_shape = np.where(mask, 1, input_shape)
target_rank = np.random.randint(low=rank, high=6)
target_shape = [np.random.randint(low=2, high=8) if (-i > rank or input_shape[i] == 1)
else input_shape[i] for i in range(-1, -target_rank - 1, -1)][::-1]
input_features = [('data', datatypes.Array(*input_shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
builder.add_broadcast_to_static(name='broadcast_to_static',
input_name='data',
output_name='output',
output_shape=list(target_shape))
data = np.random.rand(*input_shape)
input = {'data': data}
expected = {'output': np.broadcast_to(data, target_shape)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_broadcast_to_dynamic_cpu(self):
for rank in range(1, 6):
input_shape = np.random.randint(low=2, high=8, size=rank)
mask = [np.random.choice([True, False, False]) for _ in range(rank)]
input_shape = np.where(mask, 1, input_shape)
target_rank = np.random.randint(low=rank, high=6)
target_shape = [np.random.randint(low=2, high=8) if (-i > rank or input_shape[i] == 1)
else input_shape[i] for i in range(-1, -target_rank - 1, -1)][::-1]
input_features = [('data', datatypes.Array(*input_shape)),
('shape', datatypes.Array(len(target_shape)))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
builder.add_broadcast_to_dynamic(name='broadcast_to_dynamic',
input_names=['data', 'shape'],
output_name='output')
data = np.random.rand(*input_shape)
inputs = {'data': data, 'shape': np.array(target_shape, dtype='float')}
expected = {'output': np.broadcast_to(data, target_shape)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_trigonometry_cpu(self):
ops = ['sin', 'cos', 'tan',
'asin', 'acos', 'atan',
'sinh', 'cosh', 'tanh',
'asinh', 'acosh', 'atanh']
for op in ops:
for rank in range(1, 6):
shape = np.random.randint(low=2, high=8, size=rank)
input_features = [('data', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
x = np.random.rand(*shape)
if op == 'sin':
builder.add_sin(name=op, input_name='data', output_name='output')
expected = {'output': np.sin(x)}
elif op == 'cos':
builder.add_cos(name=op, input_name='data', output_name='output')
expected = {'output': np.cos(x)}
elif op == 'tan':
builder.add_tan(name=op, input_name='data', output_name='output')
expected = {'output': np.tan(x)}
elif op == 'asin':
builder.add_asin(name=op, input_name='data', output_name='output')
expected = {'output': np.arcsin(x)}
elif op == 'acos':
builder.add_acos(name=op, input_name='data', output_name='output')
expected = {'output': np.arccos(x)}
elif op == 'atan':
builder.add_atan(name=op, input_name='data', output_name='output')
expected = {'output': np.arctan(x)}
elif op == 'sinh':
builder.add_sinh(name=op, input_name='data', output_name='output')
expected = {'output': np.sinh(x)}
elif op == 'cosh':
builder.add_cosh(name=op, input_name='data', output_name='output')
expected = {'output': np.cosh(x)}
elif op == 'tanh':
builder.add_tanh(name=op, input_name='data', output_name='output')
expected = {'output': np.tanh(x)}
elif op == 'asinh':
builder.add_asinh(name=op, input_name='data', output_name='output')
expected = {'output': np.arcsinh(x)}
elif op == 'acosh':
x = np.random.choice([10, np.e, 1], tuple(shape)).astype(np.float32)
builder.add_acosh(name=op, input_name='data', output_name='output')
expected = {'output': np.arccosh(x)}
elif op == 'atanh':
builder.add_atanh(name=op, input_name='data', output_name='output')
expected = {'output': np.arctanh(x)}
self._test_model(builder.spec, {'data': x}, expected, useCPUOnly=True)
def test_exp2_cpu(self):
for rank in range(1, 6):
shape = np.random.randint(low=2, high=8, size=rank)
input_features = [('data', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
builder.add_exp2(name='exp2', input_name='data', output_name='output')
x = np.random.rand(*shape)
input = {'data': x}
expected = {'output': np.exp2(x)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_elementwise_binary_cpu(self):
input_names = ['A', 'B']
test_cases = ['greater', 'less', 'equal', 'not_equal', 'greater_equal',
'less_equal', 'logical_and', 'logical_or', 'logical_xor',
'add', 'subtract', 'multiply', 'divide', 'power',
'maximum', 'minimum', 'floor_divide', 'mod']
for test_case in test_cases:
for _ in range(10):
rank_a = np.random.randint(low=1, high=6)
rank_b = np.random.randint(low=1, high=6)
rank_out = max(rank_a, rank_b)
shape_a = np.random.randint(low=2, high=8, size=rank_a)
shape_b = np.random.randint(low=2, high=8, size=rank_b)
for i in range(-1, -rank_out - 1, -1):
dims = []
if -i <= rank_a: dims.append(shape_a[i])
if -i <= rank_b: dims.append(shape_b[i])
dim = np.random.choice(dims)
if -i <= rank_a: shape_a[i] = np.random.choice([1, dim])
if -i <= rank_b: shape_b[i] = np.random.choice([1, dim])
input_shapes = [shape_a, shape_b]
input_features = [('A', datatypes.Array(*input_shapes[0])),
('B', datatypes.Array(*input_shapes[1]))]
builder = neural_network.NeuralNetworkBuilder(input_features, [
('output', None)], disable_rank5_shape_mapping=True)
func = getattr(np, test_case)
if test_case == 'greater':
builder.add_greater_than(test_case, input_names=input_names,
output_name='output')
elif test_case == 'less':
builder.add_less_than(test_case, input_names=input_names,
output_name='output')
elif test_case == 'equal':
builder.add_equal(test_case, input_names=input_names,
output_name='output')
elif test_case == 'not_equal':
builder.add_not_equal(test_case, input_names=input_names,
output_name='output')
elif test_case == 'greater_equal':
builder.add_greater_than(test_case, input_names=input_names,
output_name='output',
use_greater_than_equal=True)
elif test_case == 'less_equal':
builder.add_less_than(test_case, input_names=input_names,
output_name='output',
use_less_than_equal=True)
elif test_case == 'logical_and':
builder.add_logical(test_case, input_names=input_names,
output_name='output', mode='AND')
elif test_case == 'logical_or':
builder.add_logical(test_case, input_names=input_names,
output_name='output', mode='OR')
elif test_case == 'logical_xor':
builder.add_logical(test_case, input_names=input_names,
output_name='output', mode='XOR')
elif test_case == 'add':
builder.add_add_broadcastable(test_case, input_names=input_names,
output_name='output')
elif test_case == 'subtract':
builder.add_subtract_broadcastable(test_case,
input_names=input_names,
output_name='output')
elif test_case == 'multiply':
builder.add_multiply_broadcastable(test_case,
input_names=input_names,
output_name='output')
elif test_case == 'divide':
builder.add_divide_broadcastable(test_case,
input_names=input_names,
output_name='output')
elif test_case == 'power':
builder.add_pow_broadcastable(test_case,
input_names=input_names,
output_name='output')
elif test_case == 'maximum':
builder.add_max_broadcastable(test_case,
input_names=input_names,
output_name='output')
elif test_case == 'minimum':
builder.add_min_broadcastable(test_case,
input_names=input_names,
output_name='output')
elif test_case == 'floor_divide':
builder.add_floor_div_broadcastable(test_case,
input_names=input_names,
output_name='output')
elif test_case == 'mod':
builder.add_mod_broadcastable(test_case,
input_names=input_names,
output_name='output')
a = np.random.rand(*input_shapes[0])
b = np.random.rand(*input_shapes[1])
input = {'A': a, 'B': b}
expected = {'output': func(a, b, dtype=np.float32)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_elementwise_boolean_unary_cpu(self):
input_names = ['input']
shapes = [(1, 2, 3, 1), (3, 1, 2, 1, 2), (1, 2, 1, 3), (2, 3),
(2, 1, 1), (2, 3, 4), (2, 4), (1,), (1,)]
test_cases = ['greater', 'less', 'equal', 'not_equal', 'greater_equal',
'less_equal']
for test_case in test_cases:
for shape in shapes:
input_features = [('input', datatypes.Array(*shape))]
b = np.random.rand()
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
func = getattr(np, test_case)
if test_case == 'greater':
builder.add_greater_than(test_case, input_names=input_names,
output_name='output', alpha=b)
elif test_case == 'less':
builder.add_less_than(test_case, input_names=input_names,
output_name='output', alpha=b)
elif test_case == 'equal':
builder.add_equal(test_case, input_names=input_names,
output_name='output', alpha=b)
elif test_case == 'not_equal':
builder.add_not_equal(test_case, input_names=input_names,
output_name='output', alpha=b)
elif test_case == 'greater_equal':
builder.add_greater_than(test_case, input_names=input_names,
output_name='output',
use_greater_than_equal=True,
alpha=b)
elif test_case == 'less_equal':
builder.add_less_than(test_case, input_names=input_names,
output_name='output',
use_less_than_equal=True, alpha=b)
a = np.random.rand(*shape)
input = {'input': a}
expected = {'output': func(a, b, dtype=np.float32)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_logical_not_cpu(self):
input_names = ['input']
shapes = [(1, 2, 3, 1), (3, 1, 2, 1, 2), (1, 2, 1, 3), (2, 3),
(2, 1, 1), (2, 3, 4), (2, 4), (1,), (1,)]
for shape in shapes:
input_features = [('input', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
builder.add_logical('logical_not', input_names=input_names,
output_name='output', mode='NOT')
a = np.random.rand(*shape)
input = {'input': a}
expected = {'output': np.logical_not(a)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_stack_cpu(self):
for input_rank in range(1, 5):
for axis in range(-input_rank - 1, input_rank + 1):
n_inputs = np.random.choice(range(2, 5))
input_shape = np.random.randint(low=2, high=5, size=input_rank)
input_features = []
input_names = []
for i in range(n_inputs):
input_name = 'input_%s' % str(i)
input_names.append(input_name)
input_features.append(
(input_name, datatypes.Array(*input_shape)))
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_stack(name='stack', input_names=input_names,
output_name='output', axis=axis)
input_tensors = []
for _ in range(n_inputs):
input_tensors.append(np.random.rand(*input_shape))
input = dict(zip(input_names, input_tensors))
expected = {'output': np.stack(input_tensors, axis)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_ceil_cpu(self):
for rank in range(1, 6):
shape = np.random.randint(low=2, high=8, size=rank)
input_features = [('data', datatypes.Array(*shape))]
output_features = [('output', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_ceil(name='ceil', input_name='data', output_name='output')
x = np.random.rand(*shape)
inputs = {'data': x}
expected = {'output': np.ceil(x)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_floor_cpu(self):
for rank in range(1, 6):
shape = np.random.randint(low=2, high=8, size=rank)
input_features = [('data', datatypes.Array(*shape))]
output_features = [('output', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_floor(name='floor', input_name='data', output_name='output')
x = np.random.rand(*shape)
inputs = {'data': x}
expected = {'output': np.floor(x)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_round_cpu(self):
for rank in range(1, 6):
shape = np.random.randint(low=2, high=8, size=rank)
input_features = [('data', datatypes.Array(*shape))]
output_features = [('output', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_round(name='round', input_name='data', output_name='output')
x = np.float32(np.random.rand(*shape) * np.random.randint(low=-100, high=101))
inputs = {'data': x}
expected = {'output': np.around(x)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_sign_cpu(self):
for rank in range(1, 6):
shape = np.random.randint(low=2, high=8, size=rank)
input_features = [('data', datatypes.Array(*shape))]
output_features = [('output', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_sign(name='sign', input_name='data', output_name='output')
x = np.random.choice([-np.random.rand(1), 0.0, np.random.rand(1)],
tuple(shape)).astype(np.float32)
inputs = {'data': x}
expected = {'output': np.sign(x)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_clip_cpu(self):
for rank in range(1, 6):
shape = np.random.randint(low=2, high=6, size=rank)
input_features = [('data', datatypes.Array(*shape))]
output_features = [('output', datatypes.Array(*shape))]
x = np.random.rand(*shape)
min_value = np.percentile(x, 25)
max_value = np.percentile(x, 75)
input = {'data': x}
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_clip(name='clip', input_name='data', output_name='output',
min_value=min_value, max_value=max_value)
expected = {'output': np.clip(x, min_value, max_value)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_split_nd_cpu(self):
for rank in range(1, 6):
for axis in range(-rank, rank):
n_outputs = np.random.choice(range(2, 4))
input_shape = np.random.randint(low=2, high=5, size=rank)
input_shape[axis] = 0
output_shapes = []
output_features = []
output_names = []
almost_equal = random.choice([True, False])
remainder = np.random.choice(
range(1, n_outputs)) if almost_equal else 0
value = np.random.choice(range(2, 5))
for k in range(n_outputs):
output_shapes.append(np.copy(input_shape))
output_shapes[-1][
axis] = value + 1 if k < remainder else value
input_shape[axis] += output_shapes[-1][axis]
for i in range(n_outputs):
output_name = 'output_%s' % str(i)
output_names.append(output_name)
output_features.append(
(output_name, None))
input_features = [('data', datatypes.Array(*input_shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_split_nd(name='split_nd', input_name='data',
output_names=output_names, axis=axis,
num_splits=n_outputs)
x = np.random.rand(*input_shape)
input = {'data': x}
expected = dict(
zip(
output_names, np.array_split(x, n_outputs, axis=axis)
if almost_equal else np.split(x, n_outputs, axis=axis)
)
) # Explicitly trying to compare against both versions of numpy split
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_split_nd_with_split_sizes_cpu(self):
for rank in range(1, 6):
for axis in range(-rank, rank):
n_outputs = np.random.choice(range(2, 4))
input_shape = np.random.randint(low=2, high=5, size=rank)
input_shape[axis] = 0
output_shapes, output_features, output_names = [], [], []
sections, split_sizes = [], []
for _ in range(n_outputs):
output_shapes.append(np.copy(input_shape))
output_shapes[-1][axis] = np.random.choice(range(2, 5))
input_shape[axis] += output_shapes[-1][axis]
sections.append(input_shape[axis])
split_sizes.append(output_shapes[-1][axis])
sections.pop()
for i in range(n_outputs):
output_name = 'output_%s' % str(i)
output_names.append(output_name)
output_features.append(
(output_name, None))
input_features = [('data', datatypes.Array(*input_shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_split_nd(name='split_nd', input_name='data',
output_names=output_names, axis=axis,
split_sizes=split_sizes)
x = np.random.rand(*input_shape)
input = {'data': x}
expected = dict(
zip(output_names, np.split(x, sections, axis=axis)))
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_slice_static_cpu(self):
for rank in range(1, 6):
for _ in range(200):
input_shape = np.array([5 for _ in range(rank)])
objs, strides, begin_masks, end_ids, end_masks, begin_ids = [], [], [], [], [], []
for dim in range(rank):
stride = random.choice([-3, -1, 1, 2])
begin_mask = random.choice([True, False])
end_mask = random.choice([True, False])
length = 0
while length <= 0:
begin_id = np.random.randint(low=-input_shape[dim],
high=input_shape[dim])
end_id = np.random.randint(low=-input_shape[dim],
high=input_shape[dim])
obj = slice(None if begin_mask else begin_id,
None if end_mask else end_id, stride)
length = np.arange(input_shape[dim])[(obj,)].shape[0]
objs.append(obj), strides.append(stride), begin_masks.append(
begin_mask)
end_masks.append(end_mask), begin_ids.append(
begin_id), end_ids.append(end_id)
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_slice_static('slice_static', 'data', 'output',
begin_ids=begin_ids, end_ids=end_ids, strides=strides,
begin_masks=begin_masks, end_masks=end_masks)
x = np.random.rand(*input_shape)
inputs = {'data': x}
expected = {'output': x[tuple(objs)]}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_slice_dynamic_cpu(self):
for rank in range(1, 6):
input_shape = np.array([5 for _ in range(rank)])
objs, strides, begin_masks, end_ids, end_masks, begin_ids = [], [], [], [], [], []
for dim in range(rank):
stride = random.choice([-3, -1, 1, 2])
begin_mask = random.choice([True, False])
end_mask = random.choice([True, False])
length = 0
while length <= 0:
begin_id = np.random.randint(low=-input_shape[dim],
high=input_shape[dim])
end_id = np.random.randint(low=-input_shape[dim],
high=input_shape[dim])
obj = slice(None if begin_mask else begin_id,
None if end_mask else end_id, stride)
length = np.arange(input_shape[dim])[(obj,)].shape[0]
objs.append(obj), strides.append(stride), begin_masks.append(
begin_mask)
end_masks.append(end_mask), begin_ids.append(
begin_id), end_ids.append(end_id)
# test different number of inputs, from 2 inputs up to 6 inputs
# when num_inputs == 2, begin_ids are inputs, rest are read from parameters
# when num_inputs == 6, all read from inputs, none are read from parameters
for num_inputs in [2, 3, 4, 5, 6]:
x = np.random.rand(*input_shape)
input_features = [('data', datatypes.Array(*input_shape))]
input_names = ['data']
inputs = dict()
inputs['data'] = x
if num_inputs == 2:
input_features = [('data', datatypes.Array(*input_shape)),
('begin_ids', datatypes.Array(len(begin_ids)))]
input_names = ['data', 'begin_ids']
inputs['begin_ids'] = np.array(begin_ids, dtype=np.int32)
elif num_inputs == 3:
input_features = [('data', datatypes.Array(*input_shape)),
('begin_ids', datatypes.Array(len(begin_ids))),
('end_ids', datatypes.Array(len(end_ids)))]
input_names = ['data', 'begin_ids', 'end_ids']
inputs['begin_ids'] = np.array(begin_ids, dtype=np.int32)
inputs['end_ids'] = np.array(end_ids, dtype=np.int32)
elif num_inputs == 4:
input_features = [('data', datatypes.Array(*input_shape)),
('begin_ids', datatypes.Array(len(begin_ids))),
('end_ids', datatypes.Array(len(end_ids))),
('strides', datatypes.Array(len(strides)))]
input_names = ['data', 'begin_ids', 'end_ids', 'strides']
inputs['begin_ids'] = np.array(begin_ids, dtype=np.int32)
inputs['end_ids'] = np.array(end_ids, dtype=np.int32)
inputs['strides'] = np.array(strides, dtype=np.int32)
elif num_inputs == 5:
input_features = [('data', datatypes.Array(*input_shape)),
('begin_ids', datatypes.Array(len(begin_ids))),
('end_ids', datatypes.Array(len(end_ids))),
('strides', datatypes.Array(len(strides))),
('begin_masks', datatypes.Array(len(begin_masks)))]
input_names = ['data', 'begin_ids', 'end_ids', 'strides', 'begin_masks']
inputs['begin_ids'] = np.array(begin_ids, dtype=np.int32)
inputs['end_ids'] = np.array(end_ids, dtype=np.int32)
inputs['strides'] = np.array(strides, dtype=np.int32)
inputs['begin_masks'] = np.array(begin_masks, dtype=np.int32)
elif num_inputs == 6:
input_features = [('data', datatypes.Array(*input_shape)),
('begin_ids', datatypes.Array(len(begin_ids))),
('end_ids', datatypes.Array(len(end_ids))),
('strides', datatypes.Array(len(strides))),
('begin_masks', datatypes.Array(len(begin_masks))),
('end_masks', datatypes.Array(len(end_masks)))]
input_names = ['data', 'begin_ids', 'end_ids',
'strides', 'begin_masks', 'end_masks']
inputs['begin_ids'] = np.array(begin_ids, dtype=np.int32)
inputs['end_ids'] = np.array(end_ids, dtype=np.int32)
inputs['strides'] = np.array(strides, dtype=np.int32)
inputs['begin_masks'] = np.array(begin_masks, dtype=np.int32)
inputs['end_masks'] = np.array(end_masks, dtype=np.int32)
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
if num_inputs == 2:
builder.add_slice_dynamic('slice_dynamic', input_names, 'output',
end_ids=end_ids, strides=strides,
begin_masks=begin_masks, end_masks=end_masks)
elif num_inputs == 3:
builder.add_slice_dynamic('slice_dynamic', input_names, 'output',
strides=strides, begin_masks=begin_masks,
end_masks=end_masks)
elif num_inputs == 4:
builder.add_slice_dynamic('slice_dynamic', input_names, 'output',
begin_masks=begin_masks, end_masks=end_masks)
elif num_inputs == 5:
builder.add_slice_dynamic('slice_dynamic', input_names, 'output',
end_masks=end_masks)
elif num_inputs == 6:
builder.add_slice_dynamic('slice_dynamic', input_names, 'output')
expected = {'output': x[tuple(objs)]}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
@unittest.skip('fix')
def test_tile_cpu(self):
for rank in range(1, 6):
input_shape = np.random.randint(low=2, high=5, size=rank)
reps = list(np.random.randint(low=1, high=4, size=rank))
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True
)
builder.add_tile('Tile', 'data', 'output', reps)
x = np.random.rand(*input_shape)
input = {'data': x}
expected = {'output': np.tile(x, reps)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_sliding_windows_cpu(self):
def numpy_sliding_windows(a, np_axis, np_size, np_step):
n = (a.shape[np_axis] - np_size) // np_step + 1
shape = list(a.shape)
shape[np_axis] = n
if np_axis < 0:
np_axis += len(shape)
shape.insert(np_axis + 1, np_size)
strides = list(a.strides)
effstride = strides[np_axis] * np_step
strides.insert(np_axis, effstride)
return np.lib.stride_tricks.as_strided(a, shape, strides)
for rank in range(1, 5):
for axis in range(-rank, rank):
input_shape = np.random.randint(low=2, high=5, size=rank)
output_shape = list(input_shape)
window_size = np.random.randint(low=1, high=input_shape[axis])
length = 0
while length <= 0:
step = np.random.randint(low=1, high=input_shape[axis])
length = (input_shape[axis] - window_size) // step + 1
output_shape[axis] = length
pos_axis = axis if axis >= 0 else axis + rank
output_shape.insert(pos_axis + 1, window_size)
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_sliding_windows('sliding_windows',
input_name='data',
output_name='output',
axis=axis,
window_size=window_size,
step=step)
x = np.random.rand(*input_shape)
input = {'data': x}
expected = {'output': numpy_sliding_windows(x, axis, window_size, step)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_range_static_cpu(self):
params = [(-10.4, 23, 12.2), (0, 1000, 1), (50.5, 90.5, 1.5), (5, 8, 2),
(5, 8, 98), (5, 8, 1.5), (10, 5, -0.6), (24, -65, -2)]
for param in params:
start, end, step = param
input_features = [('multiplicative_input', datatypes.Array(1))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
builder.add_range_static('range_static', 'output_range',
end=end, start=start, step=step)
builder.add_multiply_broadcastable(
name='multiply_broadcastable',
input_names=['multiplicative_input', 'output_range'],
output_name='output')
# save the model
model_dir = tempfile.mkdtemp()
model_path = os.path.join(model_dir, 'test_layer.mlmodel')
coremltools.utils.save_spec(builder.spec, model_path)
inputs = dict()
inputs['multiplicative_input'] = np.ones((1,), dtype=np.float64)
expected = {'output': np.arange(start, end, step)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_range_dynamic_cpu(self):
params = [(-10.4, 23, 12.2), (0, 1000, 1), (50.5, 90.5, 1.5), (5, 8, 2),
(5, 8, 98), (5, 8, 1.5), (10, 5, -0.6), (24, -65, -2)]
# input size == 1: end is input, start and step are read from parameters
# input size == 2: end, start are inputs, step is read from parameters
# input size == 3: start, end, step are all inputs, none of the parameters are used.
for num_inputs in [1, 2, 3]:
for param in params:
inputs = dict()
start, end, step = param
if num_inputs == 1:
input_features = [('end', datatypes.Array(1))]
elif num_inputs == 2:
input_features = [('end', datatypes.Array(1)),
('start', datatypes.Array(1))]
elif num_inputs == 3:
input_features = [('end', datatypes.Array(1)),
('start', datatypes.Array(1)),
('step', datatypes.Array(1))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
if num_inputs == 1:
inputs['end'] = end * np.ones((1,), dtype=np.float64)
builder.add_range_dynamic('range_dynamic',
output_name='output',
input_names=['end'],
start=start, step=step)
elif num_inputs == 2:
inputs['end'] = end * np.ones((1,), dtype=np.float64)
inputs['start'] = start * np.ones((1,), dtype=np.float64)
builder.add_range_dynamic('range_dynamic',
output_name='output',
input_names=['end', 'start'],
step=step)
elif num_inputs == 3:
inputs['end'] = end * np.ones((1,), dtype=np.float64)
inputs['start'] = start * np.ones((1,), dtype=np.float64)
inputs['step'] = step * np.ones((1,), dtype=np.float64)
builder.add_range_dynamic('range_dynamic',
output_name='output',
input_names=['end', 'start', 'step'])
expected = {'output': np.arange(start, end, step)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_linear_activation_different_ranks_cpu(self):
for input_dim in [(10, 15), (10, 15, 2, 3),
(10, 2, 4, 15, 1, 4), (6,)]:
input_features = [('data', datatypes.Array(*input_dim))]
output_features = [('output', datatypes.Array(*input_dim))]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_activation(name='activation',
non_linearity='LINEAR',
input_name='data',
output_name='output', params=[34.0, 67.0])
x = np.random.rand(*input_dim)
input = {'data': x}
expected = {'output': 34.0 * x + 67.0}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_topk(self):
test_input_shapes = [(9,), (8, 6), (9, 8, 10), (5, 9, 7, 9), (12, 8, 6, 6, 7)]
K = [3, 5]
axes = [[0], [0, 1], [1, 2], [0, 3, 1], [1, 3, 4]]
for ii, input_shape in enumerate(test_input_shapes):
for k in K:
for n_inputs in [1, 2]:
for bottom_k_flag in [False, True]:
for axis in axes[ii]:
for negative_axis in [False, True]:
if negative_axis:
axis = axis - len(input_shape)
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('values', None), ('indices', None)]
input_names = ['data']
output_names = ['values', 'indices']
if n_inputs == 2:
input_names.append('k_in')
input_features.append(('k_in', datatypes.Array(1)))
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_topk('topk', input_names, output_names,
k=k, axis=axis, use_bottom_k=bottom_k_flag)
data = np.random.randint(low=0, high=int(np.prod(input_shape)), size=input_shape)
data = data.astype(np.float32)
input = {'data': data}
if n_inputs == 2:
input['k_in'] = k * np.ones([1], dtype=np.float32)
# numpy reference values
if bottom_k_flag:
ref_indices = np.argsort(data, axis=axis)
else:
ref_indices = np.argsort(-data, axis=axis)
slc = [slice(None)] * len(input_shape)
slc[axis] = slice(0, k)
ref_indices = ref_indices[tuple(slc)]
ref_values = np.take_along_axis(data, ref_indices, axis=axis)
expected = {'values': ref_values, 'indices': ref_indices}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_rank_preserving_reshape(self):
input_shapes = [(20, 10), (20, 10, 5), (10, 3, 5)]
target_shapes = [(5, -1), (0, 2, 25), (25, 0, -1)]
output_shapes = [(5, 40), (20, 2, 25), (25, 3, 2)]
for i in range(len(input_shapes)):
input_features = [('data', datatypes.Array(*input_shapes[i]))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_rank_preserving_reshape(
name='rank_preserving_reshape', input_name='data',
output_name='output', output_shape=target_shapes[i])
x = np.random.rand(*input_shapes[i])
input = {'data': x}
expected = {'output': np.reshape(x, output_shapes[i])}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_expand_dims(self):
input_shapes = [(10, 5), (10, 5), (10, 5), (10, 5), (10,)]
axes = [(0, 1), (0, 2), (2, 0), (-2, -1), (1, 0, -2)]
output_shapes = [(1, 1, 10, 5), (1, 10, 1, 5), (1, 10, 1, 5), (10, 5, 1, 1), (1, 1, 1, 10)]
for i in range(len(input_shapes)):
input_features = [('data', datatypes.Array(*input_shapes[i]))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_expand_dims(
name='expand_dims', input_name='data', output_name='output',
axes=axes[i]
)
x = np.random.rand(*input_shapes[i])
input = {'data': x}
expected = {'output': np.reshape(x, output_shapes[i])}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_squeeze(self):
input_shapes = [(1, 1, 10, 5), (1, 10, 1, 5), (10, 5, 1, 1),
(10, 5, 1, 1), (1,), (10, 5, 1, 1), (3, 1, 7)]
axes = [(0, 1), (0, 2), (-2, -1), (-1, -2), (0,), (3, -2), (1,)]
output_shapes = [(10, 5), (10, 5), (10, 5), (10, 5), (1,), (10, 5), (3, 7)]
for i in range(len(input_shapes)):
input_features = [('data', datatypes.Array(*input_shapes[i]))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True
)
builder.add_squeeze(name='squeeze_layer', input_name='data',
output_name='output', axes=list(axes[i]))
x = np.random.rand(*input_shapes[i])
input = {'data': x}
expected = {'output': np.reshape(x, output_shapes[i])}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_squeeze_all(self):
input_shapes = [
(1, 1, 10, 5), (1, 10, 1, 5), (10, 5, 1, 1), (10, 5, 1, 1), (1,),
(10, 5, 1, 1), (3, 1, 7), (3,), (5, 6)
]
for input_shape in input_shapes:
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True
)
builder.add_squeeze(name='squeeze_layer', input_name='data',
output_name='output', squeeze_all=True)
x = np.random.rand(*input_shape)
input = {'data': x}
reference = np.squeeze(x)
if not reference.shape:
reference = np.reshape(reference, (1,))
expected = {'output': reference}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_argmax_argmin(self):
test_input_shapes = [(9,), (8, 6), (9, 8, 10), (5, 9, 7, 9), (12, 8, 6, 6, 7)]
# (1+2+3+4+5) * 2^3 = 120 test cases
for input_shape in test_input_shapes:
for negative_axis in [False, True]:
for mode in ['argmax', 'argmin']:
for keep_dims in [True, False]:
for axis in np.arange(len(input_shape)):
if negative_axis:
axis_val = axis - len(input_shape)
else:
axis_val = axis
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True
)
x = np.random.rand(*input_shape)
if mode == 'argmax':
builder.add_argmax('argmax', 'data', 'output', axis=axis_val, keepdims=keep_dims)
np_out = np.argmax(x, axis=axis_val)
else:
builder.add_argmin('argmin', 'data', 'output', axis=axis_val, keepdims=keep_dims)
np_out = np.argmin(x, axis=axis_val)
if keep_dims:
np_out = np.expand_dims(np_out, axis=axis_val)
elif len(input_shape) == 1:
np_out = np.expand_dims(np_out, axis=axis_val)
input = {'data': x}
expected = {'output': np_out}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_get_shape(self):
dims = [1, 2, 3, 4, 5]
for rank in range(1, len(dims) + 1):
input_shape = dims[:rank]
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True
)
builder.add_get_shape(name='get_shape_layer', input_name='data',
output_name='output')
feed = {'data': np.random.rand(*input_shape)}
expected = {'output': np.array(input_shape)}
self._test_model(builder.spec, feed, expected, useCPUOnly=True)
def test_load_constant_nd(self):
dims = [2, 3, 4, 5, 6]
for rank in range(1, len(dims) + 1):
input_shape = dims[:rank]
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True
)
builder.add_load_constant_nd('load_const_nd_layer', 'tmp',
constant_value=np.ones(input_shape),
shape=input_shape)
builder.add_elementwise('add_layer', ['data', 'tmp'], 'output',
mode='ADD')
feed = {'data': np.random.rand(*input_shape)}
expected = {'output': feed['data'] + 1}
self._test_model(builder.spec, feed, expected, useCPUOnly=True)
@unittest.skip('fix')
def test_simple_array_alloc_scatter(self):
alloc_shape = [2, 3, 4]
value_shape = [1, 3, 4]
input_features = [('alloc_shape', datatypes.Array(len(alloc_shape))),
('value', datatypes.Array(*value_shape)),
('index', datatypes.Array(1))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features, disable_rank5_shape_mapping=True)
builder.add_fill_dynamic(name='fill_dynamic_layer', input_name='alloc_shape',
output_name='array', value=np.float(0.0))
# CoreML input order: container (array), indices, slices (value)
builder.add_scatter(name='scatter_layer',
input_names=['array', 'index', 'value'],
output_name='output')
value = np.random.rand(*value_shape).astype('float')
feed = {'alloc_shape': np.array(alloc_shape, dtype='float'),
'value': value,
'index': np.array([1], dtype='float')}
ref = np.zeros(alloc_shape)
ref[1, :, :] = value
expected = {'output': ref}
self._test_model(builder.spec, feed, expected, useCPUOnly=True)
def test_erf_activation(self):
input_features = [('data', datatypes.Array(10, 45))]
output_features = [('output', datatypes.Array(10, 45))]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features, disable_rank5_shape_mapping=True)
builder.add_erf(name='erf', input_name='data',
output_name='output')
x = np.random.rand(10, 45)
input = {'data': x}
expected = {
'output': np.asarray([math.erf(i) for i in
x.flatten().tolist()]).reshape(10, 45)
}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_gelu_activation(self):
for mode in ['EXACT', 'TANH_APPROXIMATION', 'SIGMOID_APPROXIMATION']:
for rank in range(1, 6):
shape = np.random.randint(low=2, high=5, size=rank)
input_features = [('data', datatypes.Array(*shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features, disable_rank5_shape_mapping=True)
builder.add_gelu(name='gelu', input_name='data',
output_name='output', mode=mode)
x = np.random.rand(*shape)
input = {'data': x}
exact = np.asarray([0.5 * i * (1.0 + math.erf(i / math.sqrt(2)))
for i in x.flatten().tolist()]).reshape(*shape)
expected = {'output': exact}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_lower_triangular_cpu(self):
for rank in range(2, 6):
for k in range(-7, 8):
shape = np.random.randint(low=2, high=6, size=rank)
input_features = [('data', datatypes.Array(*shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features, disable_rank5_shape_mapping=True)
builder.add_lower_triangular('tril', 'data', 'output', k=k)
x = np.random.rand(*shape)
input = {'data': x}
expected = {'output': np.tril(x, k=k)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_upper_triangular_cpu(self):
for rank in range(2, 6):
for k in range(-7, 8):
shape = np.random.randint(low=2, high=6, size=rank)
input_features = [('data', datatypes.Array(*shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features, disable_rank5_shape_mapping=True)
builder.add_upper_triangular('triu', 'data', 'output', k=k)
x = np.random.rand(*shape)
input = {'data': x}
expected = {'output': np.triu(x, k=k)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_where_broadcastable_cpu(self):
for _ in range(150):
rank_cond = np.random.randint(low=1, high=6)
rank_true = np.random.randint(low=1, high=6)
rank_false = np.random.randint(low=1, high=6)
rank_out = max(rank_cond, rank_true, rank_false)
shape_cond = np.random.randint(low=2, high=8, size=rank_cond)
shape_true = np.random.randint(low=2, high=8, size=rank_true)
shape_false = np.random.randint(low=2, high=8, size=rank_false)
for i in range(-1, -rank_out - 1, -1):
dims = []
if -i <= rank_cond: dims.append(shape_cond[i])
if -i <= rank_true: dims.append(shape_true[i])
if -i <= rank_false: dims.append(shape_false[i])
dim = np.random.choice(dims)
if -i <= rank_cond: shape_cond[i] = np.random.choice([1, dim])
if -i <= rank_true: shape_true[i] = np.random.choice([1, dim])
if -i <= rank_false: shape_false[i] = np.random.choice([1, dim])
input_features = [
('cond', datatypes.Array(*shape_cond)),
('true', datatypes.Array(*shape_true)),
('false', datatypes.Array(*shape_false))
]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features, disable_rank5_shape_mapping=True)
builder.add_where_broadcastable('if_broadcastable', input_names=['cond', 'true', 'false'],
output_name='output')
cond = np.random.choice([1.0, 0.0], size=shape_cond)
true = np.random.rand(*shape_true)
false = np.random.rand(*shape_false)
input = {'cond': cond, 'true': true, 'false': false}
expected = {'output': np.where(cond, true, false)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_random_normal_like_cpu(self):
mean, stddev, seed = 0., 1., 42
for rank in range(5, -1, -1):
if rank > 0:
low_factor = np.random.randint(low=2, high=4)
low = int(np.power(1000, 1. / rank)) * low_factor
high = int(np.power(2000, 1. / rank)) * np.random.randint(low=low_factor, high=4)
shape = np.random.randint(low=low, high=high, size=rank)
else: # one extra test to test more moments
shape = np.array([10, 10, 10, 10, 10000])
input_features = [('tensor', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
builder.add_random_normal_like(name='random_normal_like',
input_name='tensor',
output_name='output',
mean=mean, stddev=stddev, seed=seed)
inputs = {'tensor': np.random.rand(*shape)}
expected = {'output': np.random.normal(mean, stddev, shape)}
if rank > 0:
CorrectnessTest._compare_moments(builder.spec, inputs, expected, num_moments=2)
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
else: # one extra test to test more moments
CorrectnessTest._compare_moments(builder.spec, inputs, expected, num_moments=6)
def test_random_normal_static_cpu(self):
mean, stddev, seed = 0., 1., 42
for rank in range(1, 6):
low_factor = np.random.randint(low=2, high=4)
low = int(np.power(1000, 1. / rank)) * low_factor
high = int(np.power(2000, 1. / rank)) * np.random.randint(low=low_factor, high=4)
shape = np.random.randint(low=low, high=high, size=rank)
input_features = [('data', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
builder.add_random_normal_static(name='random_normal_static',
output_name='tmp',
output_shape=list(shape),
mean=mean, stddev=stddev, seed=seed)
builder.add_elementwise('add_layer', ['data', 'tmp'], 'output', mode='ADD')
data = np.zeros(shape)
inputs = {'data': data}
expected = {'output': data + np.random.normal(mean, stddev, shape)}
CorrectnessTest._compare_moments(builder.spec, inputs, expected, num_moments=2)
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_random_normal_dynamic_cpu(self):
mean, stddev, seed = 0., 1., 42
for rank in range(1, 6):
low_factor = np.random.randint(low=2, high=4)
low = int(np.power(1000, 1. / rank)) * low_factor
high = int(np.power(2000, 1. / rank)) * np.random.randint(low=low_factor, high=4)
shape = np.random.randint(low=low, high=high, size=rank)
input_features = [('shape', datatypes.Array(len(shape)))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
builder.add_random_normal_dynamic(name='random_normal_dynamic',
input_names=['shape'],
output_name='output',
mean=mean, stddev=stddev, seed=seed)
inputs = {'shape': np.array(shape, np.float)}
expected = {'output': np.random.normal(mean, stddev, shape)}
CorrectnessTest._compare_moments(builder.spec, inputs, expected, num_moments=2)
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_random_uniform_like_cpu(self):
minval, maxval, seed = 0., 1., 42
for rank in range(1, 6):
low_factor = np.random.randint(low=2, high=4)
low = int(np.power(1000, 1. / rank)) * low_factor
high = int(np.power(2000, 1. / rank)) * np.random.randint(low=low_factor, high=4)
shape = np.random.randint(low=low, high=high, size=rank)
input_features = [('tensor', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
builder.add_random_uniform_like(name='random_uniform_like',
input_name='tensor',
output_name='output',
minval=minval, maxval=maxval, seed=seed)
tensor = np.random.rand(*shape)
inputs = {'tensor': tensor}
expected = {'output': np.random.uniform(minval, maxval, shape)}
CorrectnessTest._compare_moments(builder.spec, inputs, expected)
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_random_uniform_static_cpu(self):
minval, maxval, seed = 0., 1., 42
for rank in range(1, 6):
low_factor = np.random.randint(low=2, high=4)
low = int(np.power(1000, 1. / rank)) * low_factor
high = int(np.power(2000, 1. / rank)) * np.random.randint(low=low_factor, high=4)
shape = np.random.randint(low=low, high=high, size=rank)
input_features = [('data', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
builder.add_random_uniform_static(name='random_uniform_static',
output_name='tmp',
output_shape=list(shape),
minval=minval, maxval=maxval, seed=seed)
builder.add_elementwise('add_layer', ['data', 'tmp'], 'output', mode='ADD')
data = np.zeros(shape)
inputs = {'data': data}
expected = {'output': data + np.random.uniform(minval, maxval, shape)}
CorrectnessTest._compare_moments(builder.spec, inputs, expected)
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_random_uniform_dynamic_cpu(self):
minval, maxval, seed = 0., 1., 42
for rank in range(1, 6):
low_factor = np.random.randint(low=2, high=4)
low = int(np.power(1000, 1. / rank)) * low_factor
high = int(np.power(2000, 1. / rank)) * np.random.randint(low=low_factor, high=4)
shape = np.random.randint(low=low, high=high, size=rank)
input_features = [('shape', datatypes.Array(len(shape)))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
builder.add_random_uniform_dynamic(name='random_uniform_dynamic',
input_names=['shape'],
output_name='output',
minval=minval, maxval=maxval, seed=seed)
inputs = {'shape': np.array(shape, np.float)}
expected = {'output': np.random.uniform(minval, maxval, shape)}
CorrectnessTest._compare_moments(builder.spec, inputs, expected)
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_random_bernoulli_like_cpu(self):
prob, seed = 0.5, 42
for rank in range(1, 6):
low_factor = np.random.randint(low=2, high=4)
low = int(np.power(1000, 1. / rank)) * low_factor
high = int(np.power(2000, 1. / rank)) * np.random.randint(low=low_factor, high=4)
shape = np.random.randint(low=low, high=high, size=rank)
input_features = [('tensor', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
builder.add_random_bernoulli_like(name='random_bernoulli_like',
input_name='tensor',
output_name='output',
prob=prob, seed=seed)
tensor = np.random.rand(*shape)
inputs = {'tensor': tensor}
expected = {'output': np.random.binomial(1, prob, shape)}
CorrectnessTest._compare_moments(builder.spec, inputs, expected)
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_random_bernoulli_static_cpu(self):
prob, seed = 0.5, 42
for rank in range(1, 6):
low_factor = np.random.randint(low=2, high=4)
low = int(np.power(1000, 1. / rank)) * low_factor
high = int(np.power(2000, 1. / rank)) * np.random.randint(low=low_factor, high=4)
shape = np.random.randint(low=low, high=high, size=rank)
input_features = [('data', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
builder.add_random_bernoulli_static(name='random_bernoulli_static', output_name='tmp',
output_shape=list(shape), prob=prob, seed=seed)
builder.add_elementwise('add_layer', ['data', 'tmp'], 'output', mode='ADD')
data = np.zeros(shape)
inputs = {'data': data}
expected = {'output': data + np.random.binomial(1, prob, shape)}
CorrectnessTest._compare_moments(builder.spec, inputs, expected)
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_random_bernoulli_dynamic_cpu(self):
prob, seed = 0.5, 42
for rank in range(1, 6):
low_factor = np.random.randint(low=2, high=4)
low = int(np.power(1000, 1. / rank)) * low_factor
high = int(np.power(2000, 1. / rank)) * np.random.randint(low=low_factor, high=4)
shape = np.random.randint(low=low, high=high, size=rank)
input_features = [('shape', datatypes.Array(len(shape)))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
builder.add_random_bernoulli_dynamic(name='random_bernoulli_dynamic',
input_names=['shape'],
output_name='output',
prob=prob, seed=seed)
inputs = {'shape': np.array(shape, np.float)}
expected = {'output': np.random.binomial(1, prob, shape)}
CorrectnessTest._compare_moments(builder.spec, inputs, expected)
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_categorical_distribution_cpu_shapes(self):
for rank in range(1, 6):
shape = np.random.randint(low=2, high=8, size=rank)
num_samples = np.random.randint(low=10, high=1000)
input_features = [('data', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
builder.add_categorical_distribution(name='categorical_distribution',
input_name='data',
output_name='output',
num_samples=num_samples)
x = np.random.randint(low=0, high=20, size=shape).astype(np.float32)
inputs = {'data': x}
shape[-1] = num_samples
expected = {'output': np.random.rand(*shape)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True, validate_shapes_only=True)
def test_categorical_distribution_cpu_logits(self):
def softmax(data):
e_data = np.exp(data - np.max(data))
return e_data / e_data.sum()
num_samples, num_class = 50000, 10
input_name, output_name = 'data', 'output'
shapes = [(2, num_class), (2, 1, num_class), (1, 2, num_class),
(2, 1, 1, num_class), (1, 2, 1, num_class), (1, 1, 2, num_class),
(2, 1, 1, 1, num_class), (1, 2, 1, 1, num_class),
(1, 1, 2, 1, num_class), (1, 1, 1, 2, num_class)]
for shape in shapes:
input_features = [('data', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
builder.add_categorical_distribution(name='categorical_distribution',
input_name=input_name,
output_name=output_name,
num_samples=num_samples,
is_logits=True,
seed=42)
x = np.random.rand(*shape)
inputs = {input_name: x}
model = builder.spec
if isinstance(model, str):
model = coremltools.models.MLModel(model)
model = coremltools.models.MLModel(model, useCPUOnly=True)
prediction = model.predict(inputs, useCPUOnly=True)
# validate each distribution separately
logits = x.reshape(2, num_class)
probs = [softmax(logits[0]), softmax(logits[1])]
ref0 = np.random.multinomial(num_samples, probs[0])
ref1 = np.random.multinomial(num_samples, probs[1])
pre0 = prediction[output_name].reshape(2, num_samples)[0]
pre1 = prediction[output_name].reshape(2, num_samples)[1]
expected = {output_name: np.stack((pre0, pre1))}
# convert to bincount and validate probabilities
pre0 = np.bincount(np.array(pre0).astype(np.int), minlength=num_class)
pre1 = np.bincount(np.array(pre1).astype(np.int), minlength=num_class)
assert np.allclose(np.true_divide(pre0, num_samples), probs[0], atol=1e-2)
assert np.allclose(np.true_divide(pre0, num_samples),
np.true_divide(ref0, num_samples), atol=1e-2)
assert np.allclose(np.true_divide(pre1, num_samples), probs[1], atol=1e-2)
assert np.allclose(np.true_divide(pre1, num_samples),
np.true_divide(ref1, num_samples), atol=1e-2)
self._test_model(model, inputs, expected, useCPUOnly=True,
output_name_shape_dict={'output': prediction['output'].shape})
def test_categorical_distribution_cpu_probs(self):
def softmax(data):
e_data = np.exp(data - np.max(data))
return e_data / e_data.sum()
num_samples, num_class = 50000, 10
input_name, output_name = 'data', 'output'
shapes = [(2, num_class), (2, 1, num_class), (1, 2, num_class),
(2, 1, 1, num_class), (1, 2, 1, num_class), (1, 1, 2, num_class),
(2, 1, 1, 1, num_class), (1, 2, 1, 1, num_class),
(1, 1, 2, 1, num_class), (1, 1, 1, 2, num_class)]
for shape in shapes:
input_features = [('data', datatypes.Array(*shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)], disable_rank5_shape_mapping=True)
builder.add_categorical_distribution(name='categorical_distribution',
input_name=input_name,
output_name=output_name,
num_samples=num_samples,
is_logits=False,
seed=42)
x = np.random.rand(*shape)
probs = x.reshape(2, num_class)
probs[0], probs[1] = softmax(probs[0]), softmax(probs[1])
inputs = {input_name: np.reshape(probs, shape)}
model = builder.spec
if isinstance(model, str):
model = coremltools.models.MLModel(model)
model = coremltools.models.MLModel(model, useCPUOnly=True)
prediction = model.predict(inputs, useCPUOnly=True)
# validate each distribution separately
probs = probs.reshape(2, num_class)
ref0 = np.random.multinomial(num_samples, probs[0])
ref1 = np.random.multinomial(num_samples, probs[1])
pre0 = prediction[output_name].reshape(2, num_samples)[0]
pre1 = prediction[output_name].reshape(2, num_samples)[1]
expected = {output_name: np.stack((pre0, pre1))}
# convert to bincount and validate probabilities
pre0 = np.bincount(np.array(pre0).astype(np.int), minlength=num_class)
pre1 = np.bincount(np.array(pre1).astype(np.int), minlength=num_class)
assert np.allclose(np.true_divide(pre0, num_samples), probs[0], atol=1e-2)
assert np.allclose(np.true_divide(pre0, num_samples),
np.true_divide(ref0, num_samples), atol=1e-2)
assert np.allclose(np.true_divide(pre1, num_samples), probs[1], atol=1e-2)
assert np.allclose(np.true_divide(pre1, num_samples),
np.true_divide(ref1, num_samples), atol=1e-2)
self._test_model(model, inputs, expected, useCPUOnly=True,
output_name_shape_dict={'output': prediction['output'].shape})
def test_reverse_cpu(self):
for rank in range(1, 6):
for _ in range(20):
input_shape = np.random.randint(low=2, high=8, size=rank)
reverse_dim = [np.random.choice([True, False]) for _ in range(rank)]
axes = [i for i in range(rank) if reverse_dim[i] == True]
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True)
builder.add_reverse('reverse', 'data', 'output', reverse_dim)
x = np.random.rand(*input_shape)
input = {'data': x}
expected = {'output': np.flip(x, axis=axes)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_matrix_band_part_cpu(self):
for rank in range(2, 6):
for _ in range(20):
num_lower = np.random.randint(low=-7, high=8)
num_upper = np.random.randint(low=-7, high=8)
shape = np.random.randint(low=2, high=6, size=rank)
input_features = [('data', datatypes.Array(*shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features, disable_rank5_shape_mapping=True)
builder.add_matrix_band_part('matrix_band_part', 'data', 'output',
num_lower=num_lower, num_upper=num_upper)
x = np.random.rand(*shape)
input = {'data': x}
rows, cols = shape[-2:]
band = np.ones((rows, cols))
for m in range(rows):
for n in range(cols):
band[m, n] = (num_lower < 0 or (m - n) <= num_lower) and (num_upper < 0 or (n - m) <= num_upper)
expected = {'output': np.multiply(band, x)}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_flatten_to_2d_cpu(self):
for rank in range(1, 6):
for axis in range(-rank, rank + 1):
shape = np.random.randint(low=2, high=6, size=rank)
input_features = [('data', datatypes.Array(*shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features, disable_rank5_shape_mapping=True)
builder.add_flatten_to_2d('flatten_to_2d', 'data', 'output', axis=axis)
x = np.random.rand(*shape)
np_axis = axis + rank if axis < 0 else axis
pl, pr = 1, 1
for i in range(0, np_axis):
pl *= shape[i]
for i in range(np_axis, len(shape)):
pr *= shape[i]
new_shape = [pl, pr]
ref = x.reshape(new_shape)
input = {'data': x}
expected = {'output': ref}
self._test_model(builder.spec, input, expected, useCPUOnly=True)
def test_reshape_like_cpu(self):
for rank in range(1, 6):
for _ in range(20):
input_shape = np.random.randint(low=2, high=8, size=rank)
n = int(np.prod(input_shape))
divisors = [d for d in range(1, n) if n % d == 0]
target_rank = np.random.randint(low=2, high=6)
target_shape = [1]
for i in range(target_rank - 1):
dim_size = np.random.choice(divisors)
while n % (np.prod(target_shape) * dim_size) != 0:
dim_size = np.random.choice(divisors)
target_shape.append(dim_size)
target_shape[0] = n / np.prod(target_shape)
np.random.shuffle(target_shape)
input_features = [('data', datatypes.Array(*input_shape)),
('tensor', datatypes.Array(*target_shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
builder.add_reshape_like(name='reshape_like',
input_names=['data', 'tensor'],
output_name='output')
data = np.random.rand(*input_shape)
tensor = np.random.rand(*target_shape)
inputs = {'data': data, 'tensor': tensor}
expected = {'output': np.reshape(data, target_shape)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_reshape_static_cpu(self):
for rank in range(1, 6):
for _ in range(20):
input_shape = np.random.randint(low=2, high=8, size=rank)
n = int(np.prod(input_shape))
divisors = [d for d in range(1, n) if n % d == 0]
target_rank = np.random.randint(low=2, high=6)
target_shape = [1]
for i in range(target_rank - 1):
dim_size = np.random.choice(divisors)
while n % (np.prod(target_shape) * dim_size) != 0:
dim_size = np.random.choice(divisors)
target_shape.append(dim_size)
target_shape[0] = -1
np.random.shuffle(target_shape)
input_features = [('data', datatypes.Array(*input_shape))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
builder.add_reshape_static(name='reshape_static',
input_name='data',
output_name='output',
output_shape=target_shape)
data = np.random.rand(*input_shape)
inputs = {'data': data}
expected = {'output': np.reshape(data, target_shape)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_reshape_dynamic_cpu(self):
for rank in range(1, 6):
for _ in range(20):
input_shape = np.random.randint(low=2, high=8, size=rank)
n = int(np.prod(input_shape))
divisors = [d for d in range(1, n) if n % d == 0]
target_rank = np.random.randint(low=2, high=6)
target_shape = [1]
for i in range(target_rank - 1):
dim_size = np.random.choice(divisors)
while n % (np.prod(target_shape) * dim_size) != 0:
dim_size = np.random.choice(divisors)
target_shape.append(dim_size)
target_shape[0] = -1
np.random.shuffle(target_shape)
input_features = [('data', datatypes.Array(*input_shape)),
('shape', datatypes.Array(len(target_shape)))]
builder = neural_network.NeuralNetworkBuilder(
input_features, [('output', None)],
disable_rank5_shape_mapping=True)
builder.add_reshape_dynamic(name='reshape_dynamic',
input_names=['data', 'shape'],
output_name='output')
data = np.random.rand(*input_shape)
inputs = {'data': data, 'shape': np.array(target_shape, dtype='float')}
expected = {'output': np.reshape(data, target_shape)}
self._test_model(builder.spec, inputs, expected, useCPUOnly=True)
def test_reduce_sum_cpu(self):
for rank in range(1, 6):
axes_list = [axes for len in range(1, rank + 1) for axes in itertools.combinations(range(rank), len)]
axes_list.append(None)
for axes in axes_list:
if axes:
axes = tuple([axis if np.random.choice([True, False]) else axis - rank for axis in axes])
reduce_all = False
else:
reduce_all = True
for keep_dims in [True, False]:
input_shape = np.random.randint(low=2, high=5, size=rank)
input_features = [('data', datatypes.Array(*input_shape))]
output_features = [('output', None)]
builder = neural_network.NeuralNetworkBuilder(
input_features, output_features,
disable_rank5_shape_mapping=True
)
builder.add_reduce_sum('reduce', 'data', 'output', axes, keepdims=keep_dims, reduce_all=reduce_all)
x = | np.random.rand(*input_shape) | numpy.random.rand |
# !/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Defines unit tests for :mod:`colour.appearance.hunt` module.
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.appearance import Hunt_InductionFactors, XYZ_to_Hunt
from colour.appearance.tests.common import ColourAppearanceModelTest
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2014 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = '<EMAIL>'
__status__ = 'Production'
__all__ = ['TestHuntColourAppearanceModel']
class TestHuntColourAppearanceModel(ColourAppearanceModelTest):
"""
Defines :mod:`colour.appearance.hunt` module unit tests methods for
*Hunt* colour appearance model.
"""
FIXTURE_BASENAME = 'hunt.csv'
OUTPUT_ATTRIBUTES = {'J': 'J',
'C_94': 'C',
'h_S': 'h',
's': 's',
'Q': 'Q',
'M94': 'M'}
def output_specification_from_data(self, data):
"""
Returns the *Hunt* colour appearance model output specification
from given data.
Parameters
----------
data : list
Fixture data.
Returns
-------
Hunt_Specification
*Hunt* colour appearance model specification.
"""
XYZ = np.array([data['X'], data['Y'], data['Z']])
XYZ_w = | np.array([data['X_w'], data['Y_w'], data['Z_w']]) | numpy.array |
'''Meeus: Astronomical Algorithms (2nd ed.), chapter 15'''
import numpy as np
def rising(dec,lat):
'''local hour angle for rising (alt=0 deg) - without refraction'''
#type of output (same as input - number, list, numpy.array)
out_type='lst'
if (isinstance(dec,int) or isinstance(dec,float)) and (isinstance(lat,int) or isinstance(lat,float)):
#all input args are numbers
out_type='num'
if isinstance(dec,np.ndarray) or isinstance(lat,np.ndarray):
#numpy.array
out_type='np'
if isinstance(dec,list): dec=np.array(dec)
if isinstance(lat,list): lat=np.array(lat)
if out_type=='num': dec=np.array([dec])
dec=np.deg2rad(dec)
lat=np.deg2rad(lat)
ha=np.arccos(- | np.tan(lat) | numpy.tan |
import copy
import sys
sys.path.append('SetsClustering')
from multiprocessing import Process ,Manager
import numpy as np
import LinearProgrammingInTheDarkClassVersion as LPD
from multiprocessing import Pool
from jgrapht.algorithms.shortestpaths import johnson_allpairs
import jgrapht
from SetsClustering import Utils, PointSet, KMeansAlg
from SetsClustering import KMeansForSetsSensitivityBounder as SensBounder
from SetsClustering import Coreset as CS
from scipy.spatial.distance import cdist
import seaborn as sns
from copy import deepcopy
import itertools
from scipy.ndimage import convolve
from timeit import default_timer as timer
from tqdm import tqdm
import dill
import matplotlib
matplotlib.use('agg')
import matplotlib.pyplot as plt
import matplotlib.pylab as pl
from scipy.linalg import null_space
import scipy.ndimage as ndi
from scipy.spatial import ConvexHull
import argparse, os, pickle
from scipy.io import netcdf
POWER = 4
FORCE_NEIGHBORING = 20
import psutil
CPUS = psutil.cpu_count()
# import multiprocessing
# # from pathos.multiprocessing import ProcessingPool as Pool
# # from sklearn.externals.joblib import Parallel, delayed
# from multiprocessing import Process
parser = argparse.ArgumentParser(description='Initial Location Generator')
parser.add_argument('-d', type=str, default=None, help='Directory containing all maps')
parser.add_argument('-pp', default=False, action='store_true', help='preprocess map')
parser.add_argument('-ft', default='.nc', type=str, help='Type of map file')
parser.add_argument('-nf', default=1, type=int, help='Number of files describing a map of velocities')
parser.add_argument('-eps_g', default=None, type=float, help=r'resolution of the \varepsilon-grid')
parser.add_argument('-eps_b', default=0.08, type=float,
help=r'epsilon approximation for each of the patches of the currents')
parser.add_argument('-k', default=10, type=int, help='Desired number of drifters')
parser.add_argument('-bs', default=2, type=int, help='size of the blob prior to the clustering phase')
parser.add_argument('-coreset_sample_size', default=1000, type=int,
help='The size of the coreset for the clustering phase')
parser.add_argument('-time', default=False, action='store_true', help='Apply our system over time')
parser.add_argument('-tol', default=0.2, type=float, help='Tolerance for minimum volume ellipsoid')
parser.add_argument('-resume', default=False, action='store_true', help='In case of code being killed, you can resume from last map')
parser.add_argument('-show', default=False, action='store_true', help='Show only our segementation and clustering. Must have preporcessed these data before')
class bcolors:
HEADER = '\033[95m'
OKBLUE = '\033[94m'
OKCYAN = '\033[96m'
OKGREEN = '\033[92m'
WARNING = '\033[93m'
FAIL = '\033[91m'
ENDC = '\033[0m'
BOLD = '\033[1m'
UNDERLINE = '\033[4m'
NORMAL = '\033[0m'
plt.rcParams.update({'font.size': 16})
manager = Manager()
def removeInclusionsJob(lst, ids, path_str):
global resdict
for i in range(len(lst)):
resdict[ids[i]] = True
if lst[i] in path_str:
resdict[ids[i]] = False
def removeInclusions(unified_paths, file_path='', file_prefix=''):
global manager
global resdict
global A
unified_paths_strings = [str(x[0]).strip('[]') for x in unified_paths]
unified_paths_strings.sort(key=(lambda x: len(x.split(','))))
lst = [list(grp) for i, grp in itertools.groupby(unified_paths_strings, key=(lambda x: len(x.split(','))))]
sizes = np.cumsum([len(x) for x in lst])
unique_ids = [list(range(sizes[i-1], sizes[i]) if i > 0 else range(sizes[i])) for i in range(len(sizes))]
if len(unified_paths_strings) > 10000:
with Manager() as manager:
proc_list = []
resdict = manager.dict()
for i, item in enumerate(lst):
if i != (len(lst) - 1):
proc_list.append(
Process(target=removeInclusionsJob,
args=(item, unique_ids[i], '\n'.join(unified_paths_strings[sizes[i]:])))
)
proc_list[-1].start()
for proc in proc_list:
proc.join()
mask = [x[1] for x in resdict.items()]
else:
resdict = dict()
for i, item in enumerate(lst):
if i != (len(lst) - 1):
removeInclusionsJob(item, unique_ids[i], '\n'.join(unified_paths_strings[sizes[i]:]))
mask = [x[1] for x in resdict.items()]
mask.extend([True for _ in range(len(lst[-1]))])
np.save('{}mask_unified_paths_{}.npy'.format(file_path, file_prefix), mask)
return [[int(y) for y in x.split(', ')] for x in list(itertools.compress(unified_paths_strings, mask))]
def removeDuplicates(list_1):
list2 = list(set(list_1))
list2.sort(key=list_1.index)
return list2
def makedir(dir_path):
try:
os.mkdir(dir_path)
except OSError as error:
print(error)
def saveVels(data, file_path, smoothed=True):
if smoothed:
file_path += 'Smoothed_Vel/'
else:
file_path += 'Original_Vel/'
makedir(file_path)
temp = np.tile(data[:, :, 0][:, :, np.newaxis], 10)
temp.dump(file_path + 'matrix_vel_x.dat')
temp = np.tile(data[:, :, 1][:, :, np.newaxis], 10)
temp.dump(file_path + 'matrix_vel_y.dat')
def readNetCDFFile(file_path, over_time):
file2read = netcdf.NetCDFFile(file_path, 'r')
U = file2read.variables['u'].data # velocity in x-axis
V = file2read.variables['v'].data # velocity in y-axis
mask = np.logical_and(np.abs(U) <= 1e3, np.abs(V) <= 1e3)
V = np.multiply(V, mask)
U = np.multiply(U, mask)
if not over_time:
U = U[0, :, :, :]
V = V[0, :, :, :]
return U,V
def innerFunction(current_possible_combs, unique_keys):
global resdict
for i, element in enumerate(current_possible_combs):
resdict[unique_keys[i]] = (removeDuplicates(element[0][0] + element[1][0]), element[0][1] + element[1][1])
def getAllPossiblePaths(list1, list2):
global CPUS
global manager
global resdict
if len(list1) * len(list2) > 10000:
manager = Manager()
resdict = manager.dict()
all_possible_combs = np.array_split(list(itertools.product(list1, list2)), CPUS)
unique_ids = np.array_split(np.arange(sum([x.size for x in all_possible_combs])), CPUS)
proc_list = []
for i, item in enumerate(all_possible_combs):
proc_list.append(
Process(target=innerFunction, args=(item, unique_ids[i]))
)
proc_list[-1].start()
for proc in proc_list:
proc.join()
temp = list(resdict.values())
else:
temp = []
for element in itertools.product(list1, list2):
temp.append((removeDuplicates(element[0][0] + element[1][0]), element[0][1] + element[1][1]))
return temp
class CurrentEstimation(object):
def __init__(self, grid, k=10, epsilon_grid=0.06, tolerance=0.001, epsilon_body=2, is_grid=True, is_data_vectorized=True,
blob_size=3, sens_file_name='sens.npz', coreset_sample_size = int(1e3), save_mode=True,
matrix_of_velocities=True, save_path='', file_prefix='', show=False, verbose=False):
self.grid = grid
self.is_grid=is_grid
self.d = (self.grid.ndim - 1) if matrix_of_velocities else self.grid.ndim
self.epsilon_grid = epsilon_grid
self.epsilon_body = epsilon_body
self.tolerance = tolerance
self.g = jgrapht.create_graph(directed=True)
self.cost_func = (lambda x: self.grid[tuple(x.astype("int") if is_grid else x)]) # create a simple membership cost function
self.iocsAlg = None
self.segments = []
self.eps_star = None
self.bodies = []
self.full_bodies = []
self.is_data_vectorized = is_data_vectorized
self.k = k
self.blob_size = blob_size
self.coreset_sample_size = coreset_sample_size
self.save_mode = save_mode
self.binary_grid = None
self.matrix_of_velocities = matrix_of_velocities
self.sens_file_name = sens_file_name
self.ellipsoids = []
self.convex_hulls = []
self.verbose = verbose
self.save_path = save_path
self.file_prefix = file_prefix
self.show = show
def polynomialGridSearchParallelizedVersion(self):
with Pool() as pool:
pass
def checkIfContained(self, point):
for i,body in enumerate((self.full_bodies if self.epsilon_body == 0 else self.bodies)):
if body.ndim > 1:
temp_in_body = np.equal(body, point).all(1).any()
temp_in_CH = False
if self.convex_hulls[i] is not None:
temp_in_CH = np.all(self.convex_hulls[i][:,:-1].dot(point) <= -self.convex_hulls[i][:,-1])
if temp_in_body or temp_in_CH:
return True
else:
if np.linalg.norm(body - point) == 0:
return True
return False
def IOCS(self, p):
cost_func = lambda x: 0.85 <= np.dot(np.nan_to_num(self.grid[tuple(p)]/np.linalg.norm(self.grid[tuple(p)])),
np.nan_to_num(self.grid[tuple(x)]/np.linalg.norm(self.grid[tuple(x)]))) \
<= 1 and 0.5 <= np.linalg.norm(self.grid[tuple(p)])/np.linalg.norm(self.grid[tuple(x)]) <= 2
self.iocsAlg = LPD.LinearProgrammingInTheDark(P=self.grid,cost_func=cost_func, point=p,
d=self.d, epsilon=self.tolerance, hull_hyper=None,
matrix_of_vecs=True)
if self.iocsAlg.lower_d <= 1:
if self.iocsAlg.lower_d == 0:
self.bodies.append(p)
self.full_bodies.append(p)
self.ellipsoids.append(None)
self.convex_hulls.append(None)
else:
idxs = np.where(self.iocsAlg.oracle.flattened_data == 1)[0]
Z = np.empty((idxs.shape[0], p.shape[0]))
Z[:, self.iocsAlg.irrelevant_dims] = p[self.iocsAlg.irrelevant_dims]
Z[:, self.iocsAlg.dims_to_keep[0]] = \
np.arange(*(self.iocsAlg.oracle.bounding_box[self.iocsAlg.dims_to_keep].flatten() +
np.array([0, 1])).tolist())[idxs]
self.bodies.append(Z)
self.full_bodies.append(Z)
self.ellipsoids.append(None)
self.convex_hulls.append(None)
elif self.iocsAlg.get_all_points:
idxs = np.where(self.iocsAlg.oracle.flattened_data == 1)[0]
Z = self.iocsAlg.oracle.coordinates[:-1, idxs].T
self.bodies.append(Z)
self.full_bodies.append(Z)
self.ellipsoids.append(None)
self.convex_hulls.append(None)
else:
self.ellipsoids.append(self.iocsAlg.computeAMVEE() + (p, ))
if self.epsilon_body > 0:
s = timer()
self.approximateBody(self.ellipsoids[-1][0][-1], self.ellipsoids[-1][0][-2],
idx_dims_retrieve=self.ellipsoids[-1][-3], dims_value=self.ellipsoids[-1][-1],
rest_dims=self.ellipsoids[-1][-2])
else:
self.attainWholeBody(self.ellipsoids[-1][0][-1], self.ellipsoids[-1][0][-2],
idx_dims_retrieve=self.ellipsoids[-1][-3], dims_value=self.ellipsoids[-1][-1],
rest_dims=self.ellipsoids[-1][-2])
def polynomialGridSearch(self):
dims = list(self.grid.shape[:-1] if self.matrix_of_velocities else self.grid.shape)
for i in range(len(dims)):
dims[i] = np.arange(0, dims[i], int(np.round(dims[i] * self.epsilon_grid)))
try:
X = np.array( | np.meshgrid(*dims) | numpy.meshgrid |
import pandas as pd
import numpy as np
def split_line():
print('--------------------')
print('创建 Series')
s = pd.Series([1, 2, 3, 4, np.nan, 6, 7])
print(s)
split_line()
print('创建日期 DataFrame')
dates = pd.date_range('20200314', periods=6)
print(dates)
split_line()
print('通过 numpy 创建 DataFrame')
df = pd.DataFrame(np.random.randn(6, 4), index=dates, columns=list('ABCD'))
print(df)
split_line()
print('通过 dict 创建 DataFrame')
df2 = pd.DataFrame({ 'A' : 1.,
'B' : pd.Timestamp('20130102'),
'C' : pd.Series(1,index=list(range(4)),dtype='float32'),
'D' : np.array([3]*4,dtype='int32'),
'E' : pd.Categorical(["test","train","test","train"]),
'F' : 'foo' })
print(df2)
print(df2.dtypes)
split_line()
print('查看头部几行')
print(df.head())
print('查看尾部几行')
print(df.tail())
split_line()
print('显示索引、列名及底层 numpy 数据')
print(df.index)
print(df.columns)
print(df.values)
split_line()
print('对数据进行快读统计')
print(df.describe())
split_line()
print('对数据进行转置')
print(df.T)
split_line()
print('按照列名排序')
print(df.sort_index(axis=1, ascending=False))
split_line()
print('按照某一列的值进行排序')
print(df.sort_values(by='B'))
split_line()
print('虽然标准的Python/Numpy的表达式能完成选择与赋值等功能，但我们仍推荐使用优化过的pandas数据访问方法：.at，.iat，.loc，.iloc和.ix')
print('')
print('选择某一列数据，返回 Series')
print(df['A'])
print('使用 [] 切片')
print(df[0:3])
split_line()
print('通过标签选取')
print(df.loc[dates[0]])
print('选取多列')
print(df.loc[:, ['A', 'C']])
print('行列同时选择')
print(df.loc['2020-03-14': '2020-03-16', ['A', 'C']])
print('快速获取某个值')
print(df.at[dates[0], 'D'])
split_line()
print('通过位置选取，直接传递整型')
print(df.iloc[3])
print('行列同时选择')
print(df.iloc[3:5, 0:2])
print('只选取行')
print(df.iloc[1:3, :])
print('只选取列')
print(df.iloc[:, 1:3])
print('取具体的值（两种方法）')
print(df.iloc[2,1], df.iat[2, 1])
split_line()
print('通过布尔索引取值，即通过判断过滤')
print('选取 A 列 >0')
print(df[df.A > 0])
print('选取 >0，小于 0 的会变成 NaN')
print(df[df > 0])
print('通过 isin() 过滤数据，主要针对字符串')
df2 = df.copy()
df2['E'] = ['one', 'one', 'two', 'three', 'four', 'three']
print('before', df2)
print('after', df2[df2['E'].isin(['one', 'two'])])
split_line()
print('赋值一个新的列，通过索引来自动对齐数据')
s1 = pd.Series([1,2,3,4,5], index=pd.date_range('20200314',periods=5))
print(s1)
df['F'] = s1
print(df)
print('通过标签赋值')
df.at[dates[0], 'A'] = 0
print(df)
print('通过位置赋值')
df.iat[0, 1] = 0
print('通过 numpy 赋值')
df.loc[:, 'D'] = np.array([5]*len(df))
print(df)
print('通过 where 赋值')
df2 = df.copy()
df2[df2 > 0] = -df2
print(df2)
split_line()
print('缺失值处理，在pandas中，用np.nan来代表缺失值，这些值默认不会参与运算')
df1 = df.reindex(index=dates[0:4], columns=list(df.columns)+['E'])
df1.loc[dates[0]:dates[1],'E'] = 1
print(df1)
print('删除所有包含缺失值的行数据')
print(df1.dropna(how='any'))
print('填充缺失值')
print(df1.fillna(value=5))
print('获取值是否为nan的布尔标记')
print(pd.isnull(df1))
split_line()
print('按列求平均')
print(df.mean())
print('按行求平均')
print(df.mean(1))
split_line()
print('apply 函数默认会按列进行运算')
print('apply 按列累加')
print('before', df)
print('after', df.apply(np.cumsum))
print('apply 找到每列的差值')
print(df.apply(lambda x:x.max() - x.min()))
split_line()
print('频数统计')
s = pd.Series(np.random.randint(0, 7, size=10))
print('origin data', s)
print(s.value_counts())
split_line()
print('处理字符串')
s = pd.Series(['A', 'B', 'C', 'Aaba', 'Baca', np.nan, 'CABA', 'dog', 'cat'])
print('before', s)
print('after', s.str.lower())
split_line()
print('连接 Series，DataFrame 和 Panel 对象')
df = pd.DataFrame(np.random.randn(10,4))
print(df)
print('拆分成不同元素')
pieces = [df[:3], df[3:7], df[7:]]
print(pieces[0])
print('再合并起来')
print(pd.concat(pieces))
split_line()
print('Join 操作')
left = pd.DataFrame({'key':['foo', 'foo'], 'lval':[1,2]})
right = pd.DataFrame({'key':['bar', 'foo'], 'lval':[4,5]})
print('left', left)
print('right', right)
print('merge', pd.merge(left, right, on='key'))
split_line()
print('添加行到 DataFrame 后面')
df = pd.DataFrame(np.random.randn(8, 4), columns=['A', 'B', 'C', 'D'])
print('before', df)
s = df.iloc[3]
print('after', df.append(s, ignore_index=True))
split_line()
print('分组操作，针对每组进行不同的计算，最后合并到某一个数据结构')
df = pd.DataFrame({'A' : ['foo', 'bar', 'foo', 'bar',
'foo', 'bar', 'foo', 'bar'],
'B' : ['one', 'one', 'two', 'three',
'two', 'two', 'one', 'three'],
'C' : np.random.randn(8),
'D' : np.random.randn(8)})
print(df)
print('对 A 列进行 group by')
print(df.groupby('A').sum())
print('对 A 和 B 列进行 group by')
print(df.groupby(['A', 'B']).sum())
split_line()
print('数据透视表')
df = pd.DataFrame({'A' : ['one', 'one', 'two', 'three'] * 3,
'B' : ['A', 'B', 'C'] * 4,
'C' : ['foo', 'foo', 'foo', 'bar', 'bar', 'bar'] * 2,
'D' : np.random.randn(12),
'E' : | np.random.randn(12) | numpy.random.randn |
#! python3
# coding: utf-8
# * =====================================================================================
# *
# * Filename: AMT_final.py
# *
# * Description: Python program for AMT2018 final thesis
# *
# * Version: 1.0
# * Created: 06/07/2018 07:09:10 PM
# * Revision: none
# * Interpreter: Python3.6
# *
# * Author: <NAME>, <EMAIL>
# * Organization: Tinjin University
# *
# * =====================================================================================
#
#THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
#IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
#FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
#AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
#LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
#OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
#THE SOFTWARE.
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
from scipy.fftpack import fft
import math_tool
def polyfunc(r, theta):
# description: Definition of the Zernike polynomial. Takes in r and theta, which is
# the position based on cylindrical coordinate (CC), returns Z value on that
# position, just like the literal function do.
# param: r, theta
# return: sum, which represents the value of Z
ci = np.array([0 ,0, 0, 0, 1.205834, 1.209232, -0.073527,
0.283878, -0.047157, 0.69305, 0.0821, -0.520752,
-0.054379, -0.092302, 0.02262, -0.009395], dtype=np.double)
zi = np.array([1, r*np.cos(theta), r*np.sin(theta), 2*r**2-1,
r**2*np.cos(2*theta), r**2*np.sin(2*theta),
(3*r**2-2)*r*np.cos(theta), (3*r**2-2)*r*np.sin(theta),
6*r**4-6*r**2+1, r**3*np.cos(3*theta),
r**3*np.sin(3*theta), (4*r**2-3)*r**2*np.cos(2*theta),
(4*r**2-3)*r**2*np.sin(2*theta),
(10*r**4-12*r**2+3)*r*np.cos(theta),
(10*r**4-12*r**2+3)*r*np.sin(theta),
20*r**6-30*r**4+12*r**2-1], dtype = np.double)
sum = 0
for i in np.arange(0, np.shape(ci)[0]):
sum = sum+ci[i]*zi[i]
return sum
def rot(r, theta):
# description: Definition of the conical section. Similar to polyfunc
# param: r, theta
# return: result, which represents the value of Z
c = 1/594.51107
k = 0
numerator = c*r**2
denominator = 1+(1-(1+k)*c**2*r**2)**0.5
result = numerator/denominator
return result
def zfunc(r, theta):
# description: Definition of the surface shape function. This function
# is a combination of polyfunc and rot. Meanwhile, normalization
# for r is processed.
# param: r, theta
# return: result, which represents the value of Z
result = polyfunc(r/200, theta)+rot(r, theta)
return result
def rtheta2xy(func, x, y):
# description: Takes a combination of x and y (under rectangular coordinates)(RC),
# and gives the Z value of a function which takes cylindrical
# coordinate (CC) at that point.
# param: x, y: coordinate in rectangular coordinates (RC).
# return: result, which represents the value of Z
r = (x**2+y**2)**0.5
if x > 0:
theta = np.arctan(y/x)
elif x < 0:
theta = np.arctan(y/x)+np.pi
else:
if y>=0:
theta = np.pi/2
else:
theta = -np.pi/2
result = func(r, theta)
return result
def get_rad_seq(rtfunc, r, N):
# description: For a given function in cylindrical coordinate (CC), generate a
# sample sequence of Z value on a specific circle with radius r.
# param: rtfunc: the target function which is based on CC
# r: radius of the circle
# N: number of sample points
# return: result, which is a generated sequence with length N
result = np.zeros(N)
vtheta = np.linspace(0, 2*np.pi, N)
for i in np.arange(0, N):
result[i] = rtfunc(r, vtheta[i])
return result
def get_rad_fft(rtfunc, r, N, T, with_column_zero=1, abs = 1):
# description: Generate a FFT sequence for a given function (CC).
# param: rtfunc: the target function which is based on CC
# r: radius of the circle
# N: number of sample points
# T: sample spacing
# with_column_zero: controls whether the FFT sequence will
# have 0th term, 1 (by default)
# represents yes, 0 represents no
# return: xf: frequency scale
# yf: amplitude scale
if (with_column_zero==1):
x = np.linspace(0.0, N*T, N)
y = get_rad_seq(rtfunc, r, N)
yf_complex = fft(y)
if (abs==1):
yf = 1.0/N * np.abs(yf_complex)
else:
yf = 1.0/N * yf_complex
xf = np.linspace(0.0, 1.0/T-1, N)
return xf, yf
elif (with_column_zero==0):
x = np.linspace(0.0, N*T, N)
y = get_rad_seq(rtfunc, r, N)
yf_complex = fft(y)[1:]
# yf = 1.0/N * np.abs(yf_complex)
if (abs==1):
yf = 1.0/N * np.abs(yf_complex)
else:
yf = 1.0/N * yf_complex
xf = np.linspace(0.0, 1.0/T-1, N)[1:]
return xf, yf
def get_average_mean(func, r):
# description: Calculate the mean z value at a certain r for a given function (CC).
# param: func: the target function which is based on CC
# r: radius of the circle
# return: result: z value for given r and func
count = 50
scale = np.linspace(0, 2*np.pi, count)
samples = np.zeros(count)
for i in np.arange(0, count):
samples[i] = func(r, scale[i])
# print(samples)
result = np.mean(samples)
return result
def get_average_fft(func, r):
# description: Calculate the mean z value at a certain r for a given function (CC)
# using the 2nd method: Process FFT, then pick up the zeroth term
# NOTE:######################critical############################
# THERE MIGHT BE SOMETHING WRONG WITH THIS METHOD, USE "get_average" INSTEAD!!!!!
# BECAUSE "get_rad_fft" RETURNS COMPLEX, THE RESULT IS NOT RELIABLE.
# param: func: the target function which is based on CC
# return: func_out: function that represents the rot composition,
# whose input and output are similar to that of zfunc
xf, yf = get_rad_fft(func, r, 50, 1.0/50.0, with_column_zero=1, abs=0)
result = yf[0]
return result
def get_rot_part(func):
# description: Get the rotation part in a given surface shape function
# param: func: the target function which is based on CC
# return: func_out: function that represents the rot composition,
# whose input and output are similar to that of zfunc
def func_out(r, theta):
# return get_average_fft(func, r)
return get_average_mean(func, r)
return func_out
def get_nonrot_part(func):
# description: Get the non-rotation part in a given surface shape function,
# similar to get_rot_part
# param: func: the target function which is based on CC
# return: func_out: function that represents the non-rot composition,
# whose input and output are similar to that of zfunc
rot_part = get_rot_part(func)
def func_out(r, theta):
value = func(r, theta)-rot_part(r, theta)
return value
return func_out
def tool_rad_compensate(func, r_tool):
# description: decorate func to output a compensated surface shape function
# param: func: the target function which is based on CC
# r_tool: radius of lathe tool
# return: func_out: function that represents the compensated surface shape
# function whose input and output are similar to that of zfunc
def func_out(r, theta):
def f(x):
val = func(x, theta)
return val
df = math_tool.deriv_func(f)
def diff_var_g(x):
val = x - r_tool*df(x)/np.sqrt(1+df(x)**2)-r
return val
x = math_tool.solve_newton_method(diff_var_g, r)
result = f(x)-r_tool/np.sqrt(1+df(x)**2)
return result
return func_out
def plot_surface(func ,edge_r=15, title_sub='NO TITLE'):
X=np.linspace(-edge_r, edge_r, 2*2*int(edge_r)+1)
Y=np.linspace(-edge_r, edge_r, 2*2*int(edge_r)+1)
#X, Y represent all possible values in the coordinate
#using all possible values in linspace object to map all possible points
X,Y= | np.meshgrid(X,Y) | numpy.meshgrid |
"""Script for sampling COV, burstiness and memory coeficient, and
their uncertainties, on many faults and plotting them
<NAME>
University of Otago
2020
"""
import os, sys
import ast
from glob import glob
from operator import itemgetter
from re import finditer
import numpy as np
from scipy.optimize import curve_fit
from scipy.odr import Model, RealData, ODR
import scipy.odr.odrpack as odrpack
from scipy.stats import expon, gamma, weibull_min, ks_2samp, kstest
# !!! Dangerous hack to swap Weibull for gamma
#from scipy.stats import weibull_min as gamma #
# !!!
from matplotlib import pyplot
from matplotlib.patches import PathPatch
import matplotlib.gridspec as gridspec
from matplotlib.ticker import FormatStrFormatter
from scipy.stats import binom, kde
from adjustText import adjust_text
from QuakeRates.dataman.event_dates import EventSet
from QuakeRates.dataman.parse_oxcal import parse_oxcal
from QuakeRates.dataman.parse_age_sigma import parse_age_sigma
from QuakeRates.dataman.parse_params import parse_param_file, \
get_event_sets, file_len
from QuakeRates.utilities.bilinear import bilinear_reg_zero_slope, \
bilinear_reg_fix, bilinear_reg_fix_zero_slope
from QuakeRates.utilities.memory_coefficient import burstiness, memory_coefficient
filepath = '../params'
param_file_list = glob(os.path.join(filepath, '*.txt'))
param_file_list_NZ = ['Akatore_TaylorSilva_2019.txt',
'AlpineHokuriCk_Berryman_2012_simple.txt',
'AlpineSouthWestland_Cochran_2017_simple.txt',
'AwatereEast_Nicol_2016_simple.txt',
'ClarenceEast_Nicol_2016_simple.txt',
'CloudyFault_Nicol_2016_simple.txt',
'Dunstan_GNS_unpub_simple.txt',
'HopeConway_Hatem_2019_simple.txt',
'Hope_Khajavi_2016_simple.txt',
'Ihaia_Nicol_2016_simple.txt',
'Oaonui_Nicol_2016_simple.txt',
'Ohariu_Nicol_2016_simple.txt',
'Paeroa_Nicol_2016_simple.txt',
'Pihama_Nicol_2016_simple.txt',
'PortersPassEast_Nicol_2016_simple.txt',
'Ngakuru_Nicol_2016_simple.txt',
'Mangatete_Nicol_2016_simple.txt',
'Rangipo_Nicol_2016_simple.txt',
'Rotoitipakau_Nicol_2016_simple.txt',
'Rotohauhau_Nicol_2016_simple.txt',
'Snowden_Nicol_2016_simple.txt',
'Vernon_Nicol_2016_simple.txt',
'WairarapaSouth_Nicol_2016_simple.txt',
'Wairau_Nicol_2018_simple.txt',
'Waimana_Nicol_2016_simple.txt',
'Wellington_Langridge_2011_simple.txt',
'Waitangi_GNS_unpub_simple.txt',
'Whakatane_Nicol_2016_simple.txt',
'Whirinaki_Nicol_2016_simple.txt']
# List of faults in study by Williams et al 2019
# Note this is not entirely the same, as there are some records from
# that study that are not included in ours.
param_file_list_W = ['AlpineHokuriCk_Berryman_2012_simple.txt',
'HaywardTysons_Lienkaemper_2007_simple.txt',
'SanJacintoMysticLake_Onderdonk_2018_simple.txt',
'NorthAnatolianElmacik_Fraser_2010_simple.txt',
'SanAndreasWrightwood_Weldon_2004_simple.txt',
'SanAndreasCarizzo_Akciz_2010_simple.txt',
'SanJacintoHogLake_Rockwell_2015_simple.txt',
'SanAndreasMissionCk_Fumal_2002_simple.txt',
'SanAndreasPalletCk_Scharer_2011_simple.txt',
'Xorkoli_Altyn_Tagh_Yuan_2018.txt',
'NorthAnatolianYaylabeli_Kozaci_2011_simple.txt',
'ElsinoreTemecula_Vaughan_1999_simple.txt',
'DeadSeaJordan_Ferry_2011_simple.txt',
'SanAndreasBigBend_Scharer_2017_simple.txt',
'WasatchBrigham_McCalpin_1996_simple.txt',
'Irpinia_Pantosti_1993_simple.txt',
'WasatchWeber_Duross_2011_simple.txt',
'WasatchNilphi_Duross_2017_simple.txt',
'LomaBlanca_Williams_2017_simple.txt',
'AlaskaPWSCopper_Plafker_1994_simple.txt',
'NankaiTrough_Hori_2004_simple.txt',
'CascadiaNth_Adams_1994_simple.txt',
'CascadiaSth_Goldfinger_2003_simple.txt',
'JavonCanyon_SarnaWojicki_1987_simple.txt',
'NewGuinea_Ota_1996_simple.txt',
'ChileMargin_Moernaut_2018_simple.txt']
#param_file_list = []
#for f in param_file_list_NZ:
#for f in param_file_list_W:
# param_file_list.append(os.path.join(filepath, f))
n_samples = 10000 # Number of Monte Carlo samples of the eq chronologies
half_n = int(n_samples/2)
print(half_n)
annotate_plots = False # If True, lable each fault on the plot
plot_folder = './plots'
if not os.path.exists(plot_folder):
os.makedirs(plot_folder)
# Define subset to take
#faulting_styles = ['Reverse']
#faulting_styles = ['Normal']
#faulting_styles = ['Strike_slip']
faulting_styles = ['all']
tectonic_regions = ['all']
#tectonic_regions = ['Intraplate_noncratonic', 'Intraplate_cratonic', 'Near_plate_boundary']
#tectonic_regions = ['Plate_boundary_master', 'Plate_boundary_network']
#tectonic_regions = ['Plate_boundary_network', 'Near_plate_boundary']
#tectonic_regions = ['Plate_boundary_master']
#tectonic_regions = ['Subduction']
#tectonic_regions = ['Near_plate_boundary']
min_number_events = 5 # Use for all other calculations.
min_num_events_mem = 6 # Use for memory coefficient
#Summarise for comment to add to figure filename
fig_comment = ''
#fig_comment = 'NZ_examples_'
#fig_comment = 'Williams2019_'
for f in faulting_styles:
fig_comment += f
fig_comment += '_'
for t in tectonic_regions:
fig_comment += t
fig_comment += '_'
fig_comment += str(min_number_events)
#fig_comment += 'test_add_event_data'
def piecewise_linear(x, x0, y0, k1, k2):
return np.piecewise(x, [x < x0], [lambda x:k1*x + y0-k1*x0, lambda x:k2*x + y0-k2*x0])
def camel_case_split(identifier):
matches = finditer('.+?(?:(?<=[a-z])(?=[A-Z])|(?<=[A-Z])(?=[A-Z][a-z])|$)', identifier)
return [m.group(0) for m in matches]
plot_colours = []
all_ie_times = []
added_events = [] # Store names of records where we've added an event due to
# exceptionally long current open interval
covs = []
cov_bounds = []
burstinesses = []
burstiness_bounds = []
burstiness_stds = []
burstinesses_expon = []
burstinesses_gamma = []
ie_gamma_alpha = []
memory_coefficients = []
memory_bounds = []
memory_stds = []
memory_spearman_coefficients = []
memory_spearman_bounds = []
memory_spearman_lag2_coef = []
memory_spearman_lag2_bounds = []
long_term_rates = []
long_term_rate_stds = []
slip_rates = []
slip_rate_stds = []
slip_rate_bounds = []
max_interevent_times = []
min_interevent_times = []
min_paired_interevent_times = []
std_min_paired_interevent_times = []
std_min_interevent_times = []
std_max_interevent_times = []
max_interevent_times_bounds = []
min_interevent_times_bounds = []
min_paired_interevent_times_bounds = []
ratio_min_pair_max = []
ratio_min_max = []
std_ratio_min_pair_max = []
std_ratio_min_max = []
ratio_min_pair_max_bounds =[]
ratio_min_max_bounds = []
names, event_sets, event_certainties, num_events, tect_regions, fault_styles = \
get_event_sets(param_file_list, tectonic_regions,
faulting_styles, min_number_events)
references = []
# Get citations for each dataset from filename
for s in param_file_list:
sp = s.split('_')
if sp[0].split('/')[2] in names:
references.append(sp[1] + ' ' + sp[2])
n_faults = len(names)
print('Number of faults', n_faults)
for i, event_set in enumerate(event_sets):
# Handle cases with uncertain number of events. Where events identification is
# unsure, event_certainty is given a value of 0, compared with 1 for certain
# events
# First generate chronologies assuming all events are certain
# event_set.name = names[i]
event_set.gen_chronologies(n_samples, observation_end=2020, min_separation=1)
event_set.calculate_cov()
event_set.cov_density()
event_set.memory_coefficient()
event_set.memory_spearman_rank_correlation()
# Store all inter-event times for global statistics
all_ie_times.append(event_set.interevent_times)
# Now calculate some statistics on the sampled chronologies
event_set.basic_chronology_stats()
# Plot histogram of interevent times
figfile = os.path.join(plot_folder, ('interevent_times_%s.png' % names[i]))
event_set.plot_interevent_time_hist(fig_filename=figfile)
# Fit gamma distirbution to event set data
event_set.fit_gamma()
ie_gamma_alpha.append(event_set.mean_gamma_alpha_all) # Get mean estimate of alpha
min_paired_interevent_times.append(event_set.mean_minimum_pair_interevent_time)
max_interevent_times.append(event_set.mean_maximum_interevent_time)
min_interevent_times.append(event_set.mean_minimum_interevent_time)
std_min_paired_interevent_times.append(event_set.std_minimum_pair_interevent_time)
std_min_interevent_times.append(event_set.std_minimum_interevent_time)
std_max_interevent_times.append(event_set.std_maximum_interevent_time)
if event_set.std_maximum_interevent_time == 0:
print('Zero std_maximum_interevent_time for ', names[i])
slip_rates.append(event_set.slip_rates[0])
slip_rate_bounds.append([event_set.slip_rates[1], event_set.slip_rates[2]])
slip_rate_stds.append(abs(np.log10(event_set.slip_rates[2]) - \
np.log10(event_set.slip_rates[1]))/4) # Approx from 95% intervals
max_interevent_times_bounds.append([abs(event_set.mean_maximum_interevent_time -
event_set.maximum_interevent_time_lb),
abs(event_set.mean_maximum_interevent_time -
event_set.maximum_interevent_time_ub)])
min_interevent_times_bounds.append([abs(event_set.mean_minimum_interevent_time -
event_set.minimum_interevent_time_lb),
abs(event_set.mean_minimum_interevent_time -
event_set.minimum_interevent_time_ub)])
min_paired_interevent_times_bounds.append([abs(event_set.mean_minimum_pair_interevent_time -
event_set.minimum_pair_interevent_time_lb),
abs(event_set.mean_minimum_pair_interevent_time -
event_set.minimum_pair_interevent_time_ub)])
ratio_min_pair_max.append(event_set.mean_ratio_min_pair_max)
ratio_min_max.append(event_set.mean_ratio_min_max)
std_ratio_min_pair_max.append(event_set.std_ratio_min_pair_max)
std_ratio_min_max.append(event_set.std_ratio_min_max)
ratio_min_pair_max_bounds.append([abs(event_set.mean_ratio_min_pair_max -
event_set.ratio_min_pair_max_lb),
abs(event_set.mean_ratio_min_pair_max -
event_set.ratio_min_pair_max_ub)])
ratio_min_max_bounds.append([abs(event_set.mean_ratio_min_max -
event_set.ratio_min_max_lb),
abs(event_set.mean_ratio_min_max -
event_set.ratio_min_max_ub)])
# Generate random exponentially and gamma distributed samples of length num_events - 1
# i.e. the number of inter-event times in the chronology. These will be used
# later for testing
scale = 100 # Fix scale, as burstiness is independent of scale for exponentiall distribution
ie_times_expon = expon(scale=scale).rvs(size=(n_samples*(event_set.num_events-1)))
ie_times_expon = np.reshape(np.array(ie_times_expon), (n_samples, (event_set.num_events-1)))
ie_times_expon_T = ie_times_expon.T
burst_expon = burstiness(ie_times_expon_T)
# Gamma
alpha_g = 2.3 #2.2 #1.6 ##2.35 #2.4 #2.0
ie_times_g = gamma(alpha_g, scale=scale).rvs(size=(n_samples*(event_set.num_events-1)))
ie_times_g = np.reshape(np.array(ie_times_g), (n_samples, (event_set.num_events-1)))
ie_times_g_T = ie_times_g.T
burst_g = burstiness(ie_times_g_T)
# Now generate chronologies assuming uncertain events did not occur
if sum(event_certainties[i]) < event_set.num_events:
indices = np.where(event_certainties[i] == 1)
indices = list(indices[0])
# print(indices[0], type(indices))
events_subset = list(itemgetter(*indices)(event_set.event_list))
event_set_certain = EventSet(events_subset)
event_set_certain.name = names[i]
event_set_certain.gen_chronologies(n_samples, observation_end=2019, min_separation=1)
event_set_certain.calculate_cov()
event_set_certain.cov_density()
event_set_certain.basic_chronology_stats()
event_set_certain.memory_coefficient()
event_set_certain.memory_spearman_rank_correlation()
# Generate random exponentially distributed samples of length num_events - 1
# i.e. the number of inter-event times in the chronology. These will be used
# later for testing
ie_times_expon_certain = expon(scale=scale).rvs(size=(n_samples*(len(indices)-1)))
ie_times_expon_certain = np.reshape(np.array(ie_times_expon_certain), (n_samples, (len(indices)-1)))
ie_times_expon_certain_T = ie_times_expon_certain.T
burst_expon_certain = burstiness(ie_times_expon_certain_T)
ie_times_g_certain = gamma(alpha_g, scale=scale).rvs(size=(n_samples*(event_set.num_events-1)))
ie_times_g_certain = np.reshape(np.array(ie_times_g_certain), (n_samples, (event_set.num_events-1)))
ie_times_g_certain_T = ie_times_g_certain.T
burst_g_certain = burstiness(ie_times_g_T)
# Now combine results from certain chronolgies with uncertain ones
combined_covs = np.concatenate([event_set.covs[:half_n],
event_set_certain.covs[:half_n]])
combined_burstiness = np.concatenate([event_set.burstiness[:half_n],
event_set_certain.burstiness[:half_n]])
combined_memory = np.concatenate([event_set.mem_coef[:half_n],
event_set_certain.mem_coef[:half_n]])
combined_memory_spearman = np.concatenate([event_set.rhos[:half_n],
event_set_certain.rhos[:half_n]])
combined_memory_spearman_lag2 = np.concatenate([event_set.rhos2[:half_n],
event_set_certain.rhos2[:half_n]])
combined_burst_expon = np.concatenate([burst_expon[:half_n],
burst_expon_certain[:half_n]])
combined_burst_g = np.concatenate([burst_g[:half_n],
burst_g_certain[:half_n]])
covs.append(combined_covs)
burstinesses.append(combined_burstiness)
memory_coefficients.append(combined_memory)
memory_stds.append(np.std(np.array(combined_memory)))
memory_spearman_coefficients.append(combined_memory_spearman)
memory_spearman_lag2_coef.append(combined_memory_spearman_lag2)
burstinesses_expon.append(combined_burst_expon)
burstinesses_gamma.append(combined_burst_g)
cov_bounds.append([abs(np.mean(combined_covs) - \
min(event_set.cov_lb, event_set_certain.cov_lb)),
abs(np.mean(combined_covs) - \
max(event_set.cov_ub, event_set_certain.cov_ub))])
burstiness_bounds.append([abs(np.mean(combined_burstiness) - \
min(event_set.burstiness_lb,
event_set_certain.burstiness_lb)),
abs(np.mean(combined_burstiness) - \
max(event_set.burstiness_ub,
event_set_certain.burstiness_ub))])
memory_bounds.append([abs(np.mean(combined_memory) - \
min(event_set.memory_lb,
event_set_certain.memory_lb)),
abs(np.mean(combined_memory) - \
max(event_set.memory_ub,
event_set_certain.memory_ub))])
memory_spearman_bounds.append([abs(np.mean(combined_memory_spearman) - \
min(event_set.rho_lb,
event_set_certain.rho_lb)),
abs(np.mean(combined_memory_spearman) - \
max(event_set.rho_ub,
event_set_certain.rho_ub))])
memory_spearman_lag2_bounds.append([abs(np.mean(combined_memory_spearman_lag2) - \
min(event_set.rho2_lb,
event_set_certain.rho2_lb)),
abs(np.mean(combined_memory_spearman_lag2) - \
max(event_set.rho2_ub,
event_set_certain.rho2_ub))])
# Combine, taking n/2 samples from each set
combined_ltrs = np.concatenate([event_set.long_term_rates[:half_n],
event_set_certain.long_term_rates[:half_n]])
burstiness_stds.append(np.std(combined_burstiness))
print(len(combined_ltrs))
long_term_rates.append(combined_ltrs)
long_term_rate_stds.append(np.std(combined_ltrs))
else:
covs.append(event_set.covs)
burstinesses.append(event_set.burstiness)
memory_coefficients.append(event_set.mem_coef)
memory_stds.append(np.std(np.array(event_set.mem_coef)))
memory_spearman_coefficients.append(event_set.rhos)
memory_spearman_lag2_coef.append(event_set.rhos2)
long_term_rates.append(event_set.long_term_rates)
burstinesses_expon.append(burst_expon)
burstinesses_gamma.append(burst_g)
cov_bounds.append([abs(event_set.mean_cov - event_set.cov_lb),
abs(event_set.mean_cov - event_set.cov_ub)])
burstiness_bounds.append([abs(event_set.mean_burstiness - event_set.burstiness_lb),
abs(event_set.mean_burstiness - event_set.burstiness_ub)])
memory_bounds.append([abs(event_set.mean_mem_coef - event_set.memory_lb),
abs(event_set.mean_mem_coef - event_set.memory_ub)])
memory_spearman_bounds.append([abs(event_set.mean_rho - event_set.rho_lb),
abs(event_set.mean_rho - event_set.rho_ub)])
memory_spearman_lag2_bounds.append([abs(event_set.mean_rho2 - event_set.rho2_lb),
abs(event_set.mean_rho2 - event_set.rho2_ub)])
burstiness_stds.append(event_set.std_burstiness)
long_term_rate_stds.append(np.mean(long_term_rates))
# Get colours for plotting later
if event_set.faulting_style == 'Normal':
plot_colours.append('r')
elif event_set.faulting_style == 'Reverse':
plot_colours.append('b')
elif event_set.faulting_style == 'Strike_slip':
plot_colours.append('g')
else:
plot_colours.append('k')
if event_set.add_events: # List of records where we model long open interval
added_events.append(event_set.name)
# Convert to numpy arrays and transpose where necessary
num_events = np.array(num_events)
all_ie_times = np.array(all_ie_times)
max_interevent_times = np.array(max_interevent_times)
min_interevent_times = np.array(min_interevent_times)
min_paired_interevent_times = np.array(min_paired_interevent_times)
std_max_interevent_times = np.array(std_max_interevent_times)
std_min_interevent_times = np.array(std_min_interevent_times)
std_min_paired_interevent_times = np.array(std_min_paired_interevent_times)
max_interevent_times_bounds = np.array(max_interevent_times_bounds).T
min_interevent_times_bounds = np.array(min_interevent_times_bounds).T
min_paired_interevent_times_bounds = np.array(min_paired_interevent_times_bounds).T
long_term_rates_T = np.array(long_term_rates).T
mean_ltr = np.mean(long_term_rates_T, axis = 0)
long_term_rate_stds = np.array(long_term_rate_stds)
slip_rates = np.array(slip_rates).T
slip_rate_bounds = np.array(slip_rate_bounds).T
slip_rate_stds = np.array(slip_rate_stds).T
print('Mean_ltr', mean_ltr)
std_ltr = np.std(long_term_rates_T, axis = 0)
ltr_bounds = np.array([abs(mean_ltr - (np.percentile(long_term_rates_T, 2.5, axis=0))),
abs(mean_ltr - (np.percentile(long_term_rates_T, 97.5, axis=0)))])
ratio_min_pair_max = np.array(ratio_min_pair_max)
ratio_min_max = np.array(ratio_min_max)
std_ratio_min_pair_max = np.array(std_ratio_min_pair_max)
std_ratio_min_max = np.array(std_ratio_min_max)
ratio_min_pair_max_bounds = np.array(ratio_min_pair_max_bounds).T
ratio_min_max_bounds = np.array(ratio_min_max_bounds).T
cov_bounds = np.array(cov_bounds).T
burstiness_bounds = np.array(burstiness_bounds).T
burstiness_stds = np.array(burstiness_stds)
burstiness_expon = np.array(burstinesses_expon)
burstiness_gamma = np.array(burstinesses_gamma)
inds = np.where(num_events >= min_num_events_mem) # Get memory coefficients for more than 6 events
memory_coefficients = np.array(memory_coefficients)
memory_coefficients_min = memory_coefficients[inds]
memory_stds = np.array(memory_stds)
memory_stds_min = memory_stds[inds]
memory_bounds_min = np.array(memory_bounds)[inds].T
memory_bounds = np.array(memory_bounds).T
memory_spearman_bounds = np.array(memory_spearman_bounds).T
memory_spearman_lag2_bounds = np.array(memory_spearman_lag2_bounds).T
ie_gamma_alpha = np.array(ie_gamma_alpha)
# Now plot the means and 95% error bars of COV
pyplot.clf()
ax = pyplot.subplot(111)
mean_covs = []
for i, cov_set in enumerate(covs):
mean_cov = np.mean(cov_set)
mean_covs.append(mean_cov)
colours = []
for mean_cov in mean_covs:
if mean_cov <= 0.9:
colours.append('b')
elif mean_cov > 0.9 and mean_cov <= 1.1:
colours.append('g')
else:
colours.append('r')
pyplot.errorbar(mean_ltr, mean_covs,
xerr = ltr_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(mean_ltr, mean_covs,
yerr = cov_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.scatter(mean_ltr, mean_covs, marker = 's', c=plot_colours,
s=25, zorder=2)
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(mean_ltr[i], mean_covs[i]),
fontsize=8)
ax.set_ylim([0, 2.5])
ax.set_xlim([1./1000000, 1./40])
ax.set_xscale('log')
ax.set_xlabel('Long-term rate (events per year)')
ax.set_ylabel('COV')
figname = 'mean_cov_vs_lt_rate_%s.png' % fig_comment
pyplot.savefig(figname)
################################
# Plot burstiness against mean ltr
pyplot.clf()
ax = pyplot.subplot(111)
mean_bs = []
for i, b_set in enumerate(burstinesses):
mean_b = np.mean(b_set)
mean_bs.append(mean_b)
colours = []
for mean_b in mean_bs:
if mean_b <= -0.05:
colours.append('b')
elif mean_b > -0.05 and mean_b <= 0.05:
colours.append('g')
else:
colours.append('r')
pyplot.errorbar(mean_ltr, mean_bs,
xerr = ltr_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(mean_ltr, mean_bs,
yerr = burstiness_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.scatter(mean_ltr, mean_bs, marker = 's', c=plot_colours,
s=25, zorder=2)
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(mean_ltr[i], mean_bs[i]),
fontsize=8)
# Add B=0 linear
pyplot.plot([1./1000000, 1./40], [0, 0], linestyle='dashed', linewidth=1, c='0.5')
ax.set_xscale('log')
ax.set_xlabel('Long-term rate (events per year)')
ax.set_ylabel('B')
# Now do a bi-linear fit to the data
mean_bs = np.array(mean_bs)
indices = np.flatnonzero(mean_ltr > 3e-4)
indices = indices.flatten()
indices_slow_faults = np.flatnonzero(mean_ltr <= 3e-4)
indices_slow_faults = indices_slow_faults.flatten()
# Fit fast rate faults
lf = np.polyfit(np.log10(mean_ltr[indices]),
mean_bs[indices], 1)
# Now force to be a flat line1
lf[0] = 0.
lf[1] = np.mean(mean_bs[indices])
std_lf = np.std(mean_bs[indices])
xvals_short = np.arange(1.5e-4, 2e-2, 1e-4)
yvals = lf[0]*np.log10(xvals_short) + lf[1]
pyplot.plot(xvals_short, yvals, c='0.2')
# Fit slow faults
if len(indices_slow_faults > 1):
lf_slow = np.polyfit(np.log10(mean_ltr[indices_slow_faults]),
mean_bs[indices_slow_faults], 1)
xvals_short = np.arange(1e-6, 1.5e-4, 1e-6)
yvals = lf_slow[0]*np.log10(xvals_short) + lf_slow[1]
pyplot.plot(xvals_short, yvals, c='0.2')
# Add formula for linear fits of data
print('Fits for B vs LTR')
txt = 'Y = {:=+6.2f} +/- {:4.2f}'.format(lf[1], std_lf)
print(txt)
ax.annotate(txt, (2e-4, 0.2), fontsize=8)
try:
txt = 'Y = {:4.2f}Log(x) {:=+6.2f}'.format(lf_slow[0], lf_slow[1])
print(txt)
ax.annotate(txt, (1.5e-6, 0.75), fontsize=8)
except:
pass
# Now try bilinear ODR linear fit
data = odrpack.RealData(np.log10(mean_ltr), mean_bs,
sx=np.log10(long_term_rate_stds), sy=burstiness_stds)
bilin = odrpack.Model(bilinear_reg_zero_slope)
odr = odrpack.ODR(data, bilin, beta0=[-3, -1.0, -4]) # array are starting values
odr.set_job(fit_type=0)
out = odr.run()
print(out.sum_square)
out.pprint()
a = out.beta[0]
b = out.beta[1]
hx = out.beta[2]
xvals = np.arange(1.e-6, 2e-2, 1e-6)
yrng = a*np.log10(xvals) + b #10**(b + a * xvals)
ylevel = a*hx + b #10**(b + a * hx)
print('ylevel', ylevel)
print(10**ylevel)
idx = xvals > 10**hx
yrng[idx] = (ylevel)
print('yrng', yrng)
print('hx', hx)
pyplot.plot(xvals, yrng, c='g')
# Bilinear fixed hinge
hxfix = np.log10(2e-4)
bilin_hxfix_cons_slope = odrpack.Model(bilinear_reg_fix_zero_slope)
odr = odrpack.ODR(data, bilin_hxfix_cons_slope, beta0=[-3, -1.0])
odr.set_job(fit_type=0)
out = odr.run()
print('bilinear hxfix_cons_slope')
print(out.sum_square)
out.pprint()
a = out.beta[0]
b = out.beta[1]
yrng = a*np.log10(xvals) + b
ylevel = a*hxfix + b
print('ylevel hxfix zero slope', ylevel)
print(10**ylevel)
idx = xvals > 10**hxfix
yrng[idx] = (ylevel)
print('yrng', yrng)
print('hx', hxfix)
pyplot.plot(xvals, yrng, c='r')
figname = 'burstiness_vs_lt_rate_%s.png' % fig_comment
pyplot.savefig(figname)
#########################
# Plot burstiness against slip rate
pyplot.clf()
ax = pyplot.subplot(111)
pyplot.errorbar(slip_rates, mean_bs,
xerr = slip_rate_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(slip_rates, mean_bs,
yerr = burstiness_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.scatter(slip_rates, mean_bs, marker = 's', c=plot_colours,
s=25, zorder=2)
ax.set_ylim([-1, 1])
ax.set_xlim([1./1000, 100])
# Add B=0 linear
pyplot.plot([1./1000, 100], [0, 0], linestyle='dashed', linewidth=1, c='0.5')
ax.set_xscale('log')
ax.set_xlabel('Slip rate (mm/yr)')
ax.set_ylabel('B')
# Now try linear ODR linear fit
def f(B, x):
return B[0]*x + B[1]
print(slip_rates)
print(np.log10(slip_rates))
print(slip_rate_stds)
print(np.log10(slip_rate_stds))
print(burstiness_stds)
wd = 1./np.power(burstiness_stds, 2)
print(wd)
we = 1./np.power(slip_rate_stds, 2)
print(we)
# Std dev already in log-space
data = odrpack.RealData(np.log10(slip_rates), mean_bs,
sx=np.sqrt(slip_rate_stds), sy=np.sqrt(burstiness_stds))
linear = odrpack.Model(f)
odr = odrpack.ODR(data, linear, beta0=[-1, -1.0,])
odr.set_job(fit_type=0)
out = odr.run()
out.pprint()
a = out.beta[0]
b = out.beta[1]
xvals = np.arange(1.e-4, 1e2, 1e-2)
yrng = a*np.log10(xvals) + b #10**(b + a * xvals)
pyplot.plot(xvals, yrng, c='0.6')
txt = 'Y = {:4.2f}Log(x) {:=+6.2f}'.format(a, b)
print(txt)
ax.annotate(txt, (1e0, 0.9), color='0.6')
# Now try bilinear fixed hinge
bilin = odrpack.Model(bilinear_reg_fix_zero_slope)
odr = odrpack.ODR(data, bilin, beta0=[-1, -1.0, -1])
odr.set_job(fit_type=0)
out = odr.run()
out.pprint()
a = out.beta[0]
b = out.beta[1]
yrng = a*np.log10(xvals) + b
ylevel = a*hxfix + b
print('ylevel hxfix zero slope', ylevel)
print(10**ylevel)
idx = xvals > 10**hxfix
yrng[idx] = (ylevel)
print('yrng', yrng)
print('hx', hxfix)
pyplot.plot(xvals, yrng, c='0.2')
txt = 'Y = {:4.2f}Log(x) {:=+6.2f}, x < {:4.2f}'.format(a, b, np.power(10,hxfix))
print(txt)
ax.annotate(txt, (2e-3, 0.9), color='0.2')
txt = 'Y = {:4.2f}, x >= {:4.2f}'.format(ylevel, np.power(10,hxfix))
print(txt)
ax.annotate(txt, (1.2e-2, 0.8), color='0.2')
figname = 'burstiness_vs_slip_rate_%s.png' % fig_comment
pyplot.savefig(figname)
figname = 'burstiness_vs_slip_rate_%s.pdf' % fig_comment
pyplot.savefig(figname)
# Plot memory coefficients against long term rates
pyplot.clf()
ax = pyplot.subplot(111)
mean_mems = []
mean_ltr_mem = mean_ltr[inds]
ltr_bounds_mem = ltr_bounds.T[inds].T
for i, mem_set in enumerate(memory_coefficients):
mean_mem = np.mean(mem_set)
# print('Mean memory coefficient combined', mean_mem)
mean_mems.append(mean_mem)
mean_mems = np.array(mean_mems)
colours = []
plot_colours_mem = list(np.array(plot_colours)[inds])
for mean_mem in mean_mems:
if mean_mem <= -0.05:
colours.append('b')
elif mean_mem > -0.05 and mean_mem <= 0.05:
colours.append('g')
else:
colours.append('r')
pyplot.errorbar(mean_ltr_mem, mean_mems[inds],
xerr = ltr_bounds_mem,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(mean_ltr_mem, mean_mems[inds],
yerr = memory_bounds_min,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.scatter(mean_ltr_mem, mean_mems[inds], marker = 's', c=plot_colours_mem,
s=25, zorder=2)
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(mean_ltr[i], mean_mems[i]),
fontsize=8)
ax.set_xlim([1./1000000, 1./40])
ax.set_xscale('log')
ax.set_xlabel('Long-term rate (events per year)')
ax.set_ylabel('M')
figname = 'memory_coefficient_vs_lt_rate_%s.png' % fig_comment
pyplot.savefig(figname)
# Plot Spearman Rank coefficients against long term rates
pyplot.clf()
ax = pyplot.subplot(111)
mean_mems_L1 = []
for i, mem_set in enumerate(memory_spearman_coefficients):
mean_mem = np.mean(mem_set)
mean_mems_L1.append(mean_mem)
colours = []
for mean_mem in mean_mems_L1:
if mean_mem <= -0.05:
colours.append('b')
elif mean_mem > -0.05 and mean_mem <= 0.05:
colours.append('g')
else:
colours.append('r')
pyplot.errorbar(mean_ltr, mean_mems_L1,
xerr = ltr_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(mean_ltr, mean_mems_L1,
yerr = memory_spearman_bounds,
elinewidth=0.7,
ecolor = '0.3',
linestyle="None",
zorder=1)
pyplot.scatter(mean_ltr, mean_mems_L1, marker = 's', c=plot_colours,
s=25, zorder=2)
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(mean_ltr[i], mean_mems_L1[i]),
fontsize=8)
ax.set_xlim([1./1000000, 1./40])
ax.set_xscale('log')
ax.set_xlabel('Long-term rate (events per year)')
ax.set_ylabel('M (Spearman Rank)')
figname = 'memory_coefficient_Spearman_vs_lt_rate_%s.png' % fig_comment
pyplot.savefig(figname)
# Plot Spearman Rank (Lag-2) coefficients against long term rates
pyplot.clf()
ax = pyplot.subplot(111)
mean_mems_L2 = []
for i, mem_set in enumerate(memory_spearman_lag2_coef):
mean_mem = np.mean(mem_set)
mean_mems_L2.append(mean_mem)
colours = []
for mean_mem in mean_mems_L2:
if mean_mem <= -0.05:
colours.append('b')
elif mean_mem > -0.05 and mean_mem <= 0.05:
colours.append('g')
else:
colours.append('r')
pyplot.errorbar(mean_ltr, mean_mems_L2,
xerr = ltr_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(mean_ltr, mean_mems_L2,
yerr = memory_spearman_lag2_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.scatter(mean_ltr, mean_mems_L2, marker = 's', c=plot_colours,
s=25, zorder=2)
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(mean_ltr[i], mean_mems_L2[i]),
fontsize=8)
ax.set_xlim([1./1000000, 1./40])
ax.set_xscale('log')
ax.set_xlabel('Long-term rate (events per year)')
ax.set_ylabel('M (Spearman Rank Lag-2)')
figname = 'memory_coefficient_Spearman_Lag2_vs_lt_rate_%s.png' % fig_comment
pyplot.savefig(figname)
# Plot Spearman rank Lag-1 against Lag-2
# Plot Spearman Rank coefficients against long term rates
pyplot.clf()
ax = pyplot.subplot(111)
colours = []
for mean_mem in mean_mems_L1:
if mean_mem <= -0.05:
colours.append('b')
elif mean_mem > -0.05 and mean_mem <= 0.05:
colours.append('g')
else:
colours.append('r')
pyplot.errorbar(mean_mems_L1, mean_mems_L2,
xerr = memory_spearman_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(mean_mems_L1, mean_mems_L2,
yerr = memory_spearman_lag2_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.scatter(mean_mems_L1, mean_mems_L2, marker = 's', c=plot_colours,
s=25, zorder=2)
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(mean_mems_L1[i], mean_mems_L2[i]),
fontsize=8)
ax.set_xlabel('M (Spearman Rank Lag-1)')
ax.set_ylabel('M (Spearman Rank Lag-2)')
figname = 'memory_coefficient_Spearman_L1_vs_L2_%s.png' % fig_comment
pyplot.savefig(figname)
# Plot COV against number of events to look at sampling biases
pyplot.clf()
ax = pyplot.subplot(111)
mean_covs = []
for i, cov_set in enumerate(covs):
mean_cov = np.mean(cov_set)
mean_covs.append(mean_cov)
colours = []
for mean_cov in mean_covs:
if mean_cov <= 0.9:
colours.append('b')
elif mean_cov > 0.9 and mean_cov <= 1.1:
colours.append('g')
else:
colours.append('r')
pyplot.errorbar(mean_covs, num_events,
xerr = cov_bounds,
ecolor = '0.6',
linestyle="None")
pyplot.scatter(mean_covs, num_events, marker = 's', c=plot_colours, s=25)
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(mean_covs[i], num_events[i]),
fontsize=8)
ax.set_xlabel('COV')
ax.set_ylabel('Number of events in earthquake record')
figname = 'mean_cov_vs_number_events_%s.png' % fig_comment
pyplot.savefig(figname)
# Now plot basic statistics
pyplot.clf()
ax = pyplot.subplot(111)
pyplot.errorbar(max_interevent_times, min_interevent_times,
yerr = min_interevent_times_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(max_interevent_times, min_interevent_times,
xerr = max_interevent_times_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.scatter(max_interevent_times, min_interevent_times,
marker = 's', c=colours, s=25, zorder=2)
ax.set_xlabel('Maximum interevent time')
ax.set_ylabel('Minimum interevent time')
ax.set_xscale('log')
ax.set_yscale('log')
# Label low-slip rate faults
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(max_interevent_times[i], min_interevent_times[i]),
fontsize=8)
# Linear fit only bottom end of data
indices = np.argwhere(max_interevent_times < 10000).flatten()
indices_slow_faults = np.argwhere(max_interevent_times >= 10000).flatten()
lf = np.polyfit(np.log10(max_interevent_times[indices]),
np.log10(min_interevent_times[indices]), 1)
xvals_short = np.arange(100, 1e4, 100)
log_yvals = lf[0]*np.log10(xvals_short) + lf[1]
yvals = np.power(10, log_yvals)
pyplot.plot(xvals_short, yvals)
# Add formula for linear fit to low-end of data
txt = 'Log(Y) = %.2fLog(x) + %.2f' % (lf[0], lf[1])
print(txt)
ax.annotate(txt, (800, 10000))
figname = 'min_vs_max_interevent_time_%s.png' % fig_comment
pyplot.savefig(figname)
# Plot minimum pairs
pyplot.clf()
ax = pyplot.subplot(111)
pyplot.errorbar(max_interevent_times, min_paired_interevent_times,
yerr = min_paired_interevent_times_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(max_interevent_times, min_paired_interevent_times,
xerr = max_interevent_times_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.scatter(max_interevent_times, min_paired_interevent_times,
marker = 's', c=colours, s=25, zorder=2)
ax.set_xlabel('Maximum interevent time')
ax.set_ylabel('Minimum interevent time \n(mean of two shortest consecutive interevent times)')
ax.set_xscale('log')
ax.set_yscale('log')
# Label low-slip rate faults
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(max_interevent_times[i], min_paired_interevent_times[i]),
fontsize=8)
# Now fit with a regression in log-log space
xvals = np.arange(100, 2e6, 100) # For plotting
# Linear fit
lf = np.polyfit(np.log10(max_interevent_times),
np.log10(min_paired_interevent_times), 1)
log_yvals = lf[0]*np.log10(xvals) + lf[1]
yvals = np.power(10, log_yvals)
pyplot.plot(xvals, yvals)
# Linear fit only bottom end of data
indices = np.argwhere(max_interevent_times < 10000).flatten()
lf = np.polyfit(np.log10(max_interevent_times[indices]),
np.log10(min_paired_interevent_times[indices]), 1)
xvals_short = np.arange(100, 1e4, 100)
log_yvals = lf[0]*np.log10(xvals_short) + lf[1]
yvals = np.power(10, log_yvals)
pyplot.plot(xvals_short, yvals)
# Add formula for linear fit to low-end of data
txt = 'Log(Y) = %.2fLog(x) + %.2f' % (lf[0], lf[1])
print(txt)
ax.annotate(txt, (100, 10000))
# Quadratic fit
qf = np.polyfit(np.log10(max_interevent_times),
np.log10(min_paired_interevent_times), 2)
print(qf)
log_yvals = qf[0]*np.log10(xvals)**2 + qf[1]*np.log10(xvals) + qf[2]
yvals = np.power(10, log_yvals)
pyplot.plot(xvals, yvals)
figname = 'min_pair_vs_max_interevent_time_%s.png' % fig_comment
pyplot.savefig(figname)
# Similar plots, against long term rates
pyplot.clf()
ax = pyplot.subplot(111)
pyplot.errorbar(mean_ltr, min_interevent_times,
yerr = min_interevent_times_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(mean_ltr, min_interevent_times,
xerr = ltr_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.scatter(mean_ltr, min_interevent_times,
marker='s', c=colours, s=25, zorder=2)
ax.set_xlabel('Long-term rate')
ax.set_ylabel('Minimum interevent time')
ax.set_xscale('log')
ax.set_yscale('log')
# Label low-slip rate faults
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(mean_ltr[i], min_interevent_times[i]),
fontsize=8)
# Linear fit only bottom end of data
indices = np.argwhere(mean_ltr > 2e-4).flatten()
lf = np.polyfit(np.log10(mean_ltr[indices]),
np.log10(min_interevent_times[indices]), 1)
xvals_short = np.arange(5e-4, 1e-2, 1e-4)
log_yvals = lf[0]*np.log10(xvals_short) + lf[1]
yvals = np.power(10, log_yvals)
pyplot.plot(xvals_short, yvals)
# Add formula for linear fit to low-end of data
txt = 'Log(Y) = %.2fLog(x) + %.2f' % (lf[0], lf[1])
ax.annotate(txt, (1e-4, 10000))
figname = 'min_interevent_time_vs_ltr_%s.png' % fig_comment
pyplot.savefig(figname)
# Plot long term rate against minimum pair
pyplot.clf()
ax = pyplot.subplot(111)
pyplot.errorbar(mean_ltr, min_paired_interevent_times,
yerr = min_paired_interevent_times_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(mean_ltr, min_paired_interevent_times,
xerr = ltr_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.scatter(mean_ltr, min_paired_interevent_times,
marker='s', c=colours, s=25, zorder=2)
ax.set_xlabel('Long-term rate')
ax.set_ylabel('Minimum interevent time \n(mean of two shortest consecutive interevent times)')
ax.set_xscale('log')
ax.set_yscale('log')
# Label low-slip rate faults
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(mean_ltr[i], min_paired_interevent_times[i]),
fontsize=8)
# Linear fit only bottom end of data
indices = np.argwhere(mean_ltr > 2e-4).flatten()
lf = np.polyfit(np.log10(mean_ltr[indices]),
np.log10(min_paired_interevent_times[indices]), 1)
xvals_short = np.arange(5e-4, 1e-2, 1e-4)
log_yvals = lf[0]*np.log10(xvals_short) + lf[1]
yvals = np.power(10, log_yvals)
pyplot.plot(xvals_short, yvals)
# Add formula for linear fit to low-end of data
txt = 'Log(Y) = %.2fLog(x) + %.2f' % (lf[0], lf[1])
print(txt)
ax.annotate(txt, (1e-4, 10000))
figname = 'min_pair_vs_ltr_%s.png' % fig_comment
pyplot.savefig(figname)
# Plot long term rate against maximum interevent time
pyplot.clf()
ax = pyplot.subplot(111)
pyplot.errorbar(mean_ltr, max_interevent_times,
yerr = max_interevent_times_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(mean_ltr, max_interevent_times,
xerr = ltr_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.scatter(mean_ltr, max_interevent_times,
marker='s', c=plot_colours, s=25, zorder=2)
ax.set_xlabel('Long-term rate')
ax.set_ylabel('Maximum interevent time')
ax.set_xscale('log')
ax.set_yscale('log')
# Label low-slip rate faults
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(mean_ltr[i], max_interevent_times[i]),
fontsize=8)
# Linear fit only bottom end of data
indices = np.argwhere(mean_ltr > 2e-10).flatten() # All data for now
lf = np.polyfit(np.log10(mean_ltr[indices]),
np.log10(max_interevent_times[indices]), 1)
xvals_short = np.arange(2e-6, 1e-2, 1e-6)
log_yvals = lf[0]*np.log10(xvals_short) + lf[1]
yvals = np.power(10, log_yvals)
pyplot.plot(xvals_short, yvals)
# Add formula for linear fit to low-end of data
txt = 'Log(Y) = %.2fLog(x) + %.2f' % (lf[0], lf[1])
print(txt)
ax.annotate(txt, (1e-4, 100000))
figname = 'max_interevent_time_vs_ltr_%s.png' % fig_comment
pyplot.savefig(figname)
# Now plot ratios against long term rates
pyplot.clf()
ax = pyplot.subplot(111)
pyplot.errorbar(mean_ltr, ratio_min_pair_max,
yerr = ratio_min_pair_max_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(mean_ltr, ratio_min_pair_max,
xerr = ltr_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.scatter(mean_ltr, ratio_min_pair_max,
marker='s', c=plot_colours, s=25, zorder=2)
ax.set_xlabel('Long-term rate')
ax.set_ylabel('Minimum pair interevent time: maximum interevent time')
ax.set_xscale('log')
ax.set_yscale('log')
# Label low-slip rate faults
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(mean_ltr[i], ratio_min_pair_max[i]),
fontsize=8)
# Linear fit high and low long term rate data separately
indices = np.argwhere(mean_ltr > 4e-4).flatten()
indices_slow_faults = np.argwhere(mean_ltr <= 4e-4).flatten()
lf = np.polyfit(np.log10(mean_ltr[indices]),
np.log10(ratio_min_pair_max[indices]), 1)
xvals_short = np.arange(2e-4, 5e-2, 1e-4)
log_yvals = lf[0]*np.log10(xvals_short) + lf[1]
yvals = np.power(10, log_yvals)
pyplot.plot(xvals_short, yvals, c='k')
# Add formula for linear fit to low-end of data
txt = 'Log(Y) = %.2fLog(x) + %.2f' % (lf[0], lf[1])
print(txt)
ax.annotate(txt, (5e-4, 1e-2))
# Slow long-term rates
print('At if statement')
if len(indices_slow_faults) > 0:
print('Plotting slow faults')
lf = np.polyfit(np.log10(mean_ltr[indices_slow_faults]),
np.log10(ratio_min_pair_max[indices_slow_faults]), 1)
xvals_short = np.arange(2e-6, 4e-4, 1e-6)
log_yvals = lf[0]*np.log10(xvals_short) + lf[1]
yvals = np.power(10, log_yvals)
pyplot.plot(xvals_short, yvals, c='k')
# Add formula for linear fit to low-end of data
txt = 'Log(Y) = %.2fLog(x) + %.2f' % (lf[0], lf[1])
print(txt)
ax.annotate(txt, (1e-5, 5e-3))
figname = 'min_pair_max_ratio_vs_ltr_%s.png' % fig_comment
pyplot.savefig(figname)
# Now plot ratios against long term rates
pyplot.clf()
ax = pyplot.subplot(111)
pyplot.errorbar(mean_ltr, ratio_min_max,
yerr = ratio_min_max_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None",
zorder=1)
pyplot.errorbar(mean_ltr, ratio_min_max,
xerr = ltr_bounds,
ecolor = '0.3',
elinewidth=0.7,
linestyle="None", zorder=1)
pyplot.scatter(mean_ltr, ratio_min_max,
marker = 's', c=plot_colours, s=25, zorder=2)
ax.set_xlabel('Long-term rate')
ax.set_ylabel('Minimum interevent time: maximum interevent time')
ax.set_xscale('log')
ax.set_yscale('log')
# Label low-slip rate faults
for i, txt in enumerate(names):
if max_interevent_times[i] > 10 and annotate_plots:
ax.annotate(txt[:4],
(mean_ltr[i], ratio_min_max[i]),
fontsize=8)
# Linear fit only bottom end of data
indices = | np.argwhere(mean_ltr > 9e-5) | numpy.argwhere |
#!/usr/bin/env python
import numpy as np
import matplotlib.pyplot as plt
import scipy.interpolate, scipy.integrate
from scipy import special
plt.ion()
binprec = '>f4'
flag_plot = 0
flag_bt = 0 # 1: barotropic vortex, 0: baroclinic vortex
flag_eddy = 1 # 1: isolated eddy, 2: modon
flag_surf = 0 # 0: non perturbated surface field
# # physical constants
rho_const = 999.8
alphaK = 2.0e-4
g0 = 9.8
f0 = 1e-4
eps = 1e-10 # a small number
#% ================== NEW GRID =====================================
def stretch(xf,yf,Lx,si_x,rev):
hh = np.linspace(0,1,si_x+1)
xf = Lx*np.interp(hh,xf,yf)
dx = np.diff(xf)
# reverse order to get high resolution near the bottom
if rev:
dx = dx[::-1]
xf[1:] = np.cumsum(dx)
xc = xf[0:-1] + 0.5*dx
return xc,xf,dx
si_x = 100
si_y = 100
si_z = 20
si_x1 = si_x + 1
si_y1 = si_y + 1
si_z1 = si_z + 1
# in m
Lx = 300.0e3
Ly = 300.0e3
Lz = 1300
dx = Lx/si_x;
dy = Ly/si_y;
xx = Lx*(np.arange(0,si_x) + 0.5)/(1.0*si_x)
yy = Ly*(np.arange(0,si_y) + 0.5)/(1.0*si_y)
xx1 = Lx*(np.arange(0,si_x+1) )/(1.0*si_x)
yy1 = Ly*(np.arange(0,si_y+1) )/(1.0*si_y)
xg,yg = np.meshgrid(xx,yy)
xu,yu = np.meshgrid(xx1[:-1],yy)
xv,yv = np.meshgrid(xx,yy1[:-1])
xc,yc = np.meshgrid(xx1,yy1)
dx1 = dx*np.ones((si_x))
dy1 = dy*np.ones((si_y))
slope = 4
xfz = np.linspace(0,1,1000)
yfz = np.sinh(slope*xfz)/np.sinh(slope)
zc,zf,dz1 = stretch(xfz,yfz,Lz,si_z,0)
iz = np.argmin(np.abs(zf-500.0))
print ('dx= ', dx)
print ('min dz: ', np.min(dz1))
print ('max dz: ', np.max(dz1))
print ('nb layers above 500m:', iz, '/', si_z)
if np.sum(dz1 < 0) > 0:
print ('you need you change the polynomial fit!')
dx1.astype(binprec).tofile('dx.box')
dy1.astype(binprec).tofile('dy.box')
dz1.astype(binprec).tofile('dz.box')
#% ============== background density profile ===================
N2 = 3e-5
#N2 = 0.
tref = -N2/g0/alphaK*zc
tref = tref - tref[-1]
# tref_dat = np.loadtxt('temp_winter.dat')
# # add upper and lower boundary for interpolation
# si_tref,naux = tref_dat.shape
# tref_dat2 = np.zeros((si_tref+2,2))
# tref_dat2[1:-1,:] = tref_dat
# tref_dat2[0,1] = tref_dat[0,1]
# tref_dat2[-1,:] = tref_dat[-1,:]
# tref_dat2[-1,0] = -10000
# t_interp = scipy.interpolate.interp1d(tref_dat2[:,0], tref_dat2[:,1])
# tref = t_interp(-zc)
tref = tref.reshape((si_z,1,1))
#%==================== SST - LAND ===================================
landh = np.zeros((si_y,si_x));
H = dz1.cumsum()[-1]
landh = -H + landh
#==================== Velocity and temperature profiles===============
eta = np.zeros((si_y,si_x));
theta = | np.zeros((si_z,si_y,si_x)) | numpy.zeros |
#------------------------------------------Single Rectangle dection-------------------------------------------#
## Adapted from https://github.com/jrieke/shape-detection by <NAME>
# Import libraries:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
import time
import os
# Import tensorflow to use GPUs on keras:
import tensorflow as tf
# Set keras with GPUs
import keras
config = tf.ConfigProto( device_count = {'GPU': 1 , 'CPU': 12} )
sess = tf.Session(config=config)
keras.backend.set_session(sess)
# Import keras tools:
from keras.models import Sequential
from keras.layers import Dense, Activation, Dropout
from keras.optimizers import SGD
# Create images with random rectangles and bounding boxes:
num_imgs = 50000
img_size = 8
min_object_size = 1
max_object_size = 4
num_objects = 1
bboxes = np.zeros((num_imgs, num_objects, 4))
imgs = np.zeros((num_imgs, img_size, img_size)) # set background to
# Generating random images and bounding boxes:
for i_img in range(num_imgs):
for i_object in range(num_objects):
w, h = np.random.randint(min_object_size, max_object_size, size=2) # bbox width (w) and height (h)
x = np.random.randint(0, img_size - w) # bbox x lower left corner coordinate
y = np.random.randint(0, img_size - h) # bbox y lower left corner coordinate
imgs[i_img, x:x+w, y:y+h] = 1. # set rectangle to 1
bboxes[i_img, i_object] = [x, y, w, h] # store coordinates
# Lets plot one example of generated image:
i = 0
plt.imshow(imgs[i].T, cmap='Greys', interpolation='none', origin='lower', extent=[0, img_size, 0, img_size])
for bbox in bboxes[i]:
plt.gca().add_patch(matplotlib.patches.Rectangle((bbox[0], bbox[1]), bbox[2], bbox[3], ec='r', fc='none'))
## Obs:
# - The transpose was done for using properly both plt functions
# - extent is the size of the image
# - ec is the color of the border of the bounding box
# - fc is to avoid any coloured background of the bounding box
# Display plot:
# plt.show()
# Reshape (stack rows horizontally) and normalize the image data to mean 0 and std 1:
X = (imgs.reshape(num_imgs, -1) - np.mean(imgs)) / np.std(imgs)
X.shape, np.mean(X), np.std(X)
# Normalize x, y, w, h by img_size, so that all values are between 0 and 1:
# Important: Do not shift to negative values (e.g. by setting to mean 0)
#----------- because the IOU calculation needs positive w and h
y = bboxes.reshape(num_imgs, -1) / img_size
y.shape, np.mean(y), np.std(y)
# Split training and test:
i = int(0.8 * num_imgs)
train_X = X[:i]
test_X = X[i:]
train_y = y[:i]
test_y = y[i:]
test_imgs = imgs[i:]
test_bboxes = bboxes[i:]
# Build the model:
model = Sequential([Dense(200, input_dim=X.shape[-1]),
Activation('relu'),
Dropout(0.2),
Dense(y.shape[-1])])
model.compile('adadelta', 'mse')
# Fit the model:
tic = time.time()
model.fit(train_X, train_y,nb_epoch=30, validation_data=(test_X, test_y), verbose=2)
toc = time.time() - tic
print(toc)
# Predict bounding boxes on the test images:
pred_y = model.predict(test_X)
pred_bboxes = pred_y * img_size
pred_bboxes = pred_bboxes.reshape(len(pred_bboxes), num_objects, -1)
pred_bboxes.shape
# Function to define the intersection over the union of the bounding boxes pair:
def IOU(bbox1, bbox2):
'''Calculate overlap between two bounding boxes [x, y, w, h]
as the area of intersection over the area of unity'''
x1, y1, w1, h1 = bbox1[0], bbox1[1], bbox1[2], bbox1[3]
x2, y2, w2, h2 = bbox2[0], bbox2[1], bbox2[2], bbox2[3]
w_I = min(x1 + w1, x2 + w2) - max(x1, x2)
h_I = min(y1 + h1, y2 + h2) - max(y1, y2)
if w_I <= 0 or h_I <= 0: # no overlap
return 0
else:
I = w_I * h_I
U = w1 * h1 + w2 * h2 - I
return I / U
# Show a few images and predicted bounding boxes from the test dataset.
os.chdir('/workdir/jp2476/repo/diversity-proj/files')
plt.figure(figsize=(12, 3))
for i_subplot in range(1, 5):
plt.subplot(1, 4, i_subplot)
i = np.random.randint(len(test_imgs))
plt.imshow(test_imgs[i].T, cmap='Greys',
interpolation='none',
origin='lower',
extent=[0, img_size, 0, img_size])
for pred_bbox, train_bbox in zip(pred_bboxes[i], test_bboxes[i]):
plt.gca().add_patch(matplotlib.patches.Rectangle((pred_bbox[0],
pred_bbox[1]),
pred_bbox[2],
pred_bbox[3],
ec='r', fc='none'))
plt.annotate('IOU: {:.2f}'.format(IOU(pred_bbox, train_bbox)),
(pred_bbox[0], pred_bbox[1]+pred_bbox[3]+0.2),
color='r')
# plt.savefig("simple_detection.pdf", dpi=150)
# plt.savefig("simple_detection.png", dpi=150)
plt.show()
plt.clf()
# Calculate the mean IOU (overlap) between the predicted and expected bounding boxes on the test dataset:
summed_IOU = 0.
for pred_bbox, test_bbox in zip(pred_bboxes.reshape(-1, 4), test_bboxes.reshape(-1, 4)):
summed_IOU += IOU(pred_bbox, test_bbox)
mean_IOU = summed_IOU / len(pred_bboxes)
mean_IOU
#-------------------------------------------Two Rectangle dection---------------------------------------------#
## Adapted from https://github.com/jrieke/shape-detection by <NAME>
# Import libraries:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
import time
import os
# Import tensorflow to use GPUs on keras:
import tensorflow as tf
# Set keras with GPUs
import keras
config = tf.ConfigProto( device_count = {'GPU': 1 , 'CPU': 12} )
sess = tf.Session(config=config)
keras.backend.set_session(sess)
# Import keras tools:
from keras.models import Sequential
from keras.layers import Dense, Activation, Dropout
from keras.optimizers import SGD
# Create images with random rectangles and bounding boxes:
num_imgs = 50000
# Image parameters for simulation:
img_size = 8
min_rect_size = 1
max_rect_size = 4
num_objects = 2
# Initialize objects:
bboxes = np.zeros((num_imgs, num_objects, 4))
imgs = np.zeros((num_imgs, img_size, img_size))
# Generate images and bounding boxes:
for i_img in range(num_imgs):
for i_object in range(num_objects):
w, h = np.random.randint(min_rect_size, max_rect_size, size=2)
x = np.random.randint(0, img_size - w)
y = np.random.randint(0, img_size - h)
imgs[i_img, x:x+w, y:y+h] = 1.
bboxes[i_img, i_object] = [x, y, w, h]
# Get shapes:
imgs.shape, bboxes.shape
# Plot one example of generated images:
i = 0
plt.imshow(imgs[i].T, cmap='Greys', interpolation='none', origin='lower', extent=[0, img_size, 0, img_size])
for bbox in bboxes[i]:
plt.gca().add_patch(matplotlib.patches.Rectangle((bbox[0], bbox[1]), bbox[2], bbox[3], ec='r', fc='none'))
# plt.show()
# Reshape and normalize the data to mean 0 and std 1:
X = (imgs.reshape(num_imgs, -1) - np.mean(imgs)) / np.std(imgs)
X.shape, np.mean(X), np.std(X)
# Normalize x, y, w, h by img_size, so that all values are between 0 and 1:
# Important: Do not shift to negative values (e.g. by setting to mean 0),
#---------- because the IOU calculation needs positive w and h
y = bboxes.reshape(num_imgs, -1) / img_size
y.shape, np.mean(y), np.std(y)
# Function to define the intersection over the union of the bounding boxes pair:
def IOU(bbox1, bbox2):
'''Calculate overlap between two bounding boxes [x, y, w, h]
as the area of intersection over the area of unity'''
x1, y1, w1, h1 = bbox1[0], bbox1[1], bbox1[2], bbox1[3]
x2, y2, w2, h2 = bbox2[0], bbox2[1], bbox2[2], bbox2[3]
w_I = min(x1 + w1, x2 + w2) - max(x1, x2)
h_I = min(y1 + h1, y2 + h2) - max(y1, y2)
if w_I <= 0 or h_I <= 0: # no overlap
return 0
else:
I = w_I * h_I
U = w1 * h1 + w2 * h2 - I
return I / U
# Split training and test.
i = int(0.8 * num_imgs)
train_X = X[:i]
test_X = X[i:]
train_y = y[:i]
test_y = y[i:]
test_imgs = imgs[i:]
test_bboxes = bboxes[i:]
# Build the model.
from keras.models import Sequential
from keras.layers import Dense, Activation, Dropout
from keras.optimizers import SGD
model = Sequential([
Dense(256, input_dim=X.shape[-1]),
Activation('relu'),
Dropout(0.4),
Dense(y.shape[-1])
])
model.compile('adadelta', 'mse')
# Flip bboxes during training:
# Note: The validation loss is always quite big here because we don't flip the bounding boxes for
#------ the validation data
# Define the distance between the two bounding boxes:
def distance(bbox1, bbox2):
return np.sqrt(np.sum(np.square(bbox1[:2] - bbox2[:2])))
# Parameters to fit the model:
num_epochs = 50
flipped = np.zeros((len(train_y), num_epochs))
ious_epoch = np.zeros((len(train_y), num_epochs))
dists_epoch = np.zeros((len(train_y), num_epochs))
mses_epoch = np.zeros((len(train_y), num_epochs))
# Training the model:
for epoch in range(num_epochs):
# Print the current epoch:
print('Epoch', epoch)
# Fit the model:
model.fit(train_X, train_y, nb_epoch=1, validation_data=(test_X, test_y), verbose=2)
# Get the output from the neural net:
hat_y = model.predict(train_X)
for i, (hat_bboxes, train_bboxes) in enumerate(zip(hat_y, train_y)):
# Flip the training data:
flipped_train_bboxes = np.concatenate([train_bboxes[4:], train_bboxes[:4]])
# Compute the mean-squared error for non-flipped and flipped data points:
mse = np.mean(np.square(hat_bboxes - train_bboxes))
mse_flipped = np.mean(np.square(hat_bboxes - flipped_train_bboxes))
# Compute the IOU for each variation:
iou = IOU(hat_bboxes[:4], train_bboxes[:4]) + IOU(hat_bboxes[4:], train_bboxes[4:])
iou_flipped = IOU(hat_bboxes[:4], flipped_train_bboxes[:4]) + IOU(hat_bboxes[4:], flipped_train_bboxes[4:])
# Compute the distance for each variation:
dist = distance(hat_bboxes[:4], train_bboxes[:4]) + distance(hat_bboxes[4:], train_bboxes[4:])
dist_flipped = distance(hat_bboxes[:4], flipped_train_bboxes[:4]) + distance(hat_bboxes[4:], flipped_train_bboxes[4:])
# Store stats:
if mse_flipped < mse: # you can also use iou or dist here
train_y[i] = flipped_train_bboxes
flipped[i, epoch] = 1
mses_epoch[i, epoch] = mse_flipped
ious_epoch[i, epoch] = iou_flipped / 2.
dists_epoch[i, epoch] = dist_flipped / 2.
else:
mses_epoch[i, epoch] = mse
ious_epoch[i, epoch] = iou / 2.
dists_epoch[i, epoch] = dist / 2.
print('Flipped {} training samples ({} %)'.format(np.sum(flipped[:, epoch]), np.mean(flipped[:, epoch]) * 100.))
print('Mean IOU: {}'.format( | np.mean(ious_epoch[:, epoch]) | numpy.mean |
# -*- coding: utf-8 -*-
"""
Created on Sat Aug 3 14:10:12 2019
@author: Dominic
"""
from numba import njit, float64, int64
from scipy import integrate
from math import exp, log, pi
import numpy as np # I USE NUMPY FOR EXP, LOG AND SQRT AS THEY HANDLE IMAGINARY PARTS
from ..finutils.FinGlobalVariables import gDaysInYear
from ..products.equity.FinEquityOption import FinEquityOptionTypes
from ..finutils.FinMath import norminvcdf
##########################################################################
# Heston Process
# dS = rS dt + sqrt(V) * S * dz
# dV = kappa(theta-V) dt + sigma sqrt(V) dz
# corr(dV,dS) = rho dt
# Rewritten as
# dS = rS dt + sqrt(V) * S * (rhohat dz1 + rho dz2)
# dV = kappa(theta-V) dt + sigma sqrt(V) dz2
# where rhohat = sqrt(1-rho*rho)
##########################################################################
# TODO - DECIDE WHETHER TO OO MODEL
# TODO - NEEDS CHECKING FOR MC CONVERGENCE
##########################################################################
from enum import Enum
class FinHestonNumericalScheme(Enum):
EULER = 1
EULERLOG = 2
QUADEXP = 3
##########################################################################
@njit(float64[:, :](float64, float64, float64, float64, float64, float64,
float64, float64, float64, float64, int64, int64, int64),
fastmath=True)
def getPaths(
s0,
r,
q,
v0,
kappa,
theta,
sigma,
rho,
t,
dt,
numPaths,
seed,
scheme):
np.random.seed(seed)
numSteps = int(t / dt)
sPaths = np.zeros(shape=(numPaths, numSteps))
sPaths[:, 0] = s0
sdt = np.sqrt(dt)
rhohat = np.sqrt(1.0 - rho * rho)
sigma2 = sigma * sigma
if scheme == FinHestonNumericalScheme.EULER.value:
# Basic scheme to first order with truncation on variance
for iPath in range(0, numPaths):
s = s0
v = v0
for iStep in range(1, numSteps):
z1 = np.random.normal(0.0, 1.0) * sdt
z2 = np.random.normal(0.0, 1.0) * sdt
zV = z1
zS = rho * z1 + rhohat * z2
vplus = max(v, 0.0)
rtvplus = np.sqrt(vplus)
v += kappa * (theta - vplus) * dt + sigma * \
rtvplus * zV + 0.25 * sigma2 * (zV * zV - dt)
s += (r - q) * s * dt + rtvplus * s * \
zS + 0.5 * s * vplus * (zV * zV - dt)
sPaths[iPath, iStep] = s
elif scheme == FinHestonNumericalScheme.EULERLOG.value:
# Basic scheme to first order with truncation on variance
for iPath in range(0, numPaths):
x = log(s0)
v = v0
for iStep in range(1, numSteps):
zV = | np.random.normal(0.0, 1.0) | numpy.random.normal |
import abc
import numpy as np
import scipy.stats as spst
import scipy.optimize as spop
class AssetAllocABC(abc.ABC):
n_asset = 1
rho = None
sigma = np.array([1.0])
ret = np.array([0.0])
cor_m = np.eye(1)
cov_m = np.eye(1)
longshort = np.array([1], dtype=np.int8)
def __init__(self, sigma=None, cor=None, cov=None, ret=None, longshort=1):
"""
Args:
sigma: asset volatilities of `n_asset` assets. (n_asset, ) array
cor: asset correlation. If matrix with shape (n_asset, n_asset), used as it is.
If scalar, correlation matrix is constructed with all same off-diagonal values.
cov: asset covariance
ret: expected return
longshort: long/short constraint. 1 for long-only, -1 for short, 0 for no constraint
"""
if cov is None:
# when sigma and cor are given
self.sigma = np.atleast_1d(sigma)
self.n_asset = len(self.sigma)
if self.n_asset == 1:
raise ValueError(f"The number of assets should be more than one.")
if np.isscalar(cor):
self.cor_m = cor * np.ones((self.n_asset, self.n_asset)) \
+ (1 - cor) * np.eye(self.n_asset)
self.rho = cor
else:
assert cor.shape == (self.n_asset, self.n_asset)
self.cor_m = cor
if self.n_asset == 2:
self.rho = cor[0, 1]
self.cov_m = self.sigma * self.cor_m * sigma[:, None]
else:
# When covariance is given directly
self.n_asset = cov.shape[0]
self.cov_m = cov
self.sigma = np.sqrt(np.diag(cov))
self.cor_m = cov.copy()
self.cor_m /= self.sigma[:, None]
self.cor_m /= self.sigma
if ret is not None:
self.ret = ret * np.ones(self.n_asset)
if longshort is None:
self.longshort = np.full(self.n_asset, 1, dtype=np.int8) # long-only
elif np.isscalar(longshort):
self.longshort = np.full(self.n_asset, | np.sign(longshort) | numpy.sign |
# coding=utf-8
# Copyright (C) 2020 NumS Development Team.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import Tuple, Iterator
import itertools
import numpy as np
import scipy.special
from nums.core.settings import np_ufunc_map
# pylint: disable = no-member
def get_uop_output_type(op_name, dtype):
a = np.array(1, dtype=dtype)
result_dtype = np.__getattribute__(op_name)(a).dtype
return np.__getattribute__(str(result_dtype))
def get_bop_output_type(op_name, dtype_a, dtype_b):
a = np.array(1, dtype=dtype_a)
b = np.array(2, dtype=dtype_b)
op_name = np_ufunc_map.get(op_name, op_name)
try:
dtype = np.__getattribute__(op_name)(a, b).dtype
return np.__getattribute__(str(dtype))
except Exception as _:
dtype = scipy.special.__getattribute__(op_name)(a, b).dtype
return np.__getattribute__(str(dtype))
def is_int(val):
return isinstance(val, (int, np.int, np.int8, np.int16, np.int32, np.int64))
def get_reduce_output_type(op_name, dtype):
a = np.array([0, 1], dtype=dtype)
dtype = np.__getattribute__(op_name)(a).dtype
return np.__getattribute__(str(dtype))
def shape_from_block_array(arr: np.ndarray):
grid_shape = arr.shape
num_axes = len(arr.shape)
shape = np.zeros(num_axes, dtype=np.int)
for j in range(num_axes):
pos = [[0]] * num_axes
pos[j] = range(grid_shape[j])
j_iter = list(itertools.product(*pos))
for j_access in j_iter:
shape[j] += arr[j_access].shape[j]
return tuple(shape)
def broadcast(a_shape, b_shape):
a_view = np.lib.stride_tricks.broadcast_to(0, a_shape)
b_view = np.lib.stride_tricks.broadcast_to(0, b_shape)
return np.broadcast(a_view, b_view)
def broadcast_block_shape(a_shape, b_shape, a_block_shape):
# Starting from last block shape dim and
# map each shape dim to block shape dim as already defined,
# and for the rest of dims, set block shape to 1.
result_shape = broadcast(a_shape, b_shape).shape
result_block_shape = []
a_block_shape_r = list(reversed(a_block_shape))
for i, _ in enumerate(reversed(result_shape)):
if i < len(a_block_shape_r):
result_block_shape.append(a_block_shape_r[i])
else:
result_block_shape.append(1)
return tuple(reversed(result_block_shape))
def broadcast_shape(a_shape, b_shape):
return broadcast(a_shape, b_shape).shape
def can_broadcast_shapes(a_shape, b_shape):
try:
assert broadcast_shape(a_shape, b_shape) is not None
return True
except ValueError as _:
return False
def broadcast_shape_to(from_shape, to_shape):
# Enforce broadcasting rules from an
# array of references to 0 with shape from_shape.
from_view = np.lib.stride_tricks.broadcast_to(0, from_shape)
return np.lib.stride_tricks.broadcast_to(from_view, to_shape)
def can_broadcast_shape_to(from_shape, to_shape):
# See: https://numpy.org/devdocs/user/theory.broadcasting.html
try:
broadcast_shape_to(from_shape, to_shape)
return True
except ValueError as _:
return False
def broadcast_shape_to_alt(from_shape, to_shape):
# This is heavily tested with shapes up to length 5.
from_num_axes = len(from_shape)
to_num_axes = len(to_shape)
result_shape = []
if to_num_axes < from_num_axes:
raise ValueError("Input shape has more dimensions than allowed by the axis remapping.")
if to_num_axes == 0 and from_shape != 0:
raise ValueError("Cannot broadcast non-scalar shape to scalar shape ().")
from_shape_r = list(reversed(from_shape))
to_shape_r = list(reversed(to_shape))
for i, from_dim in enumerate(from_shape_r):
to_dim = to_shape_r[i]
if from_dim == 1:
result_shape.append(to_dim)
elif to_dim == from_dim:
result_shape.append(to_dim)
else:
raise ValueError("Cannot broadcast %s to %s." % (str(from_shape), str(to_shape)))
return tuple(reversed(result_shape + to_shape_r[from_num_axes:]))
def is_array_like(obj):
return isinstance(obj, (tuple, list, np.ndarray))
def block_shape_from_subscript(subscript: tuple, block_shape: tuple):
new_block_shape = []
for i, obj in enumerate(subscript):
if isinstance(obj, slice):
new_block_shape.append(block_shape[i])
elif isinstance(obj, (int, np.intp)):
continue
else:
raise NotImplementedError("No support for advanced indexing.")
return tuple(new_block_shape)
def get_slices(total_size, batch_size, order, reverse_blocks=False):
assert order in (-1, 1)
if order > 0:
if reverse_blocks:
result = list(reversed(list(range(total_size, 0, -batch_size)) + [0]))
else:
result = list(range(0, total_size, batch_size)) + [total_size]
return list(map(lambda s: slice(*s, order), zip(*(result[:-1], result[1:]))))
else:
if reverse_blocks:
# If reverse order blocks are not multiples of axis dimension,
# then the last block is smaller than block size and should be
# the first block.
result = list(reversed(list(range(-total_size-1, -1, batch_size)) + [-1]))
else:
result = list(range(-1, -total_size - 1, -batch_size)) + [-total_size - 1]
return list(map(lambda s: slice(*s, order), zip(*(result[:-1], result[1:]))))
class OrderedGrid(object):
def __init__(self, shape: Tuple, block_shape: Tuple, order: Tuple,
block_order=None):
if block_order is not None:
assert len(block_order) == len(shape)
self.shape = tuple(shape)
self.block_shape = tuple(np.min([shape, block_shape], axis=0))
self.order = tuple(order)
self.grid_shape = []
self.grid_slices = []
for i in range(len(self.shape)):
dim = self.shape[i]
block_dim = block_shape[i]
axis_order = order[i]
reverse_blocks = False
if block_order is not None:
reverse_blocks = block_order[i] == -1
axis_slices = get_slices(dim, block_dim, axis_order, reverse_blocks)
self.grid_slices.append(axis_slices)
self.grid_shape.append(len(axis_slices))
self.grid_shape = tuple(self.grid_shape)
# Assumes C-style ordering.
# We add len(shape) to allow for axis consisting of the actual slices.
self.slices = np.array(list(itertools.product(*self.grid_slices)),
dtype=slice).reshape(tuple(list(self.grid_shape) + [len(shape)]))
def index_iterator(self) -> Iterator[Tuple]:
if 0 in self.shape:
return []
return itertools.product(*map(range, self.grid_shape))
def idx2addr(index: tuple, shape: tuple):
strides = [np.product(shape[i:]) for i in range(1, len(shape))] + [1]
addr: int = sum(np.array(index) * strides)
return addr
def addr2idx(addr: int, shape: tuple):
strides = [ | np.product(shape[i:]) | numpy.product |
#!/usr/bin/env python
"""
GeoData.py
Created on Thu Jul 17 12:46:46 2014
@author: <NAME>
"""
from __future__ import division,absolute_import
from six import integer_types,string_types
#import os
#import time
import posixpath
from copy import deepcopy
from datetime import datetime
import numpy as np
import scipy as sp
import scipy.interpolate as spinterp
from scipy.spatial import Delaunay
import tables
from pandas import DataFrame
import pdb
from warnings import warn
#
from . import CoordTransforms as CT
from .utilityfuncs import read_h5_main
VARNAMES = ['data','coordnames','dataloc','sensorloc','times']
class GeoData(object):
'''This class will hold the information for geophysical data.
Variables
data - This is a dictionary with strings for keys only. The strings are
the given names of the data.
coordnames - A string that holds the type of coordinate system.
dataloc - A numpy array that holds the locations of the samples
sensorloc - A numpy array with the WGS coordinates of the sensor.
times - A numpy array that is holding the times associated with the measurements.'''
def __init__(self,readmethod,inputs):
if isinstance(readmethod,string_types):
(self.data,self.coordnames,self.dataloc,self.sensorloc,self.times) = inputs
else:
'''This will create an instance of the GeoData class by giving it a read method and the inputs in a tuple'''
(self.data,self.coordnames,self.dataloc,self.sensorloc,self.times) = readmethod(*inputs)
# Assert that the data types are correct
numerics = (np.ndarray,integer_types,float)
assert isinstance(self.data,dict),"data needs to be a dictionary"
assert isinstance(self.coordnames,str), "coordnames needs to be a string"
assert isinstance(self.dataloc,numerics),"dataloc needs to be a numpy array"
assert isinstance(self.sensorloc,numerics),"sensorloc needs to be a numpy array"
assert isinstance(self.times,numerics),"times needs to be a numpy array"
self.times = timerepair(self.times)
# Make sure the times vector is sorted
if not self.issatellite():
timestemp = self.times[:,0]
sortvec = sp.argsort(timestemp)
self.times=self.times[sortvec]
for ikey in self.datanames():
self.data[ikey]=self.data[ikey][:,sortvec]
def datanames(self):
'''Returns the data names in a list.'''
return self.data.keys()
def write_h5(self,filename):
'''Writes out the structured h5 files for the class.
inputs
filename - The filename of the output.'''
with tables.openFile(filename, mode = "w", title = "GeoData Out") as h5file:
# get the names of all the variables set in the init function
varnames = self.__dict__.keys()
vardict = self.__dict__
try:
# XXX only allow 1 level of dictionaries, do not allow for dictionary of dictionaries.
# Make group for each dictionary
for cvar in varnames:
#group = h5file.create_group(posixpath.sep, cvar,cvar +'dictionary')
if isinstance(vardict[cvar],dict): # Check if dictionary
dictkeys = vardict[cvar].keys()
group2 = h5file.create_group('/',cvar,cvar+' dictionary')
for ikeys in dictkeys:
h5file.create_array(group2,ikeys,vardict[cvar][ikeys])#,'Static array')
else:
if isinstance(vardict[cvar],string_types):
vardict[cvar] = | np.string_(vardict[cvar]) | numpy.string_ |
import cv2
from PIL import Image
import urllib.request,io, time
import numpy as np
from matplotlib import pyplot as plt
def normalize(v):
norm = np.linalg.norm(v)
if norm == 0:
return v
return v / norm
def randcolors(elemlist):
for elem in elemlist:
yield elem, tuple(int(x) for x in list(np.random.choice(range(256), size=3)))
nfeatures = 2000
fastTreshold = 5
path = io.BytesIO(urllib.request.urlopen('http://10.0.0.128/capture').read())
previmg = np.array(Image.open(path).convert('RGB'))
previmg = cv2.rotate(previmg[:,:,::-1], cv2.ROTATE_90_CLOCKWISE) # RBG to BGR
img = previmg
while 1:
previmg = img
path = io.BytesIO(urllib.request.urlopen('http://10.0.0.128/capture').read())
img = np.array(Image.open(path).convert('RGB'))
img = cv2.rotate(img[:,:,::-1], cv2.ROTATE_90_CLOCKWISE) # RBG to BGR
# cv2.imshow('capture', img)
# k = cv2.waitKey(1) & 0xFF
# if k == 27:
# break
# continue
orb = cv2.ORB_create(nfeatures=nfeatures, fastThreshold=fastTreshold)
kp1, des1 = orb.detectAndCompute(previmg, None)
kp2, des2 = orb.detectAndCompute(img, None)
if len(kp1) == 0 or len(kp2) == 0:
continue
desc_matcher = cv2.BFMatcher(cv2.NORM_HAMMING, crossCheck=False)
matches = desc_matcher.match(des1,des2)
matches = sorted(matches, key = lambda x:x.distance)
if len(matches) < nfeatures / 2 and fastTreshold > 3:
fastTreshold -= 1
print('fastTreshold-- (' + str(fastTreshold) + ')')
if len(matches) == nfeatures:
fastTreshold += 1
print('fastTreshold++ (' + str(fastTreshold) + ')')
vectors = [np.subtract(kp1[m.queryIdx].pt, kp2[m.trainIdx].pt) for m in matches]
median = normalize(np.median(vectors, axis=0))
rated = np.array([
(m, v, (np.dot(normalize(v), median) if | np.any(v) | numpy.any |
# 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]) | numpy.array |
import os
import tensorflow as tf
import matplotlib.pyplot as plt
import random
import pandas as pd
import numpy as np
import keras.initializers
import keras.optimizers
from networkx import Graph, find_cliques
from sklearn.metrics import roc_curve, auc
from keras.layers import Concatenate, Input, Embedding, Lambda, Activation, BatchNormalization
from keras.layers.core import Dense, Dropout, Reshape
from keras.models import load_model, model_from_json, model_from_yaml, Model
from keras.utils.vis_utils import plot_model
from keras.callbacks import TensorBoard
from .datasets import DataSet
from .importing_modules import *
class NeuralNetworkConfig:
def __init__(self, categorical_input: str="cat_input", continuous_input: str="cont_input", output: str="output",
reshaped_output: str="reshaped_output", noisy_layer: str="noisy", kernel_initializer: str="uniform",
hidden: str = "hidden", reshaped: str="reshaped", dropout: str="dropout", merge: str="merge",
activation: str="relu", output_activation: str="sigmoid", batch_normalization: bool=False):
self.kernel_initializer = kernel_initializer
self.activation = activation
self.output_activation = output_activation
self.cont_input = continuous_input
self.cat_input = categorical_input
self.hidden = hidden
self.noisy_layer = noisy_layer
self.reshaped = reshaped
self.merge = merge
self.dropout = dropout
self.output = output
self.reshaped_output = reshaped_output
self.batch_normalization = batch_normalization
class NeuralNetwork:
def __init__(self, model):
self.__model = model
def get_model(self):
return self.__model
@classmethod
def from_file(cls, from_file: str):
model = load_model(from_file)
return cls(model)
def get_layer(self, name):
return self.__model.get_layer(name)
def get_weights(self):
return self.__model.get_weights()
def set_weights(self, weights):
self.__model.set_weights(weights)
def get_weights_for_layer(self, feature):
return self.__model.get_layer(feature).get_weights()
def get_weights_with_name(self):
model = self.__model
names = [layer.name for layer in model.layers]
weights = []
for name in names:
weights.append(model.get_layer(name).get_weights())
return dict(zip(names, weights))
def set_weights_by_name(self, weights):
for name, weight in weights.items():
self.__model.get_layer(name).set_weights(weight)
def save_plot(self, to_file='model_plot.svg', shapes=False, layer_names=False):
if to_file:
plot_model(self.__model, to_file=to_file, show_shapes=shapes, show_layer_names=layer_names)
def compile(self, loss='binary_crossentropy', lr=0.001):
optimizer=keras.optimizers.Adam(lr=lr)
self.__model.compile(loss=loss, optimizer=optimizer, metrics=['accuracy'])
def export(self, to_file):
if to_file:
name, ext = os.path.splitext(to_file)
if ext == '.h5':
self.__model.save(to_file)
elif ext == '.json':
model_json = self.__model.to_json()
with(to_file, 'w') as json_file:
json_file.write(model_json)
elif ext == '.yaml':
model_yaml = self.__model.to_yaml()
with(to_file, 'w') as yaml_file:
yaml_file.write(model_yaml)
class DenseNeuralNetwork(NeuralNetwork):
@classmethod
def from_scratch(cls, config: NeuralNetworkConfig, dataset, hidden_units: int,
embedding_size: int = 10, dropout_rate: float = 0.0,
output_units=1, embedding_layers_trainable=True):
categorical_data = dataset.get_data(without_resulting_feature=True).select_dtypes(include='category')
continuous_features = dataset.get_data(without_resulting_feature=True).select_dtypes(
exclude='category').columns.size
if isinstance(categorical_data, pd.DataFrame):
categorical_data_categories = {}
for column in categorical_data:
categorical_data_categories[column] = categorical_data[column].cat.categories.size
categorical_data = categorical_data_categories
model = DenseNeuralNetwork._build(config, categorical_data, continuous_features, hidden_units, embedding_size,
dropout_rate, output_units, embedding_layers_trainable)
return cls(model)
@staticmethod
def _build(config, categorical_data_categories, continuous_features: int, hidden_units: int, embedding_size: int,
dropout_rate, output_units: int, embedding_layers_trainable):
# create input layer for continuous data
continuous_input = Input(shape=(continuous_features,), name=config.cont_input)
reshaped_continuous_input = Reshape((1, continuous_features),
name=config.reshaped)(continuous_input)
# create input layers complemented by embedding layers to handle categorical features
embedding_layers = []
categorical_inputs = []
for feature, size in categorical_data_categories.items():
categorical_input = Input((1,), name=config.cat_input + "_" + feature)
categorical_inputs.append(categorical_input)
embedding_layer = Embedding(size, embedding_size, name=feature, trainable=embedding_layers_trainable)(
categorical_input)
embedding_layers.append(embedding_layer)
# merge all inputs
merge_layer = Concatenate(name=config.merge)(embedding_layers + [reshaped_continuous_input])
# hidden layers
hidden_layer = Dense(hidden_units, kernel_initializer=config.kernel_initializer,
name=config.hidden)(merge_layer)
if config.batch_normalization:
hidden_layer = BatchNormalization()(hidden_layer)
hidden_layer = Activation(config.activation)(hidden_layer)
dropout_layer = Dropout(dropout_rate, name=config.dropout)(hidden_layer)
# output_layer
output_layer = Dense(output_units, name=config.output)(dropout_layer)
output_layer = Activation(config.output_activation)(output_layer)
# add reshape layer since output should be vector
output_layer = Reshape((1,), name=config.reshaped_output)(output_layer)
# create final model
model = Model(inputs=categorical_inputs + [continuous_input], outputs=output_layer)
return model
class OptimizedNeuralNetwork(NeuralNetwork):
@classmethod
def from_scratch(cls, config: NeuralNetworkConfig, dataset: DataSet, correlation_info: list, embedding_size: int=10,
dropout_rate: float=0.0, output_units=1):
flatten_correlation = [item for sublist in correlation_info for item in sublist]
features = dataset.get_data(without_resulting_feature=True).columns
if not all(elem in features for elem in flatten_correlation):
return None
diff = list(set(features) - set(flatten_correlation))
diff = [[item] for item in diff]
correlation_info.extend(diff)
categorical_data = dataset.get_data(without_resulting_feature=True).select_dtypes(include='category')
continuous_features = dataset.get_data(without_resulting_feature=True).select_dtypes(exclude='category').columns
if isinstance(categorical_data, pd.DataFrame):
categorical_data_categories = {}
for column in categorical_data:
categorical_data_categories[column] = categorical_data[column].cat.categories.size
categorical_data = categorical_data_categories
model = OptimizedNeuralNetwork._build(config, categorical_data, continuous_features, correlation_info,
embedding_size, dropout_rate, output_units)
return cls(model)
@staticmethod
def _build(config: NeuralNetworkConfig, categorical_data_categories: dict, continuous_features: list,
correlation_info: list,embedding_size: int, dropout_rate: float, output_units: int):
feature_layers = {}
hidden_layers = []
inputs = []
for feature, size in categorical_data_categories.items():
categorical_input = Input((1,), name=config.cat_input + "_" + feature)
inputs.append(categorical_input)
embedding_layer = Embedding(size, embedding_size, name=feature)(categorical_input)
feature_layers[feature] = embedding_layer
for feature in continuous_features:
continuous_input = Input((1,), name=config.cont_input + "_" + feature)
inputs.append(continuous_input)
reshaped_continuous_input = Reshape((1, 1), name=feature)(continuous_input)
feature_layers[feature] = reshaped_continuous_input
for couple in correlation_info:
coupled_layers = [feature_layers[feature] for feature in couple]
if len(couple) > 1:
merge_layer = Concatenate()(coupled_layers)
hidden_layer = Dense(1, kernel_initializer=config.kernel_initializer)(merge_layer)
if config.batch_normalization:
hidden_layer = BatchNormalization()(hidden_layer)
hidden_layer = Activation(config.activation)(hidden_layer)
else:
hidden_layer = Dense(1, kernel_initializer=config.kernel_initializer)(coupled_layers[0])
if config.batch_normalization:
hidden_layer = BatchNormalization()(hidden_layer)
hidden_layer = Activation(config.activation)(hidden_layer)
hidden_layers.append(hidden_layer)
merge_layer = Concatenate()(hidden_layers)
dropout_layer = Dropout(dropout_rate, name=config.dropout)(merge_layer)
# output_layer
output_layer = Dense(1, name=config.output)(dropout_layer)
output_layer = Activation(config.output_activation)(output_layer)
# add reshape layer since output should be vector
output_layer = Reshape((output_units,), name=config.reshaped_output)(output_layer)
# create final model
model = Model(inputs=inputs, outputs=output_layer)
return model
class Trainer:
def __init__(self, nnet: NeuralNetwork, training_dataset, training_target, batch_size=32, epochs=1000):
self.__nnet = nnet
self.__training_dataset = training_dataset
self.__training_target = training_target
self.__batch_size = batch_size
self.__epochs = epochs
self.__score = None
self._preprocess_dataset()
def _preprocess_dataset(self):
categorical_data = DataSet.dataframe_to_series(self.__training_dataset.get_data(without_resulting_feature=True).select_dtypes(include='category'))
if isinstance(self.__nnet, OptimizedNeuralNetwork):
continuous_data = DataSet.dataframe_to_series(self.__training_dataset.get_data(without_resulting_feature=True).select_dtypes(exclude='category'))
self.__training_dataset = [*categorical_data, *continuous_data]
else:
continuous_data = self.__training_dataset.get_data().select_dtypes(exclude='category').values
self.__training_dataset = [*categorical_data, continuous_data]
def train(self, verbose=1):
tensorboard = TensorBoard(log_dir="./logs")
self.__nnet.get_model().fit(self.__training_dataset, self.__training_target, batch_size=self.__batch_size,
epochs=self.__epochs, verbose=verbose, shuffle=False, callbacks=[tensorboard])
def evaluate(self, verbose=1):
self.__score = self.__nnet.get_model().evaluate(self.__training_dataset, self.__training_target,
batch_size=self.__batch_size, verbose=verbose)
def get_score(self):
return self.__score
class Predictor:
def __init__(self, nnet: NeuralNetwork, dataset: DataSet):
self._nnet = nnet
self._dataset = dataset
self._score = {}
self._prediction = []
self._preprocess()
def _preprocess(self):
categorical_data = DataSet.dataframe_to_series(self._dataset.get_data().select_dtypes(include='category'))
if isinstance(self._nnet, OptimizedNeuralNetwork):
continuous_data = DataSet.dataframe_to_series(self._dataset.get_data().select_dtypes(exclude='category'))
self._dataset = [*categorical_data, *continuous_data]
else:
continuous_data = self._dataset.get_data().select_dtypes(exclude='category').values
self._dataset = [*categorical_data, continuous_data]
def predict(self):
self._prediction = self._nnet.get_model().predict(self._dataset).flatten()
return self._prediction
def evaluate(self, real_values, show_plot: bool = False):
if len(self._prediction) > 0:
rounded_pred = np.round(self._prediction)
tp = np.sum(np.logical_and(rounded_pred == 1, real_values == 1))
tn = np.sum(np.logical_and(rounded_pred == 0, real_values == 0))
fp = np.sum(np.logical_and(rounded_pred == 1, real_values == 0))
fn = np.sum( | np.logical_and(rounded_pred == 0, real_values == 1) | numpy.logical_and |
import sys
import tensorflow as tf
import pdb
import numpy as np
import myParams
import GTools as GT
import scipy.io
import h5py
import time
FLAGS = tf.app.flags.FLAGS
def setup_inputs(sess, filenames, image_size=None, capacity_factor=3, TestStuff=False):
batch_size=myParams.myDict['batch_size']
channelsIn=myParams.myDict['channelsIn']
channelsOut=myParams.myDict['channelsOut']
DataH=myParams.myDict['DataH']
DataW=myParams.myDict['DataW']
LabelsH=myParams.myDict['LabelsH']
LabelsW=myParams.myDict['LabelsW']
if myParams.myDict['InputMode'] == 'I2I_ApplySens':
print('I2I loading labels ' + time.strftime("%Y-%m-%d %H:%M:%S"))
DatasetMatFN=myParams.myDict['LabelsMatFN']
f = h5py.File(DatasetMatFN, 'r')
nToLoad=myParams.myDict['nToLoad']
LoadAndRunOnData=myParams.myDict['LoadAndRunOnData']>0
if LoadAndRunOnData:
nToLoad=3
labels=f['Data'][1:nToLoad]
print('Loaded images ' + time.strftime("%Y-%m-%d %H:%M:%S"))
SensFN='/media/a/H2/home/a/gUM/ESensCC128.mat'
SensCC=scipy.io.loadmat(SensFN)
Sens=SensCC['ESensCC128']
SensMsk=SensCC['MskS']
SensMsk=np.reshape(SensMsk,(SensMsk.shape[0],SensMsk.shape[1],1))
def ConcatCOnDim(X,dim): return tf.cast(tf.concat([tf.real(X),tf.imag(X)],axis=dim),tf.float32)
def myrot90(X): return tf.transpose(X, perm=[1,0,2])
with tf.device('/gpu:0'):
TFL = tf.constant(np.int32(labels))
Idx=tf.random_uniform([1],minval=0,maxval=TFL.shape[0],dtype=tf.int32)
labelR=tf.slice(TFL,[Idx[0],0,0,0],[1,-1,-1,1])
labelI=tf.slice(TFL,[Idx[0],0,0,1],[1,-1,-1,1])
labelR=tf.cast(labelR,tf.complex64)
labelI=tf.cast(labelI,tf.complex64)
label=tf.cast((labelR + 1j*labelI)/30000.0, tf.complex64)
myParams.myDict['channelsOut']=1
myParams.myDict['LabelsH']=labels.shape[1]
myParams.myDict['LabelsW']=labels.shape[2]
myParams.myDict['DataH']=labels.shape[1]
myParams.myDict['DataW']=labels.shape[2]
label = tf.reshape(label, [LabelsH, LabelsW, 1])
label = tf.image.random_flip_left_right(label)
label = tf.image.random_flip_up_down(label)
u1=tf.random_uniform([1])
label=tf.cond(u1[0]<0.5, lambda: tf.identity(label), lambda: myrot90(label))
TFMsk = tf.constant(np.complex64(SensMsk))
TFSens = tf.constant(np.complex64(Sens))
label=tf.multiply(label,TFMsk)
feature=label
# label=ConcatCOnDim(label,2)
label = tf.cast(tf.abs(label),tf.float32)
feature=tf.multiply(feature,TFSens)
feature=ConcatCOnDim(feature,2)
features, labels = tf.train.batch([feature, label],batch_size=batch_size,num_threads=4,capacity = capacity_factor*batch_size,name='labels_and_features')
tf.train.start_queue_runners(sess=sess)
return features, labels
if myParams.myDict['InputMode'] == 'I2I_B0':
print('I2I loading labels ' + time.strftime("%Y-%m-%d %H:%M:%S"))
DatasetMatFN=myParams.myDict['LabelsMatFN']
f = h5py.File(DatasetMatFN, 'r')
nToLoad=myParams.myDict['nToLoad']
LoadAndRunOnData=myParams.myDict['LoadAndRunOnData']>0
if LoadAndRunOnData:
nToLoad=3
labels=f['Data'][1:nToLoad]
LMin=np.float32(f['Min'])
LRange=np.float32(f['Range'])
print('Min, Range: %f,%f' % (LMin,LRange))
print('Loaded images ' + time.strftime("%Y-%m-%d %H:%M:%S"))
print('I2I loading features ' + time.strftime("%Y-%m-%d %H:%M:%S"))
DatasetMatFN=myParams.myDict['FeaturesMatFN']
f = h5py.File(DatasetMatFN, 'r')
features=f['Data'][1:nToLoad]
FMin=np.float32(f['Min'])
FRange=np.float32(f['Range'])
print('Min, Range: %f,%f' % (FMin,FRange))
print('Loaded featuress ' + time.strftime("%Y-%m-%d %H:%M:%S"))
TFL = tf.constant(np.int16(labels))
TFF = tf.constant(np.int16(features))
Idx=tf.random_uniform([1],minval=0,maxval=TFL.shape[0],dtype=tf.int32)
label=tf.slice(TFL,[Idx[0],0,0],[1,-1,-1,])
feature=tf.slice(TFF,[Idx[0],0,0,0],[1,-1,-1,-1])
label = tf.cast(label, tf.float32)
feature = tf.cast(feature, tf.float32)
label=(label*LRange/30000.0)+LMin
feature=(feature*FRange/30000.0)+FMin
if labels.ndim==4:
label = tf.reshape(label, [LabelsH, LabelsW, TFL.shape[3]])
else:
label = tf.reshape(label, [LabelsH, LabelsW, 1])
if features.ndim==4:
feature = tf.reshape(feature, [LabelsH, LabelsW, TFF.shape[3]])
else:
feature = tf.reshape(feature, [LabelsH, LabelsW, 1])
features, labels = tf.train.batch([feature, label],batch_size=batch_size,num_threads=4,capacity = capacity_factor*batch_size,name='labels_and_features')
tf.train.start_queue_runners(sess=sess)
return features, labels
if myParams.myDict['InputMode'] == 'I2I':
print('I2I loading labels ' + time.strftime("%Y-%m-%d %H:%M:%S"))
DatasetMatFN=myParams.myDict['LabelsMatFN']
# DatasetMatFN='/media/a/H2/home/a/gUM/GRE_U1.4_Labels.mat'
f = h5py.File(DatasetMatFN, 'r')
nToLoad=myParams.myDict['nToLoad']
LoadAndRunOnData=myParams.myDict['LoadAndRunOnData']>0
if LoadAndRunOnData:
nToLoad=3
labels=f['labels'][1:nToLoad]
print('Loaded images ' + time.strftime("%Y-%m-%d %H:%M:%S"))
print('I2I loading features ' + time.strftime("%Y-%m-%d %H:%M:%S"))
DatasetMatFN=myParams.myDict['FeaturesMatFN']
# DatasetMatFN='/media/a/H2/home/a/gUM/GRE_U1.4_Features.mat'
f = h5py.File(DatasetMatFN, 'r')
features=f['features'][1:nToLoad]
print('Loaded featuress ' + time.strftime("%Y-%m-%d %H:%M:%S"))
TFL = tf.constant(np.int16(labels))
TFF = tf.constant(np.int16(features))
Idx=tf.random_uniform([1],minval=0,maxval=TFL.shape[0],dtype=tf.int32)
# label=tf.slice(TFL,[Idx[0],0,0],[1,-1,-1])
label=tf.slice(TFL,[Idx[0],0,0,0],[1,-1,-1,-1])
feature=tf.slice(TFF,[Idx[0],0,0,0],[1,-1,-1,-1])
label = tf.cast(label, tf.float32)
feature = tf.cast(feature, tf.float32)
if labels.ndim==4:
label = tf.reshape(label, [LabelsH, LabelsW, TFL.shape[3]])
else:
label = tf.reshape(label, [LabelsH, LabelsW, 1])
if features.ndim==4:
feature = tf.reshape(feature, [LabelsH, LabelsW, TFF.shape[3]])
else:
feature = tf.reshape(feature, [LabelsH, LabelsW, 1])
features, labels = tf.train.batch([feature, label],batch_size=batch_size,num_threads=4,capacity = capacity_factor*batch_size,name='labels_and_features')
tf.train.start_queue_runners(sess=sess)
return features, labels
if myParams.myDict['InputMode'] == 'RegridTry3FMB':
BaseTSDataP=myParams.myDict['BaseTSDataP']
BaseNUFTDataP=myParams.myDict['BaseNUFTDataP']
B0Data=scipy.io.loadmat(BaseTSDataP + 'B0TS.mat')
TSBFA=B0Data['TSBFA']
TSCA=B0Data['TSCA']
TSBFB=B0Data['TSBFB']
TSCB=B0Data['TSCB']
SensCC=scipy.io.loadmat(BaseTSDataP + 'SensCC1.mat')
SensA=SensCC['SensCCA']
SensMskA=SensCC['SensMskA']
SensB=SensCC['SensCCB']
SensMskB=SensCC['SensMskB']
SensMskA=np.reshape(SensMskA,(SensMskA.shape[0],SensMskA.shape[1],1))
SensMskB=np.reshape(SensMskB,(SensMskB.shape[0],SensMskB.shape[1],1))
TFMskA = tf.constant(np.complex64(SensMskA))
TFMskB = tf.constant(np.complex64(SensMskB))
print('loading images ' + time.strftime("%Y-%m-%d %H:%M:%S"))
# f = h5py.File('/media/a/H1/HCPData_256x256_int16.mat', 'r')
DatasetMatFN=myParams.myDict['DatasetMatFN']
f = h5py.File(DatasetMatFN, 'r')
nToLoad=myParams.myDict['nToLoad']
# nToLoad=10000
LoadAndRunOnData=myParams.myDict['LoadAndRunOnData']>0
if LoadAndRunOnData:
nToLoad=3
I=f['HCPData'][1:nToLoad]
print('Loaded images ' + time.strftime("%Y-%m-%d %H:%M:%S"))
H=LabelsH
W=LabelsW
TFI = tf.constant(np.int16(I))
IdxA=tf.random_uniform([1],minval=0,maxval=I.shape[0],dtype=tf.int32)
IdxB=tf.random_uniform([1],minval=0,maxval=I.shape[0],dtype=tf.int32)
featureA=tf.slice(TFI,[IdxA[0],0,0],[1,-1,-1])
featureB=tf.slice(TFI,[IdxB[0],0,0],[1,-1,-1])
featureA=tf.transpose(featureA, perm=[1,2,0])
featureB=tf.transpose(featureB, perm=[1,2,0])
featureA = tf.image.random_flip_left_right(featureA)
featureA = tf.image.random_flip_up_down(featureA)
u1=tf.random_uniform([1])
featureA=tf.cond(u1[0]<0.5, lambda: tf.identity(featureA), lambda: tf.image.rot90(featureA))
featureB = tf.image.random_flip_left_right(featureB)
featureB = tf.image.random_flip_up_down(featureB)
u1=tf.random_uniform([1])
featureB=tf.cond(u1[0]<0.5, lambda: tf.identity(featureB), lambda: tf.image.rot90(featureB))
featureA = tf.random_crop(featureA, [H, W, 1])
featureB = tf.random_crop(featureB, [H, W, 1])
featureA = tf.cast(featureA, tf.int32)
featureB = tf.cast(featureB, tf.int32)
mxA=tf.maximum(tf.reduce_max(featureA),1)
mxB=tf.maximum(tf.reduce_max(featureB),1)
featureA = tf.cast(featureA/mxA, tf.complex64)
featureB = tf.cast(featureB/mxB, tf.complex64)
featureA=tf.multiply(featureA,TFMskA)
featureB=tf.multiply(featureB,TFMskB)
LFac=myParams.myDict['RandomPhaseLinearFac']
QFac=myParams.myDict['RandomPhaseQuadraticFac']
SFac=myParams.myDict['RandomPhaseScaleFac']
QA=GT.TFGenerateRandomSinPhase(H, W,LFac,QFac,SFac) # (nx=100,ny=120,LFac=5,QFac=0.1,SFac=2):
QB=GT.TFGenerateRandomSinPhase(H, W,LFac,QFac,SFac)
CurIWithPhaseA=featureA*tf.reshape(QA,[H,W,1])
CurIWithPhaseB=featureB*tf.reshape(QB,[H,W,1])
NUFTData=scipy.io.loadmat(BaseNUFTDataP + 'TrajForNUFT.mat')
Kd=NUFTData['Kd']
P=NUFTData['P']
SN=NUFTData['SN']
Trajm2=NUFTData['Trajm2']
nTraj=Trajm2.shape[1]
nCh=SensA.shape[2]
nTSC=TSCA.shape[2]
# ggg Arrived till here. CAIPI supposed to be into TSB anyway
SNcA,paddings,sp_R,sp_I,TSBFXA=GT.TF_TSNUFFT_Prepare(SN,SensA,TSCA,TSBFA,Kd,P)
SNcB,paddings,sp_R,sp_I,TSBFXB=GT.TF_TSNUFFT_Prepare(SN,SensB,TSCB,TSBFB,Kd,P)
def ConcatCI(X): return tf.concat([tf.real(X),tf.imag(X)],axis=0)
def ConcatCIOn2(X): return tf.concat([tf.real(X),tf.imag(X)],axis=2)
if myParams.myDict['BankSize']>0:
BankSize=myParams.myDict['BankSize']
BankK=myParams.myDict['BankK']
label_indexes = tf.constant(np.int32(np.arange(0,BankSize)),dtype=tf.int32)
BankK_indexes = tf.constant(np.int32(np.arange(0,BankSize*BankK)),dtype=tf.int32)
Bankdataset = tf.data.Dataset.from_tensor_slices(label_indexes)
Bankdataset = Bankdataset.repeat(count=None)
Bankiter = Bankdataset.make_one_shot_iterator()
label_index = Bankiter.get_next()
label_index=tf.cast(label_index,tf.int32)
label_index=label_index*2
BankKdataset = tf.data.Dataset.from_tensor_slices(BankK_indexes)
BankKdataset = BankKdataset.repeat(count=None)
BankKiter = BankKdataset.make_one_shot_iterator()
label_indexK = BankKiter.get_next()
label_indexK=tf.cast(label_indexK,tf.int32)
label_indexK=label_indexK*2
IdxAX=tf.random_uniform([1],minval=0,maxval=BankSize,dtype=tf.int32)
IdxBX=tf.random_uniform([1],minval=0,maxval=BankSize,dtype=tf.int32)
with tf.device('/gpu:0'):
OnlyTakeFromBank=tf.greater(label_indexK,label_index)
with tf.variable_scope("aaa", reuse=True):
Bank=tf.get_variable("Bank",dtype=tf.float32)
LBank=tf.get_variable("LBank",dtype=tf.float32)
def f2(): return tf.scatter_nd_update(Bank,[[label_index],[label_index+1]], [ConcatCI(tf.reshape(tf.transpose(GT.TF_TSNUFFT_Run(CurIWithPhaseA,SNcA,paddings,nTraj,nTSC,nCh,sp_R,sp_I,TSBFXA), perm=[1,0]),[nTraj*nCh,1,1])),ConcatCI(tf.reshape(tf.transpose(GT.TF_TSNUFFT_Run(CurIWithPhaseB,SNcB,paddings,nTraj,nTSC,nCh,sp_R,sp_I,TSBFXB), perm=[1,0]),[nTraj*nCh,1,1]))])
def f2L(): return tf.scatter_nd_update(LBank,[[label_index],[label_index+1]], [ConcatCIOn2(CurIWithPhaseA),ConcatCIOn2(CurIWithPhaseB)])
Bank = tf.cond(OnlyTakeFromBank, lambda: tf.identity(Bank), f2)
LBank = tf.cond(OnlyTakeFromBank, lambda: tf.identity(LBank), f2L)
IdxAF = tf.cond(OnlyTakeFromBank, lambda: tf.identity(IdxAX[0]*2), lambda: tf.identity(label_index))
IdxBF = tf.cond(OnlyTakeFromBank, lambda: tf.identity(IdxBX[0]*2+1), lambda: tf.identity(label_index+1))
# Take from bank in any case
featureAX = tf.slice(Bank,[IdxAF,0,0,0],[1,-1,-1,-1])
featureAX = tf.reshape(featureAX, [DataH, 1, 1])
featureBX = tf.slice(Bank,[IdxBF,0,0,0],[1,-1,-1,-1])
featureBX = tf.reshape(featureBX, [DataH, 1, 1])
featureX=featureAX+featureBX # That's MB
labelAX = tf.slice(LBank,[IdxAF,0,0,0],[1,-1,-1,-1])
labelAX = tf.reshape(labelAX, [H, W, 2])
labelBX = tf.slice(LBank,[IdxBF,0,0,0],[1,-1,-1,-1])
labelBX = tf.reshape(labelBX, [H, W, 2])
labelX = tf.concat([labelAX,labelBX],axis=1);
features, labels = tf.train.batch([featureX, labelX],batch_size=batch_size,num_threads=4,capacity = capacity_factor*batch_size,name='labels_and_features')
else:
featureA=GT.TF_TSNUFFT_Run(CurIWithPhaseA,SNcA,paddings,nTraj,nTSC,nCh,sp_R,sp_I,TSBFXA)
featureB=GT.TF_TSNUFFT_Run(CurIWithPhaseB,SNcB,paddings,nTraj,nTSC,nCh,sp_R,sp_I,TSBFXB)
feature=featureA+featureB # That's MB
feature=tf.transpose(feature, perm=[1,0])
F=tf.reshape(feature,[nTraj*nCh,1,1])
feature=ConcatCI(F)
CurIWithPhase=tf.concat([CurIWithPhaseA,CurIWithPhaseB],axis=1);
label=tf.concat([tf.real(CurIWithPhase),tf.imag(CurIWithPhase)],axis=2)
features, labels = tf.train.batch([feature, label],batch_size=batch_size,num_threads=4,capacity = capacity_factor*batch_size,name='labels_and_features')
tf.train.start_queue_runners(sess=sess)
return features, labels
if myParams.myDict['InputMode'] == 'RegridTry3F':
BaseTSDataP=myParams.myDict['BaseTSDataP']
BaseNUFTDataP=myParams.myDict['BaseNUFTDataP']
B0Data=scipy.io.loadmat(BaseTSDataP + 'B0TS.mat')
# Sens=B0Data['Sens']
TSBF=B0Data['TSBF']
TSC=B0Data['TSC']
SensCC=scipy.io.loadmat(BaseTSDataP + 'SensCC1.mat')
Sens=SensCC['SensCC']
SensMsk=SensCC['SensMsk']
SensMsk=np.reshape(SensMsk,(SensMsk.shape[0],SensMsk.shape[1],1))
TFMsk = tf.constant(np.complex64(SensMsk))
print('loading images ' + time.strftime("%Y-%m-%d %H:%M:%S"))
# I=scipy.io.loadmat('/media/a/H1/First3kIm256x256Magint16.mat')
# I=I['First3kIm256x256Magint16']
DatasetMatFN=myParams.myDict['DatasetMatFN']
# f = h5py.File('/media/a/H1/HCPData_256x256_int16.mat', 'r')
f = h5py.File(DatasetMatFN, 'r')
# nToLoad=10000
nToLoad=myParams.myDict['nToLoad']
LoadAndRunOnData=myParams.myDict['LoadAndRunOnData']>0
if LoadAndRunOnData:
nToLoad=3
I=f['HCPData'][1:nToLoad]
print('Loaded images ' + time.strftime("%Y-%m-%d %H:%M:%S"))
# I=scipy.io.loadmat('/media/a/H1/First1kIm256x256Magint16.mat')
# I=I['First1kIm256x256Magint16']
H=LabelsH
W=LabelsW
TFI = tf.constant(np.int16(I))
Idx=tf.random_uniform([1],minval=0,maxval=I.shape[0],dtype=tf.int32)
feature=tf.slice(TFI,[Idx[0],0,0],[1,-1,-1])
feature=tf.transpose(feature, perm=[1,2,0])
feature = tf.image.random_flip_left_right(feature)
feature = tf.image.random_flip_up_down(feature)
# u1 = tf.distributions.Uniform(low=0.0, high=1.0)
u1=tf.random_uniform([1])
feature=tf.cond(u1[0]<0.5, lambda: tf.identity(feature), lambda: tf.image.rot90(feature))
# tf.image.rot90( image, k=1, name=None)
# MYGlobalStep = tf.Variable(0, trainable=False, name='Myglobal_step')
# MYGlobalStep = MYGlobalStep+1
# feature=tf.cond(MYGlobalStep>0, lambda: tf.identity(feature), lambda: tf.identity(feature))
# feature = tf.Print(feature,[MYGlobalStep,],message='MYGlobalStep:')
# image = tf.image.random_saturation(image, .95, 1.05)
# image = tf.image.random_brightness(image, .05)
#image = tf.image.random_contrast(image, .95, 1.05)
feature = tf.random_crop(feature, [H, W, 1])
feature = tf.cast(feature, tf.int32)
mx=tf.reduce_max(feature)
mx=tf.maximum(mx,1)
feature = tf.cast(feature/mx, tf.complex64)
feature=tf.multiply(feature,TFMsk)
Q=GT.TFGenerateRandomSinPhase(H, W)
CurIWithPhase=feature*tf.reshape(Q,[H,W,1])
label=tf.concat([tf.real(CurIWithPhase),tf.imag(CurIWithPhase)],axis=2)
NUFTData=scipy.io.loadmat(BaseNUFTDataP + 'TrajForNUFT.mat')
Kd=NUFTData['Kd']
P=NUFTData['P']
SN=NUFTData['SN']
Trajm2=NUFTData['Trajm2']
nTraj=Trajm2.shape[1]
nCh=Sens.shape[2]
nTSC=TSC.shape[2]
SNc,paddings,sp_R,sp_I,TSBFX=GT.TF_TSNUFFT_Prepare(SN,Sens,TSC,TSBF,Kd,P)
# feature=GT.TF_TSNUFFT_Run(CurIWithPhase,SNc,paddings,nTraj,nTSC,nCh,sp_R,sp_I,TSBFX)
# feature=tf.transpose(feature, perm=[1,0])
# F=tf.reshape(feature,[nTraj*nCh,1,1])
# feature=tf.concat([tf.real(F),tf.imag(F)],axis=0)
def ConcatCI(X): return tf.concat([tf.real(X),tf.imag(X)],axis=0)
# feature=ConcatCI(F)
# feature=ConcatCI(tf.reshape(tf.transpose(GT.TF_TSNUFFT_Run(CurIWithPhase,SNc,paddings,nTraj,nTSC,nCh,sp_R,sp_I,TSBFX), perm=[1,0]),[nTraj*nCh,1,1]))
# ggg Signal Bank stuff:
if myParams.myDict['BankSize']>0:
BankSize=myParams.myDict['BankSize']
BankK=myParams.myDict['BankK']
label_indexes = tf.constant(np.int32(np.arange(0,BankSize)),dtype=tf.int32)
BankK_indexes = tf.constant(np.int32(np.arange(0,BankSize*BankK)),dtype=tf.int32)
Bankdataset = tf.data.Dataset.from_tensor_slices(label_indexes)
Bankdataset = Bankdataset.repeat(count=None)
Bankiter = Bankdataset.make_one_shot_iterator()
label_index = Bankiter.get_next()
label_index=tf.cast(label_index,tf.int32)
BankKdataset = tf.data.Dataset.from_tensor_slices(BankK_indexes)
BankKdataset = BankKdataset.repeat(count=None)
BankKiter = BankKdataset.make_one_shot_iterator()
label_indexK = BankKiter.get_next()
label_indexK=tf.cast(label_indexK,tf.int32)
with tf.device('/gpu:0'):
OnlyTakeFromBank=tf.greater(label_indexK,label_index)
with tf.variable_scope("aaa", reuse=True):
Bank=tf.get_variable("Bank",dtype=tf.float32)
LBank=tf.get_variable("LBank",dtype=tf.float32)
def f2(): return tf.scatter_nd_update(Bank,[[label_index]], [ConcatCI(tf.reshape(tf.transpose(GT.TF_TSNUFFT_Run(CurIWithPhase,SNc,paddings,nTraj,nTSC,nCh,sp_R,sp_I,TSBFX), perm=[1,0]),[nTraj*nCh,1,1]))])
def f2L(): return tf.scatter_nd_update(LBank,[[label_index]], [label])
Bank = tf.cond(OnlyTakeFromBank, lambda: tf.identity(Bank), f2)
LBank = tf.cond(OnlyTakeFromBank, lambda: tf.identity(LBank), f2L)
# Take from bank in any case
featureX = tf.slice(Bank,[label_index,0,0,0],[1,-1,-1,-1])
featureX = tf.reshape(featureX, [DataH, 1, 1])
# featureX = tf.Print(featureX,[label_index,label_indexK],message='Taking from bank:')
labelX = tf.slice(LBank,[label_index,0,0,0],[1,-1,-1,-1])
labelX = tf.reshape(labelX, [H, W, 2])
features, labels = tf.train.batch([featureX, labelX],batch_size=batch_size,num_threads=4,capacity = capacity_factor*batch_size,name='labels_and_features')
# feature = tf.cond(TakeFromBank, lambda: tf.identity(Bfeature), lambda: tf.identity(Afeature))
# label = tf.cond(TakeFromBank, lambda: tf.identity(Blabel), lambda: tf.identity(Alabel))
else:
feature=ConcatCI(tf.reshape(tf.transpose(GT.TF_TSNUFFT_Run(CurIWithPhase,SNc,paddings,nTraj,nTSC,nCh,sp_R,sp_I,TSBFX), perm=[1,0]),[nTraj*nCh,1,1]))
features, labels = tf.train.batch([feature, label],batch_size=batch_size,num_threads=4,capacity = capacity_factor*batch_size,name='labels_and_features')
# ggg end Signal Bank stuff:
tf.train.start_queue_runners(sess=sess)
return features, labels
if myParams.myDict['InputMode'] == 'RegridTry3M':
Msk=scipy.io.loadmat('/media/a/DATA/meas_MID244_gBP_VD11_U19_G35S155_4min_FID22439/Sli08/Msk.mat')
Msk=Msk['Msk']
TFMsk = tf.constant(Msk)
FN='/media/a/H1/meas_MID244_gBP_VD11_U19_G35S155_4min_FID22439/AllData_Sli8_6k.mat'
if TestStuff:
print('setup_inputs Test')
ChunkSize=100
ChunkSizeL=400
FN='/media/a/H1/meas_MID244_gBP_VD11_U19_G35S155_4min_FID22439/AllData_Sli8_100.mat'
else:
print('setup_inputs Train')
ChunkSize=1000
ChunkSizeL=4000
f = h5py.File(FN, 'r')
print('loading Data ' + time.strftime("%Y-%m-%d %H:%M:%S"))
I=f['AllDatax'][:]
print('Loaded labels ' + time.strftime("%Y-%m-%d %H:%M:%S"))
f.close()
I=I.astype(np.float32)
f = h5py.File('/media/a/H1/AllImWithPhaseComplexSingle_h5.mat', 'r')
print('Loading labels ' + time.strftime("%Y-%m-%d %H:%M:%S"))
L=f['AllLh5'][0:(ChunkSizeL)]
print('Loaded labels ' + time.strftime("%Y-%m-%d %H:%M:%S"))
f.close()
L=L.astype(np.float32)
TFI = tf.constant(I[0:ChunkSize])
TFIb = tf.constant(I[(ChunkSize):(2*ChunkSize)])
TFIc = tf.constant(I[(2*ChunkSize):(3*ChunkSize)])
TFId = tf.constant(I[(3*ChunkSize):(4*ChunkSize)])
TFL = tf.constant(L)
# place = tf.placeholder(tf.float32, shape=(DataH, DataW, channelsIn))
# placeL = tf.placeholder(tf.float32, shape=(LabelsH, LabelsW, channelsOut))
Idx=tf.random_uniform([1],minval=0,maxval=ChunkSizeL,dtype=tf.int32)
def f1(): return tf.cond(Idx[0]<ChunkSize, lambda: tf.slice(TFI,[Idx[0],0],[1,-1]), lambda: tf.slice(TFIb,[Idx[0]-ChunkSize,0],[1,-1]))
def f2(): return tf.cond(Idx[0]<(3*ChunkSize), lambda: tf.slice(TFIc,[Idx[0]-2*ChunkSize,0],[1,-1]), lambda: tf.slice(TFId,[Idx[0]-3*ChunkSize,0],[1,-1]))
feature=tf.cond(Idx[0]<(2*ChunkSize), f1, f2)
# feature=tf.cond(Idx[0]<ChunkSize, lambda: tf.slice(TFI,[Idx[0],0],[1,-1]), lambda: tf.slice(TFIb,[Idx[0]-ChunkSize,0],[1,-1]))
# feature=tf.slice(TFI,[Idx[0],0],[1,-1])
# feature = tmp.assign(place)
feature = tf.reshape(feature, [DataH, DataW, channelsIn])
feature = tf.cast(feature, tf.float32)
labels = tf.slice(TFL,[Idx[0],0,0,0],[1,-1,-1,-1])
# feature = tmpL.assign(placeL)
labels = tf.reshape(labels, [LabelsH, LabelsW, channelsOut])
label = tf.cast(labels, tf.float32)
label=tf.multiply(label,TFMsk)
# Using asynchronous queues
features, labels = tf.train.batch([feature, label],
batch_size=batch_size,
num_threads=4,
capacity = capacity_factor*batch_size,
name='labels_and_features')
tf.train.start_queue_runners(sess=sess)
return features, labels
if myParams.myDict['InputMode'] == 'SPEN_Local':
SR=scipy.io.loadmat('/media/a/H1/SR.mat')
SR=SR['SR']
SR=np.reshape(SR,[DataH,DataH,1])
SR=np.transpose(SR, (2,0,1))
SR_TF=tf.constant(SR)
# I=scipy.io.loadmat('/media/a/H1/First1kIm256x256Magint16.mat')
# I=I['First1kIm256x256Magint16']
I=scipy.io.loadmat('/media/a/H1/First3kIm256x256Magint16.mat')
I=I['First3kIm256x256Magint16']
TFI = tf.constant(np.float32(I))
Idx=tf.random_uniform([1],minval=0,maxval=3000,dtype=tf.int32)
feature=tf.slice(TFI,[Idx[0],0,0],[1,-1,-1])
feature=tf.transpose(feature, perm=[1,2,0])
feature = tf.random_crop(feature, [DataH, DataW, 1])
mx=tf.reduce_max(feature)
mx=tf.maximum(mx,1)
feature = tf.cast(feature/mx, tf.complex64)
Q=GT.TFGenerateRandomSinPhase(DataH, DataW)
CurIWithPhase=feature*tf.reshape(Q,[DataH,DataW,1])
label=tf.concat([tf.real(CurIWithPhase),tf.imag(CurIWithPhase)],axis=2)
P=tf.transpose(CurIWithPhase, perm=[2,1,0])
F=tf.matmul(P,SR_TF)
F=tf.transpose(F, perm=[2,1,0])
SPENLocalFactor=myParams.myDict['SPENLocalFactor']
F=GT.ExpandWithCopiesOn2(F,DataH,SPENLocalFactor)
feature=tf.concat([tf.real(F),tf.imag(F)],axis=2)
features, labels = tf.train.batch([feature, label],batch_size=batch_size,num_threads=4,capacity = capacity_factor*batch_size,name='labels_and_features')
tf.train.start_queue_runners(sess=sess)
return features, labels
if myParams.myDict['InputMode'] == 'SPEN_FC':
SR=scipy.io.loadmat('/media/a/H1/SR.mat')
SR=SR['SR']
SR=np.reshape(SR,[DataH,DataH,1])
SR=np.transpose(SR, (2,0,1))
SR_TF=tf.constant(SR)
I=scipy.io.loadmat('/media/a/H1/First1kIm256x256Magint16.mat')
I=I['First1kIm256x256Magint16']
TFI = tf.constant( | np.float32(I) | numpy.float32 |
import numpy as np
from . import box # NOQA
from . import Geometry # NOQA
from . import GeometryType, lib
from .decorators import multithreading_enabled, requires_geos, UnsupportedGEOSOperation
__all__ = [
"difference",
"intersection",
"intersection_all",
"symmetric_difference",
"symmetric_difference_all",
"union",
"union_all",
"coverage_union",
"coverage_union_all",
]
@multithreading_enabled
def difference(a, b, grid_size=None, **kwargs):
"""Returns the part of geometry A that does not intersect with geometry B.
If grid_size is nonzero, input coordinates will be snapped to a precision
grid of that size and resulting coordinates will be snapped to that same
grid. If 0, this operation will use double precision coordinates. If None,
the highest precision of the inputs will be used, which may be previously
set using set_precision. Note: returned geometry does not have precision
set unless specified previously by set_precision.
Parameters
----------
a : Geometry or array_like
b : Geometry or array_like
grid_size : float, optional
Precision grid size; requires GEOS >= 3.9.0. Will use the highest
precision of the inputs by default.
**kwargs
For other keyword-only arguments, see the
`NumPy ufunc docs <https://numpy.org/doc/stable/reference/ufuncs.html#ufuncs-kwargs>`_.
See also
--------
set_precision
Examples
--------
>>> from shapely.constructive import normalize
>>> line = Geometry("LINESTRING (0 0, 2 2)")
>>> difference(line, Geometry("LINESTRING (1 1, 3 3)"))
<pygeos.Geometry LINESTRING (0 0, 1 1)>
>>> difference(line, Geometry("LINESTRING EMPTY"))
<pygeos.Geometry LINESTRING (0 0, 2 2)>
>>> difference(line, None) is None
True
>>> box1 = box(0, 0, 2, 2)
>>> box2 = box(1, 1, 3, 3)
>>> normalize(difference(box1, box2))
<pygeos.Geometry POLYGON ((0 0, 0 2, 1 2, 1 1, 2 1, 2 0, 0 0))>
>>> box1 = box(0.1, 0.2, 2.1, 2.1)
>>> difference(box1, box2, grid_size=1) # doctest: +SKIP
<pygeos.Geometry POLYGON ((0 0, 0 2, 1 2, 1 1, 2 1, 2 0, 0 0))>
"""
if grid_size is not None:
if lib.geos_version < (3, 9, 0):
raise UnsupportedGEOSOperation("grid_size parameter requires GEOS >= 3.9.0")
if not np.isscalar(grid_size):
raise ValueError("grid_size parameter only accepts scalar values")
return lib.difference_prec(a, b, grid_size, **kwargs)
return lib.difference(a, b, **kwargs)
@multithreading_enabled
def intersection(a, b, grid_size=None, **kwargs):
"""Returns the geometry that is shared between input geometries.
If grid_size is nonzero, input coordinates will be snapped to a precision
grid of that size and resulting coordinates will be snapped to that same
grid. If 0, this operation will use double precision coordinates. If None,
the highest precision of the inputs will be used, which may be previously
set using set_precision. Note: returned geometry does not have precision
set unless specified previously by set_precision.
Parameters
----------
a : Geometry or array_like
b : Geometry or array_like
grid_size : float, optional
Precision grid size; requires GEOS >= 3.9.0. Will use the highest
precision of the inputs by default.
**kwargs
For other keyword-only arguments, see the
`NumPy ufunc docs <https://numpy.org/doc/stable/reference/ufuncs.html#ufuncs-kwargs>`_.
See also
--------
intersection_all
set_precision
Examples
--------
>>> from shapely.constructive import normalize
>>> line = Geometry("LINESTRING(0 0, 2 2)")
>>> intersection(line, Geometry("LINESTRING(1 1, 3 3)"))
<pygeos.Geometry LINESTRING (1 1, 2 2)>
>>> box1 = box(0, 0, 2, 2)
>>> box2 = box(1, 1, 3, 3)
>>> normalize(intersection(box1, box2))
<pygeos.Geometry POLYGON ((1 1, 1 2, 2 2, 2 1, 1 1))>
>>> box1 = box(0.1, 0.2, 2.1, 2.1)
>>> intersection(box1, box2, grid_size=1) # doctest: +SKIP
<pygeos.Geometry POLYGON ((1 1, 1 2, 2 2, 2 1, 1 1))>
"""
if grid_size is not None:
if lib.geos_version < (3, 9, 0):
raise UnsupportedGEOSOperation("grid_size parameter requires GEOS >= 3.9.0")
if not np.isscalar(grid_size):
raise ValueError("grid_size parameter only accepts scalar values")
return lib.intersection_prec(a, b, grid_size, **kwargs)
return lib.intersection(a, b, **kwargs)
@multithreading_enabled
def intersection_all(geometries, axis=None, **kwargs):
"""Returns the intersection of multiple geometries.
This function ignores None values when other Geometry elements are present.
If all elements of the given axis are None, None is returned.
Parameters
----------
geometries : array_like
axis : int, optional
Axis along which the operation is performed. The default (None)
performs the operation over all axes, returning a scalar value.
Axis may be negative, in which case it counts from the last to the
first axis.
**kwargs
For other keyword-only arguments, see the
`NumPy ufunc.reduce docs <https://numpy.org/doc/stable/reference/generated/numpy.ufunc.reduce.html#numpy.ufunc.reduce>`_.
See also
--------
intersection
Examples
--------
>>> line_1 = Geometry("LINESTRING(0 0, 2 2)")
>>> line_2 = Geometry("LINESTRING(1 1, 3 3)")
>>> intersection_all([line_1, line_2])
<pygeos.Geometry LINESTRING (1 1, 2 2)>
>>> intersection_all([[line_1, line_2, None]], axis=1).tolist()
[<pygeos.Geometry LINESTRING (1 1, 2 2)>]
"""
return lib.intersection.reduce(geometries, axis=axis, **kwargs)
@multithreading_enabled
def symmetric_difference(a, b, grid_size=None, **kwargs):
"""Returns the geometry that represents the portions of input geometries
that do not intersect.
If grid_size is nonzero, input coordinates will be snapped to a precision
grid of that size and resulting coordinates will be snapped to that same
grid. If 0, this operation will use double precision coordinates. If None,
the highest precision of the inputs will be used, which may be previously
set using set_precision. Note: returned geometry does not have precision
set unless specified previously by set_precision.
Parameters
----------
a : Geometry or array_like
b : Geometry or array_like
grid_size : float, optional
Precision grid size; requires GEOS >= 3.9.0. Will use the highest
precision of the inputs by default.
**kwargs
For other keyword-only arguments, see the
`NumPy ufunc docs <https://numpy.org/doc/stable/reference/ufuncs.html#ufuncs-kwargs>`_.
See also
--------
symmetric_difference_all
set_precision
Examples
--------
>>> from shapely.constructive import normalize
>>> line = Geometry("LINESTRING(0 0, 2 2)")
>>> symmetric_difference(line, Geometry("LINESTRING(1 1, 3 3)"))
<pygeos.Geometry MULTILINESTRING ((0 0, 1 1), (2 2, 3 3))>
>>> box1 = box(0, 0, 2, 2)
>>> box2 = box(1, 1, 3, 3)
>>> normalize(symmetric_difference(box1, box2))
<pygeos.Geometry MULTIPOLYGON (((1 2, 1 3, 3 3, 3 1, 2 1, 2 2, 1 2)), ((0 0,...>
>>> box1 = box(0.1, 0.2, 2.1, 2.1)
>>> symmetric_difference(box1, box2, grid_size=1) # doctest: +SKIP
<pygeos.Geometry MULTIPOLYGON (((1 2, 1 3, 3 3, 3 1, 2 1, 2 2, 1 2)), ((0 0,...>
"""
if grid_size is not None:
if lib.geos_version < (3, 9, 0):
raise UnsupportedGEOSOperation("grid_size parameter requires GEOS >= 3.9.0")
if not np.isscalar(grid_size):
raise ValueError("grid_size parameter only accepts scalar values")
return lib.symmetric_difference_prec(a, b, grid_size, **kwargs)
return lib.symmetric_difference(a, b, **kwargs)
@multithreading_enabled
def symmetric_difference_all(geometries, axis=None, **kwargs):
"""Returns the symmetric difference of multiple geometries.
This function ignores None values when other Geometry elements are present.
If all elements of the given axis are None, None is returned.
Parameters
----------
geometries : array_like
axis : int, optional
Axis along which the operation is performed. The default (None)
performs the operation over all axes, returning a scalar value.
Axis may be negative, in which case it counts from the last to the
first axis.
**kwargs
For other keyword-only arguments, see the
`NumPy ufunc.reduce docs <https://numpy.org/doc/stable/reference/generated/numpy.ufunc.reduce.html#numpy.ufunc.reduce>`_.
See also
--------
symmetric_difference
Examples
--------
>>> line_1 = Geometry("LINESTRING(0 0, 2 2)")
>>> line_2 = Geometry("LINESTRING(1 1, 3 3)")
>>> symmetric_difference_all([line_1, line_2])
<pygeos.Geometry MULTILINESTRING ((0 0, 1 1), (2 2, 3 3))>
>>> symmetric_difference_all([[line_1, line_2, None]], axis=1).tolist()
[<pygeos.Geometry MULTILINESTRING ((0 0, 1 1), (2 2, 3 3))>]
"""
return lib.symmetric_difference.reduce(geometries, axis=axis, **kwargs)
@multithreading_enabled
def union(a, b, grid_size=None, **kwargs):
"""Merges geometries into one.
If grid_size is nonzero, input coordinates will be snapped to a precision
grid of that size and resulting coordinates will be snapped to that same
grid. If 0, this operation will use double precision coordinates. If None,
the highest precision of the inputs will be used, which may be previously
set using set_precision. Note: returned geometry does not have precision
set unless specified previously by set_precision.
Parameters
----------
a : Geometry or array_like
b : Geometry or array_like
grid_size : float, optional
Precision grid size; requires GEOS >= 3.9.0. Will use the highest
precision of the inputs by default.
**kwargs
For other keyword-only arguments, see the
`NumPy ufunc docs <https://numpy.org/doc/stable/reference/ufuncs.html#ufuncs-kwargs>`_.
See also
--------
union_all
set_precision
Examples
--------
>>> from shapely.constructive import normalize
>>> line = Geometry("LINESTRING(0 0, 2 2)")
>>> union(line, Geometry("LINESTRING(2 2, 3 3)"))
<pygeos.Geometry MULTILINESTRING ((0 0, 2 2), (2 2, 3 3))>
>>> union(line, None) is None
True
>>> box1 = box(0, 0, 2, 2)
>>> box2 = box(1, 1, 3, 3)
>>> normalize(union(box1, box2))
<pygeos.Geometry POLYGON ((0 0, 0 2, 1 2, 1 3, 3 3, 3 1, 2 1, 2 0, 0 0))>
>>> box1 = box(0.1, 0.2, 2.1, 2.1)
>>> union(box1, box2, grid_size=1) # doctest: +SKIP
<pygeos.Geometry POLYGON ((0 0, 0 2, 1 2, 1 3, 3 3, 3 1, 2 1, 2 0, 0 0))>
"""
if grid_size is not None:
if lib.geos_version < (3, 9, 0):
raise UnsupportedGEOSOperation("grid_size parameter requires GEOS >= 3.9.0")
if not np.isscalar(grid_size):
raise ValueError("grid_size parameter only accepts scalar values")
return lib.union_prec(a, b, grid_size, **kwargs)
return lib.union(a, b, **kwargs)
@multithreading_enabled
def union_all(geometries, grid_size=None, axis=None, **kwargs):
"""Returns the union of multiple geometries.
This function ignores None values when other Geometry elements are present.
If all elements of the given axis are None, None is returned.
If grid_size is nonzero, input coordinates will be snapped to a precision
grid of that size and resulting coordinates will be snapped to that same
grid. If 0, this operation will use double precision coordinates. If None,
the highest precision of the inputs will be used, which may be previously
set using set_precision. Note: returned geometry does not have precision
set unless specified previously by set_precision.
Parameters
----------
geometries : array_like
grid_size : float, optional
Precision grid size; requires GEOS >= 3.9.0. Will use the highest
precision of the inputs by default.
axis : int, optional
Axis along which the operation is performed. The default (None)
performs the operation over all axes, returning a scalar value.
Axis may be negative, in which case it counts from the last to the
first axis.
**kwargs
For other keyword-only arguments, see the
`NumPy ufunc docs <https://numpy.org/doc/stable/reference/ufuncs.html#ufuncs-kwargs>`_.
See also
--------
union
set_precision
Examples
--------
>>> from shapely.constructive import normalize
>>> line_1 = Geometry("LINESTRING(0 0, 2 2)")
>>> line_2 = Geometry("LINESTRING(2 2, 3 3)")
>>> union_all([line_1, line_2])
<pygeos.Geometry MULTILINESTRING ((0 0, 2 2), (2 2, 3 3))>
>>> union_all([[line_1, line_2, None]], axis=1).tolist()
[<pygeos.Geometry MULTILINESTRING ((0 0, 2 2), (2 2, 3 3))>]
>>> box1 = box(0, 0, 2, 2)
>>> box2 = box(1, 1, 3, 3)
>>> normalize(union_all([box1, box2]))
<pygeos.Geometry POLYGON ((0 0, 0 2, 1 2, 1 3, 3 3, 3 1, 2 1, 2 0, 0 0))>
>>> box1 = box(0.1, 0.2, 2.1, 2.1)
>>> union_all([box1, box2], grid_size=1) # doctest: +SKIP
<pygeos.Geometry POLYGON ((0 0, 0 2, 1 2, 1 3, 3 3, 3 1, 2 1, 2 0, 0 0))>
"""
# for union_all, GEOS provides an efficient route through first creating
# GeometryCollections
# first roll the aggregation axis backwards
geometries = np.asarray(geometries)
if axis is None:
geometries = geometries.ravel()
else:
geometries = np.rollaxis(
np.asarray(geometries), axis=axis, start=geometries.ndim
)
# create_collection acts on the inner axis
collections = lib.create_collection(geometries, GeometryType.GEOMETRYCOLLECTION)
if grid_size is not None:
if lib.geos_version < (3, 9, 0):
raise UnsupportedGEOSOperation("grid_size parameter requires GEOS >= 3.9.0")
if not | np.isscalar(grid_size) | numpy.isscalar |
import loader as ld
import fun_basicas as fun
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
import scipy.optimize as opt
from scipy.optimize import minimize
def coste(theta1, theta2, X, Y, num_etiquetas): # Y preparada
A1, A2, h = forward_prop(X, theta1, theta2)
sum1 = Y * np.log(h)
sum2 = (1 - Y) * | np.log(1 - h + 1e-6) | numpy.log |
############## music generation with 3 layer LSTM ######################
#
# Distributed under the MIT license by <NAME>
########################################################################
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import math
import copy as cp
from copy import deepcopy
import pickle as pkl
import time
import os
import theano #typical 2x speed up for small network, 400x600x600 net ~6x speed up
from theano import tensor as T, function, printing
from theano.sandbox.rng_mrg import MRG_RandomStreams as RandomStreams
import theano.sandbox.cuda as cuda
from random import shuffle
#from theano.compile.nanguardmode import NanGuardMode
import LSTMmusicMB
from LSTMmusicMB import RNN4Music
# midi utility scripts should be installed in ./midi/utils.py
import midi.MidiOutStream
import midi.MidiInStream
import midi.MidiInFile
import midi.MidiToText
from midi.utils import midiread
from midi.utils import midiwrite
# set plot sizes if this code is copied to ipython/jupyter notebook
import pylab
pylab.rcParams['figure.figsize'] = (20, 5)
np.set_printoptions(threshold='nan')
def main():
#--- import data ---#
sizeOfMiniBatch = 5 #how many tunes per miniBatch
noOfEpoch = 100
noOfEpochPerMB = 2
lengthOfMB = 100
sparseParam = np.float32(0.01) #increases with no. of cells
path = './Piano-midi.de/train-individual/hpps'
#path = './Piano-midi.de/train'
files = os.listdir(path)
assert len(files) > 0, 'Training set is empty!' \
' (did you download the data files?)'
#pitch range is from 21 to 109
dataset = [midiread((path + "/" + f), (21, 109),0.3).piano_roll.astype(theano.config.floatX) for f in files]
#check number of notes for each tune:
print(str([np.array(dataset[n]).shape[0] for n in np.arange(np.array(dataset).shape[0])]))
# set "silent" to zero in 1-hot format
for k in np.arange(np.array(dataset).shape[0]):
for n in np.arange(0,np.array(dataset[k]).shape[0],1):
if np.sum(dataset[k][n], dtype=theano.config.floatX) == 0 :
dataset[k][n][0] = np.float32(1.0)
#--- training with data ---#
myRNN4Music = RNN4Music(h1_length=176, h2_length=176, h3_length=176, io_length=88, R1=np.float32(0.001), R2=np.float32(0.001), R3= | np.float32(0.001) | numpy.float32 |
import numpy
import math
from scipy.interpolate import InterpolatedUnivariateSpline as interpolate
from scipy.integrate import simps
import sys
sys.path.append("/global/homes/c/chmodi/Programs/Py_codes/modules/")
import cosmology as cosmo_lib
class s_cross():
def __init__(self, power_file, M, L, R = 0., H0 = 100.):
self.M = M
self.L = L
self.ktrue, self.ptrue = numpy.loadtxt(power_file, unpack = True)
self.H0 = H0
self.R = R
self.rhoc = 3 * H0**2 /(8 * math.pi * 43.007)
self.rhom = self.rhoc*M
self.cosmo = cosmo_lib.Cosmology(M= M, L = L)
self.masses = 10**numpy.arange(9, 18, 0.01)
self.sigma = numpy.zeros_like(self.masses)
self.calc_sigma()
def calc_sigma(self):
M = self.masses
for foo in range(len(M)):
self.sigma[foo] = self.sigmasq(M[foo])**0.5
def tophat(self, k, R):
kr = k*R
wt = 3 * (numpy.sin(kr)/kr - | numpy.cos(kr) | numpy.cos |
"""Description of Pd2d class."""
__author__ = 'ikibalin'
__version__ = "2020_08_19"
from warnings import warn
import numpy
from typing import List, NoReturn
from cryspy.A_functions_base.function_2_crystallography_base import \
calc_cos_ang
from cryspy.A_functions_base.matrix_operations import calc_m1_m2_m1t
from cryspy.A_functions_base.unit_cell import calc_matrix_t
from cryspy.A_functions_base.powder_diffraction_const_wavelength import \
calc_ttheta_phi_by_gamma_nu
from cryspy.B_parent_classes.cl_1_item import ItemN
from cryspy.B_parent_classes.cl_2_loop import LoopN
from cryspy.B_parent_classes.cl_3_data import DataN
from cryspy.B_parent_classes.preocedures import take_items_by_class
from cryspy.C_item_loop_classes.cl_1_setup import Setup
from cryspy.C_item_loop_classes.cl_1_diffrn_radiation import \
DiffrnRadiation
from cryspy.C_item_loop_classes.cl_1_extinction import Extinction
from cryspy.C_item_loop_classes.cl_1_phase import PhaseL
from cryspy.C_item_loop_classes.cl_1_pd_peak import PdPeakL
from cryspy.C_item_loop_classes.cl_1_refln import ReflnL
from cryspy.C_item_loop_classes.cl_1_refln_susceptibility import \
ReflnSusceptibilityL
from cryspy.C_item_loop_classes.cl_1_refine_ls import RefineLs
from cryspy.C_item_loop_classes.cl_1_pd2d_background import \
Pd2dBackground
from cryspy.C_item_loop_classes.cl_1_pd2d_instr_reflex_asymmetry import\
Pd2dInstrReflexAsymmetry
from cryspy.C_item_loop_classes.cl_1_pd2d_instr_resolution import \
Pd2dInstrResolution
from cryspy.C_item_loop_classes.cl_1_pd2d_meas import Pd2dMeas
from cryspy.C_item_loop_classes.cl_1_pd2d_proc import Pd2dProc
from cryspy.C_item_loop_classes.cl_1_pd2d_peak import Pd2dPeakL
from cryspy.C_item_loop_classes.cl_1_chi2 import Chi2
from cryspy.C_item_loop_classes.cl_1_range import Range
from cryspy.C_item_loop_classes.cl_1_texture import TextureL
from cryspy.C_item_loop_classes.cl_1_exclude import ExcludeL
from cryspy.E_data_classes.cl_1_crystal import Crystal
na = numpy.newaxis
class Pd2d(DataN):
"""
Powder diffraction experiment with polarized or unpolarized neutrons (2d).
Data items in the DIFFRN category record details about
2d powder diffraction measurements.
Methods
-------
- calc_iint_u_d_flip_ratio
- calc_fr
- calc_fm_perp_loc
- calc_chi_sq
- params_to_cif
- data_to_cif
- calc_to_cif
- estimate_FM
Attributes
----------
- setup (mandatory)
- pd2d_instr_resolution (mandatory)
- phase (mandatory)
- pd2d_background (mandatory)
- pd_meas (mandatory)
- diffrn_radiation
- chi2
- range
- extinction
- pd2d_instr_reflex_asymmetry
- texture
- exclude
- pd2d_proc
- pd2d_peak
- refine_ls
- refln_#phase_name
- refln_susceptibility_#phase_name
"""
CLASSES_MANDATORY = (Pd2dInstrResolution, PhaseL, DiffrnRadiation,
Setup, Range, Pd2dBackground, Pd2dMeas)
CLASSES_OPTIONAL = (Extinction, ExcludeL, Chi2, Pd2dInstrReflexAsymmetry,
TextureL, RefineLs, ReflnL, ReflnSusceptibilityL,
Pd2dPeakL, Pd2dProc, PdPeakL)
# CLASSES_INTERNAL = ()
CLASSES = CLASSES_MANDATORY + CLASSES_OPTIONAL
PREFIX = "pd2d"
# default values for the parameters
D_DEFAULT = {}
def __init__(self, data_name=None, **kwargs) -> NoReturn:
super(Pd2d, self).__init__()
self.__dict__["items"] = []
self.__dict__["data_name"] = data_name
for key, attr in self.D_DEFAULT.items():
setattr(self, key, attr)
for key, attr in kwargs.items():
setattr(self, key, attr)
def calc_profile(self, tth, phi, l_crystal: List[Crystal], l_peak_in=None,
l_refln_in=None, l_refln_susceptibility_in=None,
l_dd_in=None, flag_internal: bool = True):
"""Calculate intensity for the given diffraction angle."""
proc = Pd2dProc() # it is output
proc.ttheta = tth
proc.phi = phi
background = self.pd2d_background
int_bkgd = background.interpolate_by_points(tth, phi)
proc.intensity_bkg_calc = int_bkgd
tth_rad = tth*numpy.pi/180.
phi_rad = phi*numpy.pi/180.
cos_theta_1d = numpy.cos(0.5*tth_rad)
sin_phi_1d = numpy.sin(phi_rad)
setup = self.setup
wavelength = setup.wavelength
diffrn_radiation = self.diffrn_radiation
if setup.offset_phi is None:
setup.offset_phi = 0.
phi_0 = setup.offset_phi
phi_rad = (phi-phi_0)*numpy.pi/180.
sin_phi_1d = numpy.sin(phi_rad)
p_u = float(diffrn_radiation.polarization)
p_d = (2.*float(diffrn_radiation.efficiency)-1.)*p_u
tth_min = tth.min()
tth_max = tth.max()+3.
if tth_max > 180.:
tth_max = 180.
sthovl_min = numpy.sin(0.5*tth_min*numpy.pi/180.)/wavelength
sthovl_max = numpy.sin(0.5*tth_max*numpy.pi/180.)/wavelength
res_u_2d = numpy.zeros((tth.shape[0], phi.shape[0]), dtype=float)
res_d_2d = numpy.zeros((tth.shape[0], phi.shape[0]), dtype=float)
try:
texture = self.texture
h_ax, k_ax = float(texture.h_ax[0]), float(texture.k_ax[0]) # FIXME
l_ax = float(texture.l_ax[0])
g_1, g_2 = float(texture.g_1[0]), float(texture.g_2[0])
except AttributeError:
texture = None
phase = self.phase
_h = len(phase.label)
if l_peak_in is None:
l_peak_in = len(phase.label) * [None]
else:
if _h != len(l_peak_in):
l_peak_in = len(phase.label) * [None]
if l_refln_in is None:
l_refln_in = len(phase.label) * [None]
else:
if _h != len(l_refln_in):
l_refln_in = len(phase.label) * [None]
if l_refln_susceptibility_in is None:
l_refln_susceptibility_in = len(phase.label) * [None]
else:
if _h != len(l_refln_susceptibility_in):
l_refln_susceptibility_in = len(phase.label) * [None]
if l_dd_in is None:
l_dd_in = len(phase.label) * [None]
else:
if _h != len(l_dd_in):
l_dd_in = len(phase.label) * [None]
l_peak, l_dd_out = [], []
l_refln, l_refln_s = [], []
for item_phase, peak_in, refln_in, refln_susceptibility_in, dd_in in \
zip(phase.items, l_peak_in, l_refln_in,
l_refln_susceptibility_in, l_dd_in):
phase_label = item_phase.label
phase_scale = item_phase.scale
try:
phase_igsize = item_phase.igsize
if phase_igsize is None: phase_igsize = 0. # temporary solution
except AttributeError:
phase_igsize = 0.
try:
phase_u = item_phase.u
if phase_u is None: phase_u = 0. # temporary solution
except AttributeError:
phase_u = 0.
try:
phase_v = item_phase.v
if phase_v is None: phase_v = 0. # temporary solution
except AttributeError:
phase_v = 0.
try:
phase_w = item_phase.w
if phase_w is None: phase_w = 0. # temporary solution
except AttributeError:
phase_w = 0.
try:
phase_x = item_phase.x
if phase_x is None: phase_x = 0. # temporary solution
except AttributeError:
phase_x = 0.
try:
phase_y = item_phase.y
if phase_y is None: phase_y = 0. # temporary solution
except AttributeError:
phase_y = 0.
dd_out = {}
for i_crystal, crystal in enumerate(l_crystal):
if crystal.data_name.lower() == phase_label.lower():
ind_cry = i_crystal
break
if ind_cry is None:
warn(f"Crystal with name '{phase_label:}' is not found.",
UserWarning)
return
crystal = l_crystal[ind_cry]
cell = crystal.cell
# space_group = crystal.space_group
if peak_in is not None:
index_h = peak_in.numpy_index_h
index_k = peak_in.numpy_index_k
index_l = peak_in.numpy_index_l
mult = peak_in.numpy_index_mult
else:
if texture is None:
ind_hkl_mult = crystal.calc_hkl(sthovl_min, sthovl_max)
else:
ind_hkl_mult = crystal.calc_hkl_in_range(sthovl_min, sthovl_max)
index_h, index_k, index_l, mult = ind_hkl_mult[0], ind_hkl_mult[1], ind_hkl_mult[2], ind_hkl_mult[3]
peak = Pd2dPeakL(loop_name=phase_label)
peak.numpy_index_h = index_h
peak.numpy_index_k = index_k
peak.numpy_index_l = index_l
peak.numpy_index_mult = mult
peak.numpy_to_items()
cond_1 = len(crystal.get_variable_names()) == 0
cond_2 = (peak_in is not None) & (refln_in is not None)
if (cond_1 & cond_2):
f_nucl_sq = peak_in.numpy_f_nucl_sq
f_m_p_sin_sq = peak_in.numpy_f_m_p_sin_sq
f_m_p_cos_sq = peak_in.numpy_f_m_p_cos_sq
cross_sin = peak_in.numpy_cross_sin
refln = refln_in
refln_s = refln_susceptibility_in
else:
f_nucl_sq, f_m_p_sin_sq, f_m_p_cos_sq, cross_sin, refln, \
refln_s = self.calc_for_iint(index_h, index_k, index_l,
crystal)
refln.loop_name = phase_label
refln_s.loop_name = phase_label
l_refln.append(refln)
l_refln_s.append(refln_s)
peak.numpy_f_nucl_sq = f_nucl_sq
peak.numpy_f_m_p_sin_sq = f_m_p_sin_sq
peak.numpy_f_m_p_cos_sq = f_m_p_cos_sq
peak.numpy_cross_sin = cross_sin
cond_1 = dd_in is not None
cond_2 = ((len(crystal.get_variable_names()) == 0) &
(not(diffrn_radiation.polarization_refinement)) &
(not(diffrn_radiation.efficiency_refinement)))
if cond_1 & cond_2:
iint_u_3d, iint_d_3d = dd_in["iint_u_3d"], dd_in["iint_d_3d"]
cos_theta_3d = dd_in["cos_theta_3d"]
sin_phi_3d = dd_in["sin_phi_3d"]
else:
cos_theta_3d, sin_phi_3d, mult_f_n_3d = numpy.meshgrid(
cos_theta_1d, sin_phi_1d, mult*f_nucl_sq, indexing="ij")
mult_f_m_c_3d = numpy.meshgrid(
tth_rad, phi_rad, mult*f_m_p_cos_sq, indexing="ij")[2]
hh_u_s_3d = numpy.meshgrid(
tth_rad, phi_rad, mult*(f_m_p_sin_sq+p_u*cross_sin),
indexing="ij")[2]
hh_d_s_3d = numpy.meshgrid(
tth_rad, phi_rad, mult*(f_m_p_sin_sq-p_d*cross_sin),
indexing="ij")[2]
c_a_sq_3d = (cos_theta_3d * sin_phi_3d)**2
s_a_sq_3d = 1.-c_a_sq_3d
iint_u_3d = (mult_f_n_3d + hh_u_s_3d*s_a_sq_3d +
mult_f_m_c_3d*c_a_sq_3d)
iint_d_3d = (mult_f_n_3d + hh_d_s_3d*s_a_sq_3d +
mult_f_m_c_3d*c_a_sq_3d)
dd_out["cos_theta_3d"] = cos_theta_3d
dd_out["sin_phi_3d"] = sin_phi_3d
dd_out["iint_u_3d"] = iint_u_3d
dd_out["iint_d_3d"] = iint_d_3d
sthovl_hkl = cell.calc_sthovl(index_h, index_k, index_l)
tth_hkl_rad = numpy.where(sthovl_hkl*wavelength < 1.,
2.*numpy.arcsin(sthovl_hkl*wavelength),
numpy.pi)
tth_hkl = tth_hkl_rad*180./numpy.pi
cond_1 = dd_in is not None
flag_phase_uvwxy_ref = (
item_phase.igsize_refinement | item_phase.u_refinement |
item_phase.v_refinement | item_phase.w_refinement |
item_phase.x_refinement | item_phase.y_refinement)
cond_2 = ((not(flag_phase_uvwxy_ref)) &
(not(self.pd2d_instr_resolution.is_variables())) &
(not(setup.is_variables())))
if cond_1 & cond_2:
profile_3d, tth_zs = dd_in["profile_3d"], dd_in["tth_zs"]
h_pv = dd_in["h_pv"]
else:
profile_3d, tth_zs, h_pv = self.calc_shape_profile(
tth, phi, tth_hkl, phase_igsize=phase_igsize,
phase_u=phase_u, phase_v=phase_v, phase_w=phase_w,
phase_x=phase_x, phase_y=phase_y)
dd_out["profile_3d"] = profile_3d
dd_out["tth_zs"] = tth_zs
dd_out["h_pv"] = h_pv
peak.numpy_ttheta = tth_hkl + setup.offset_ttheta
peak.width_ttheta = h_pv
peak.numpy_to_items()
# texture
if texture is not None:
cond_1 = dd_in is not None
cond_2 = ((not(setup.offset_phi_refinement)))
if cond_1 & cond_2:
cos_alpha_ang_3d = dd_in["cos_alpha_ang_3d"]
sin_alpha_ang_3d = dd_in["sin_alpha_ang_3d"]
else:
cos_alpha_ang_3d = cos_theta_3d * sin_phi_3d
sin_alpha_ang_3d = numpy.sqrt(1.-cos_alpha_ang_3d**2)
dd_out["cos_alpha_ang_3d"] = cos_alpha_ang_3d
dd_out["sin_alpha_ang_3d"] = sin_alpha_ang_3d
cond_2 = (cond_2 & (not(texture.is_variables())) &
(not(cell.is_variables())))
if cond_1 & cond_2:
texture_3d = dd_in["texture_3d"]
else:
cos_alpha_ax = calc_cos_ang(cell, h_ax, k_ax, l_ax,
index_h, index_k, index_l)
c_help = 1.-cos_alpha_ax**2
c_help[c_help < 0.] = 0.
sin_alpha_ax = numpy.sqrt(c_help)
cos_alpha_ax_3d = numpy.meshgrid(tth, phi, cos_alpha_ax,
indexing="ij")[2]
sin_alpha_ax_3d = numpy.meshgrid(tth, phi, sin_alpha_ax,
indexing="ij")[2]
cos_alpha_3d = cos_alpha_ax_3d*cos_alpha_ang_3d + \
sin_alpha_ax_3d*sin_alpha_ang_3d
texture_3d = g_2 + (1.-g_2) * \
(1./g_1 + (g_1**2-1./g_1)*cos_alpha_3d**2)**(-1.5)
dd_out["texture_3d"] = texture_3d
profile_3d = profile_3d*texture_3d
res_u_3d = profile_3d*iint_u_3d
res_d_3d = profile_3d*iint_d_3d
# 0.5 to have the same meaning for scale factor as in FullProf
res_u_2d += 0.5*phase_scale*res_u_3d.sum(axis=2)
res_d_2d += 0.5*phase_scale*res_d_3d.sum(axis=2)
l_peak.append(peak)
l_dd_out.append(dd_out)
proc.ttheta_corrected = tth_zs
proc.intensity_plus_net = res_u_2d
proc.intensity_minus_net = res_d_2d
proc.intensity_plus_total = res_u_2d+int_bkgd
proc.intensity_minus_total = res_d_2d+int_bkgd
if flag_internal:
if background.is_variables():
background.form_ttheta_phi_intensity()
proc.form_ttheta_phi_intensity_plus_net()
proc.form_ttheta_phi_intensity_minus_net()
proc.form_ttheta_phi_intensity_plus_total()
proc.form_ttheta_phi_intensity_minus_total()
l_calc_objs = l_refln + l_refln_s + l_peak
l_calc_objs.append(proc)
self.add_items(l_calc_objs)
return proc, l_peak, l_refln, l_dd_out
def calc_chi_sq(self, l_crystal, flag_internal: bool = True):
"""
Calculate chi square.
Arguments
---------
- l_crystal: a list of Crystal objects of cryspy library
- flag_internal: a flag to calculate internal objects
(default is True)
Output arguments
----------------
- chi_sq_val: chi square of flip ratio
(Sum_i ((y_e_i - y_m_i) / sigma_i)**2)
- n: number of measured reflections
"""
meas = self.pd2d_meas
tth = meas.ttheta
phi = meas.phi
int_u_exp = meas.intensity_plus
sint_u_exp = meas.intensity_plus_sigma
int_d_exp = meas.intensity_minus
sint_d_exp = meas.intensity_minus_sigma
l_peak_in, l_refln_in = [], []
l_refln_susceptibility_in = []
l_dd_in = []
flag_1 = not(flag_internal)
try:
dd = self.dd
flag_2 = True
except AttributeError:
flag_2 = False
if (flag_1 & flag_2):
for phase_item in self.phase.items:
crystal = None
for cryst in l_crystal:
if cryst.data_name.lower() == phase_item.label.lower():
crystal = cryst
break
attr_peak = f"pd2d_peak_{crystal.data_name:}"
attr_refln = f"refln_{crystal.data_name:}"
attr_refln_s = f"refln_susceptibility_{crystal.data_name:}"
l_peak_in.append(getattr(self, attr_peak))
l_refln_in.append(getattr(self, attr_refln))
l_refln_susceptibility_in.append(getattr(self, attr_refln_s))
cond_tth_in = numpy.ones(tth.size, dtype=bool)
cond_phi_in = numpy.ones(phi.size, dtype=bool)
try:
range_ = self.range
cond_tth_in = numpy.logical_and(cond_tth_in, tth >=
range_.ttheta_min)
cond_tth_in = numpy.logical_and(cond_tth_in, tth <=
range_.ttheta_max)
cond_phi_in = numpy.logical_and(cond_phi_in, phi >= range_.phi_min)
cond_phi_in = numpy.logical_and(cond_phi_in, phi <= range_.phi_max)
except AttributeError:
pass
# cond_1_in, cond_2_in = numpy.meshgrid(cond_tth_in, cond_phi_in,
# indexing="ij")
# cond_in = numpy.logical_and(cond_1_in, cond_2_in)
tth_in = tth[cond_tth_in]
phi_in = phi[cond_phi_in]
int_u_exp_in = int_u_exp[cond_tth_in, :][:, cond_phi_in]
sint_u_exp_in = sint_u_exp[cond_tth_in, :][:, cond_phi_in]
int_d_exp_in = int_d_exp[cond_tth_in, :][:, cond_phi_in]
sint_d_exp_in = sint_d_exp[cond_tth_in, :][:, cond_phi_in]
proc, l_peak, l_refln, l_dd_out = self.calc_profile(
tth_in, phi_in, l_crystal, l_peak_in=l_peak_in,
l_refln_in=l_refln_in,
l_refln_susceptibility_in=l_refln_susceptibility_in,
l_dd_in=l_dd_in, flag_internal=flag_internal)
proc.intensity_plus = int_u_exp_in
proc.intensity_plus_sigma = sint_u_exp_in
proc.intensity_minus = int_d_exp_in
proc.intensity_minus_sigma = sint_d_exp_in
# self.proc = proc
# self.peaks = l_peak
# self.reflns = l_refln
self.dd = l_dd_out
int_u_mod = proc.intensity_plus_total
int_d_mod = proc.intensity_minus_total
sint_sum_exp_in = (sint_u_exp_in**2 + sint_d_exp_in**2)**0.5
chi_sq_u = ((int_u_mod-int_u_exp_in)/sint_u_exp_in)**2
chi_sq_d = ((int_d_mod-int_d_exp_in)/sint_d_exp_in)**2
chi_sq_sum = ((int_u_mod+int_d_mod-int_u_exp_in-int_d_exp_in) /
sint_sum_exp_in)**2
chi_sq_dif = ((int_u_mod-int_d_mod-int_u_exp_in+int_d_exp_in) /
sint_sum_exp_in)**2
cond_u = numpy.logical_not(numpy.isnan(chi_sq_u))
cond_d = numpy.logical_not(numpy.isnan(chi_sq_d))
cond_sum = numpy.logical_not(numpy.isnan(chi_sq_sum))
cond_dif = numpy.logical_not(numpy.isnan(chi_sq_dif))
# exclude region
try:
exclude = self.exclude
l_excl_tth_min = exclude.numpy_ttheta_min
l_excl_tth_max = exclude.numpy_ttheta_max
l_excl_phi_min = exclude.numpy_phi_min
l_excl_phi_max = exclude.numpy_phi_max
for excl_tth_min, excl_tth_max, excl_phi_min, excl_phi_max in \
zip(l_excl_tth_min, l_excl_tth_max, l_excl_phi_min,
l_excl_phi_max):
cond_1 = numpy.logical_or(tth_in < 1.*excl_tth_min,
tth_in > 1.*excl_tth_max)
cond_2 = numpy.logical_or(phi_in < 1.*excl_phi_min,
phi_in > 1.*excl_phi_max)
cond_11, cond_22 = numpy.meshgrid(cond_1, cond_2,
indexing="ij")
cond_12 = numpy.logical_or(cond_11, cond_22)
cond_u = numpy.logical_and(cond_u, cond_12)
cond_d = numpy.logical_and(cond_d, cond_12)
cond_sum = numpy.logical_and(cond_sum, cond_12)
except AttributeError:
pass
chi_sq_u_val = (chi_sq_u[cond_u]).sum()
n_u = cond_u.sum()
chi_sq_d_val = (chi_sq_d[cond_d]).sum()
n_d = cond_d.sum()
chi_sq_sum_val = (chi_sq_sum[cond_sum]).sum()
n_sum = cond_sum.sum()
chi_sq_dif_val = (chi_sq_dif[cond_dif]).sum()
n_dif = cond_dif.sum()
chi2 = self.chi2
flag_u = chi2.up
flag_d = chi2.down
flag_sum = chi2.sum
flag_dif = chi2.diff
chi_sq_val = (int(flag_u)*chi_sq_u_val + int(flag_d)*chi_sq_d_val +
int(flag_sum)*chi_sq_sum_val +
int(flag_dif)*chi_sq_dif_val)
n = (int(flag_u)*n_u + int(flag_d)*n_d + int(flag_sum)*n_sum +
int(flag_dif)*n_dif)
# print(f"chi_sq_val/n: {chi_sq_val/n:.2f} \
# chi_sq_val: {chi_sq_val: .2f}")
# d_exp_out = {"chi_sq_val": chi_sq_val, "n": n}
# d_exp_out.update(d_exp_prof_out)
if flag_internal:
refine_ls = RefineLs(number_reflns=n,
goodness_of_fit_all=chi_sq_val/float(n),
weighting_scheme="sigma")
self.refine_ls = refine_ls
proc.form_ttheta_phi_intensity_bkg_calc()
proc.form_ttheta_phi_intensity_plus()
proc.form_ttheta_phi_intensity_plus_sigma()
proc.form_ttheta_phi_intensity_minus()
proc.form_ttheta_phi_intensity_minus_sigma()
return chi_sq_val, n
def calc_for_iint(self, index_h, index_k, index_l, crystal,
flag_internal: bool = True):
"""Calculate the integral intensity for h, k, l reflections."""
index_hkl = numpy.stack([index_h, index_k, index_l], axis=0)
setup = self.setup
field = float(setup.field)
refln = crystal.calc_refln(index_hkl)
f_nucl = refln.numpy_f_calc
f_nucl_sq = abs(f_nucl*f_nucl.conjugate())
refln_s = crystal.calc_refln_susceptibility(index_hkl)
sft_11 = refln_s.numpy_chi_11_calc
sft_12 = refln_s.numpy_chi_12_calc
sft_13 = refln_s.numpy_chi_13_calc
sft_21 = refln_s.numpy_chi_21_calc
sft_22 = refln_s.numpy_chi_22_calc
sft_23 = refln_s.numpy_chi_23_calc
sft_31 = refln_s.numpy_chi_31_calc
sft_32 = refln_s.numpy_chi_32_calc
sft_33 = refln_s.numpy_chi_33_calc
_ij = numpy.stack([sft_11, sft_12, sft_13, sft_21, sft_22, sft_23, sft_31, sft_32, sft_33], axis=0)
cell = crystal.cell
unit_cell_parameters = cell.get_unit_cell_parameters()
t_ij = calc_matrix_t(index_hkl, unit_cell_parameters, flag_unit_cell_parameters=False)[0]
#SIGMA = T CHI T^-1 = T chi T^T (because T is rotation matrix, therefore T^-1 = T^T)
th_ij = calc_m1_m2_m1t(t_ij, _ij)[0]
th_11, th_12, th_13, th_22, th_23 = th_ij[0], th_ij[1], th_ij[2], th_ij[4], th_ij[5]
# f_m_p_sin_sq = (field**2)*abs(0.5*(th_11*th_11.conjugate()+\
# th_22*th_22.conjugate())+th_12*th_12.conjugate())
# f_m_p_cos_sq = (field**2)*abs(th_13*th_13.conjugate()+\
# th_23*th_23.conjugate())
# f_m_p_field = 0.5*field*(th_11+th_22)
f_m_p_sin_sq = abs(0.5 * (th_11 * th_11.conjugate()+th_22 *
th_22.conjugate())+th_12 * th_12.conjugate())
f_m_p_cos_sq = abs(th_13 * th_13.conjugate() +
th_23 * th_23.conjugate())
f_m_p_field = 0.5 * (th_11+th_22)
cross_sin = 2. * (f_nucl.real * f_m_p_field.real +
f_nucl.imag * f_m_p_field.imag)
return f_nucl_sq, f_m_p_sin_sq, f_m_p_cos_sq, cross_sin, refln, refln_s
def _gauss_pd(self, tth_2d):
"""One dimensional gauss powder diffraction."""
ag, bg = self.ag, self.bg
val_1 = bg*tth_2d**2
val_2 = numpy.where(val_1 < 5., numpy.exp(-val_1), 0.)
self.gauss_pd = ag*val_2
def _lor_pd(self, tth_2d):
"""One dimensional lorentz powder diffraction."""
al, bl = self.al, self.bl
self.lor_pd = al*1./(1.+bl*tth_2d**2)
def calc_shape_profile(
self, tth, phi, tth_hkl, phase_igsize: float = 0.,
phase_u: float = 0., phase_v: float = 0., phase_w: float = 0.,
phase_x: float = 0., phase_y: float = 0.):
"""
Calculate profile in the range ttheta.
For reflections placed on
ttheta_hkl with i_g parameter by default equal to zero
tth, phi, tth_hkl in degrees
"""
setup = self.setup
zero_shift = float(setup.offset_ttheta)
tth_zs = tth-zero_shift
resolution = self.pd2d_instr_resolution
h_pv, eta, h_g, h_l, a_g, b_g, a_l, b_l = resolution.calc_resolution(
tth_hkl, phase_igsize=phase_igsize, phase_u=phase_u,
phase_v=phase_v, phase_w=phase_w, phase_x=phase_x, phase_y=phase_y)
tth_3d, phi_3d, tth_hkl_3d = numpy.meshgrid(tth_zs, phi, tth_hkl,
indexing="ij")
self.ag = numpy.meshgrid(tth_zs, phi, a_g, indexing="ij")[2]
self.bg = numpy.meshgrid(tth_zs, phi, b_g, indexing="ij")[2]
self.al = numpy.meshgrid(tth_zs, phi, a_l, indexing="ij")[2]
self.bl = numpy.meshgrid(tth_zs, phi, b_l, indexing="ij")[2]
eta_3d = numpy.meshgrid(tth_zs, phi, eta, indexing="ij")[2]
self.eta = eta_3d
self._gauss_pd(tth_3d-tth_hkl_3d)
self._lor_pd(tth_3d-tth_hkl_3d)
g_pd2d_3d = self.gauss_pd
l_pd2d_3d = self.lor_pd
np_shape_3d = eta_3d * l_pd2d_3d + (1.-eta_3d) * g_pd2d_3d
asymmetry = self.pd2d_instr_reflex_asymmetry
np_ass_2d = asymmetry.calc_asymmetry(tth_zs, tth_hkl, h_pv)
np_ass_3d = np_ass_2d[:, numpy.newaxis, :] * numpy.ones(
phi.size, dtype=float)[numpy.newaxis, :, numpy.newaxis]
# Lorentz factor
tth_rad = tth_zs*numpy.pi/180.
np_lor_1d = 1./(numpy.sin(tth_rad)*numpy.sin(0.5*tth_rad))
np_lor_3d = numpy.meshgrid(np_lor_1d, phi, tth_hkl, indexing="ij")[0]
profile_3d = np_shape_3d*np_ass_3d*np_lor_3d
return profile_3d, tth_zs, h_pv
def params_to_cif(self, separator="_", flag: bool = False,
flag_minimal: bool = True) -> str:
"""Save parameters to cif format."""
ls_out = []
l_cls = (Pd2dBackground, Pd2dInstrResolution, PhaseL, DiffrnRadiation,
Setup, Range, Chi2, Extinction, ExcludeL,
Pd2dInstrReflexAsymmetry, TextureL)
l_obj = [item for item in self.items if type(item) in l_cls]
l_itemn = [item for item in l_obj if isinstance(item, ItemN)]
l_loopn = [item for item in l_obj if isinstance(item, LoopN)]
ls_out.extend([_.to_cif(separator=separator)+"\n" for _ in l_itemn])
ls_out.extend([_.to_cif(separator=separator)+"\n" for _ in l_loopn])
return "\n".join(ls_out)
def data_to_cif(self, separator="_", flag: bool = False,
flag_minimal: bool = True) -> str:
"""Save data to cif format."""
ls_out = []
l_cls = (Pd2dMeas, )
l_obj = [item for item in self.items if type(item) in l_cls]
l_itemn = [item for item in l_obj if isinstance(item, ItemN)]
l_loopn = [item for item in l_obj if isinstance(item, LoopN)]
ls_out.extend([_.to_cif(separator=separator)+"\n" for _ in l_itemn])
ls_out.extend([_.to_cif(separator=separator)+"\n" for _ in l_loopn])
return "\n".join(ls_out)
def calc_to_cif(self, separator="_", flag=False, flag_minimal=True) -> str:
"""Save calculations to cif format."""
ls_out = []
l_cls = (RefineLs, ReflnL, ReflnSusceptibilityL, Pd2dPeakL, Pd2dProc)
l_obj = [item for item in self.items if type(item) in l_cls]
l_itemn = [item for item in l_obj if isinstance(item, ItemN)]
l_loopn = [item for item in l_obj if isinstance(item, LoopN)]
ls_out.extend([_.to_cif(separator=separator)+"\n" for _ in l_itemn])
ls_out.extend([_.to_cif(separator=separator)+"\n" for _ in l_loopn])
return "\n".join(ls_out)
def apply_constraints(self):
"""Apply constraints."""
pass
def plots(self):
if self.is_attribute("pd2d_proc"):
pd2d_proc = self.pd2d_proc
fig = pd2d_proc.plot_gamma_nu()[0]
l_pd_peak = [item for item in self.items if isinstance(item, PdPeakL)]
[ax1, ax2] = fig.axes[:2]
gamma_min, gamma_max = ax1.get_xlim()
nu_min, nu_max = ax1.get_ylim()
for pd_peak in l_pd_peak:
if pd_peak.is_attribute("gamma"):
index_h = numpy.array(pd_peak.index_h, dtype=int)
index_k = numpy.array(pd_peak.index_k, dtype=int)
index_l = numpy.array(pd_peak.index_l, dtype=int)
gamma = numpy.array(pd_peak.gamma, dtype=float)
nu = numpy.array(pd_peak.nu, dtype=float)
flag_gn = numpy.logical_and(
numpy.logical_and(gamma>=gamma_min, gamma<=gamma_max),
numpy.logical_and(nu>=nu_min, nu<=nu_max))
if (pd_peak.is_attribute("intensity_plus") and pd_peak.is_attribute("intensity_minus")):
i_plus = numpy.array(pd_peak.intensity_plus, dtype=float)
i_minus = numpy.array(pd_peak.intensity_minus, dtype=float)
inv_lf = numpy.sin(gamma*numpy.pi/180)*numpy.sin(0.5*gamma*numpy.pi/180)
i_sum = numpy.abs(i_plus*flag_gn+i_minus*flag_gn)
i_difference = numpy.abs(i_plus*flag_gn-i_minus*flag_gn)
flag_i_plus = (i_sum-i_sum.min()) > 0.01 * (i_sum.max() - i_sum.min())
flag_i_difference = i_difference > 0.01 * i_difference.max()
flag_i = numpy.logical_or(flag_i_plus, flag_i_difference)
flag_gn = numpy.logical_and(flag_gn, flag_i)
ax1.plot(gamma[flag_gn], 0.5*(nu[flag_gn]+nu_max), "k.", alpha=0.3)
ax2.plot(gamma[flag_gn], 0.5*(nu[flag_gn]+nu_max), "k.", alpha=0.3)
ax1.plot(gamma[flag_gn], nu_min+0.5*(-nu[flag_gn]+nu_max), "k.", alpha=0.3)
ax2.plot(gamma[flag_gn], nu_min+0.5*(-nu[flag_gn]+nu_max), "k.", alpha=0.3)
if (pd_peak.is_attribute("intensity_plus") and pd_peak.is_attribute("intensity_minus")):
i_plus = numpy.array(pd_peak.intensity_plus, dtype=float)
i_minus = numpy.array(pd_peak.intensity_minus, dtype=float)
inv_lf = numpy.sin(gamma*numpy.pi/180)*numpy.sin(0.5*gamma*numpy.pi/180)
i_sum = numpy.abs(i_plus*flag_gn+i_minus*flag_gn)
i_difference = numpy.abs(i_plus*flag_gn-i_minus*flag_gn)
flag_i_plus = (i_sum-i_sum.min()) > 0.2 * (i_sum.max() - i_sum.min())
flag_i_difference = i_difference > 0.2 * i_difference.max()
flag_i = numpy.logical_or(flag_i_plus, flag_i_difference)
flag_gn = numpy.logical_and(flag_gn, flag_i)
l_gn = []
for i_h, i_k, i_l, i_g, i_n in zip(
index_h[flag_gn], index_k[flag_gn], index_l[flag_gn], gamma[flag_gn], nu[flag_gn]):
if not((i_g, i_n) in l_gn):
s_text = f"({i_h:}{i_k:}{i_l:})"
ax1.text(i_g, 0.5*(+i_n+nu_max), s_text, alpha=0.5, color="k")
ax2.text(i_g, 0.5*(+i_n+nu_max), s_text, alpha=0.5, color="k")
ax1.text(i_g, 0.5*(-i_n+nu_max)+nu_min, s_text, alpha=0.5, color="k")
ax2.text(i_g, 0.5*(-i_n+nu_max)+nu_min, s_text, alpha=0.5, color="k")
l_gn.append((i_g, i_n))
return [(fig, ax1), ]
if self.is_attribute("chi2"):
flag_up = self.chi2.up
flag_down = self.chi2.down
flag_sum = self.chi2.sum
flag_diff = self.chi2.diff
else:
flag_up, flag_down, flag_sum = False, False, True
flag_diff = False
if flag_sum:
fig_s, ax_s = pd2d_proc.plot_projection_sum()
ax_s.set_title(self.data_name + " - "+ax_s.title.get_text())
y_min_s, y_max_s = ax_s.get_ylim()
y_dist_s = y_max_s-y_min_s
y_step_s = 0.
if flag_diff:
fig_d, ax_d = pd2d_proc.plot_projection_diff()
ax_d.set_title(self.data_name + " - "+ax_d.title.get_text())
y_min_d, y_max_d = ax_d.get_ylim()
y_dist_d = y_max_d-y_min_d
y_step_d = 0.
for item in self.items:
if isinstance(item, Pd2dPeakL):
np_tth = item.numpy_ttheta
if flag_sum:
ax_s.plot(np_tth, 0.*np_tth+y_min_s-y_step_s, "|",
label=item.loop_name)
y_step_s += 0.05*y_dist_s
if flag_diff:
ax_d.plot(np_tth, 0.*np_tth+y_min_d-y_step_d, "|",
label=item.loop_name)
y_step_d += 0.05*y_dist_d
res = []
if flag_sum:
ax_s.legend(loc='upper right')
res.append((fig_s, ax_s))
if flag_diff:
ax_d.legend(loc='upper right')
res.append((fig_d, ax_d))
return res
elif self.is_attribute("pd2d_meas"):
return self.pd2d_meas.plots()
return []
def get_dictionary(self):
"""Form dictionary. See documentation moduel CrysPy using Jupyter notebook.
"""
self.form_object()
ddict = {}
setup, pd2d_meas, resolution = None, None, None
pd2d_background, range_, exclude = None, None, None
asymmetry, diffrn_radiation = None, None
phase, texture, chi2 = None, None, None
l_obj = take_items_by_class(self, (Setup, ))
if len(l_obj) > 0:
setup = l_obj[0]
l_obj = take_items_by_class(self, (Pd2dMeas, ))
if len(l_obj) > 0:
pd2d_meas = l_obj[0]
l_obj = take_items_by_class(self, (Pd2dInstrResolution, ))
if len(l_obj) > 0:
resolution = l_obj[0]
l_obj = take_items_by_class(self, (Pd2dBackground, ))
if len(l_obj) > 0:
pd2d_background = l_obj[0]
l_obj = take_items_by_class(self, (Range, ))
if len(l_obj) > 0:
range_ = l_obj[0]
l_obj = take_items_by_class(self, (ExcludeL, ))
if len(l_obj) > 0:
exclude = l_obj[0]
l_obj = take_items_by_class(self, (Pd2dInstrReflexAsymmetry, ))
if len(l_obj) > 0:
asymmetry = l_obj[0]
l_obj = take_items_by_class(self, (DiffrnRadiation, ))
if len(l_obj) > 0:
diffrn_radiation = l_obj[0]
l_obj = take_items_by_class(self, (PhaseL, ))
if len(l_obj) > 0:
phase = l_obj[0]
l_obj = take_items_by_class(self, (TextureL, ))
if len(l_obj) > 0:
texture = l_obj[0]
l_obj = take_items_by_class(self, (Chi2, ))
if len(l_obj) > 0:
chi2 = l_obj[0]
ddict["name"] = self.data_name
ddict["type_name"] = self.get_name()
if setup is not None:
ddict["magnetic_field"] = numpy.array([setup.field], dtype=float)
ddict["wavelength"] = numpy.array([setup.wavelength], dtype=float)
ddict["flags_wavelength"] = | numpy.array([setup.wavelength_refinement], dtype=bool) | numpy.array |
import os
import time
import numpy as np
import configparser
from PIL import Image
import matplotlib.pyplot as plt
from matplotlib.pyplot import figure
# Puzzles Type
puz = "Houses"
config = configparser.ConfigParser()
config.read(puz + '/Cards/Cards.ini')
num_of_cards = len(config.sections())
# Create Tiles
sides = []
colors = []
num_colors = []
tiles = np.zeros([num_of_cards, 3, 3])
for i in range(num_of_cards):
for j in range(4):
temp = config['Card_' + str(i+1)]['loc' + str(j+1)]
temp = temp.split(' ')
temp_side = temp[1]
if temp_side not in sides:
sides.append(temp_side)
temp_color = temp[0]
if temp_color not in colors:
colors.append(temp_color)
num_colors.append(len(colors))
if j==0:
for c, color in enumerate(colors):
if temp_color==color:
tiles[i][0][1] = num_colors[c]
if temp_side==sides[0]:
tiles[i][0][1] = -1 * tiles[i][0][1]
break;
elif j==1:
for c, color in enumerate(colors):
if temp_color==color:
tiles[i][1][0] = num_colors[c]
if temp_side==sides[0]:
tiles[i][1][0] = -1 * tiles[i][1][0]
break;
elif j==2:
for c, color in enumerate(colors):
if temp_color==color:
tiles[i][1][2] = num_colors[c]
if temp_side==sides[0]:
tiles[i][1][2] = -1 * tiles[i][1][2]
break;
elif j==3:
for c, color in enumerate(colors):
if temp_color==color:
tiles[i][2][1] = num_colors[c]
if temp_side==sides[0]:
tiles[i][2][1] = -1 * tiles[i][2][1]
break;
# Rotate {tile} 90 degrees {rotations} times
def turn_tile(tile, rotations):
new_tile = np.zeros([tile.shape[0], tile.shape[1]])
for r in range(rotations):
new_tile[0][1] = tile[1][0]
new_tile[1][0] = tile[2][1]
new_tile[1][2] = tile[0][1]
new_tile[2][1] = tile[1][2]
tile[:][:] = new_tile[:][:]
return tile
# Find identical Cards
double_cards = []
for i in range(tiles.shape[0]-1):
for j in range(i+1, tiles.shape[0]):
rot = 0
tile_to_check = np.array(tiles[i])
while rot<4:
if ((tile_to_check[0][1]==tiles[j][0][1]) and
(tile_to_check[1][0]==tiles[j][1][0]) and
(tile_to_check[1][2]==tiles[j][1][2]) and
(tile_to_check[2][1]==tiles[j][2][1])):
double_cards.append(np.array([i+1, j+1]))
rot = rot + 1
turn_tile(tile_to_check, rot)
# Check if the combination is legal
def is_legal(tiles, position, tile, turn, sol_tiles, sol_turns):
# Positions = | 0 | 1 | 2 |
# | 3 | 4 | 5 |
# | 6 | 7 | 8 |
if position==0:
return True
elif position==1:
tile1 = turn_tile(np.array(tiles[tile]), turn)
tile0 = turn_tile(np.array(tiles[sol_tiles[0]-1]), sol_turns[0])
if tile1[1][0]+tile0[1][2]==0:
return True
elif position==2:
tile2 = turn_tile(np.array(tiles[tile]), turn)
tile1 = turn_tile(np.array(tiles[sol_tiles[1]-1]), sol_turns[1])
if tile2[1][0]+tile1[1][2]==0:
return True
elif position==3:
tile3 = turn_tile(np.array(tiles[tile]), turn)
tile0 = turn_tile( | np.array(tiles[sol_tiles[0]-1]) | numpy.array |
"""
Created on Mon Feb 22 15:52:51 2021
@author: <NAME>
"""
import pandas as pd
import numpy as np
import os
import pickle
import calendar
import time
import warnings
from pyproj import Transformer
import networkx as nx
import matplotlib as mpl
import matplotlib.pyplot as plt
from requests import get
import dataframe_key
def compile_chicago_stations():
"""
Reads data files containing information about docking stations in Chicago
and compiles the data into a dataframe. The dataframe is then saved as a
pickle for further use.
The relevant files can be found at:
https://divvy-tripdata.s3.amazonaws.com/index.html
https://data.cityofchicago.org/Transportation/Divvy-Bicycle-Stations-All-Map/bk89-9dk7
Raises
------
FileNotFoundError
Raised if no data files containing station data are found.
Returns
-------
stat_df : pandas DataFrame
Dataframe of all docking station information.
"""
try:
with open('./python_variables/Chicago_stations.pickle', 'rb') as file:
stat_df = pickle.load(file)
except FileNotFoundError as exc:
print('No pickle found. Creating pickle...')
stat_files = [file for file in os.listdir('data') if 'Divvy_Stations' in file]
col_list = ['id', 'name', 'latitude', 'longitude']
key = {'ID':'id', 'Station Name':'name', 'Latitude':'latitude','Longitude':'longitude'}
try:
stat_df = pd.read_csv(
'data/Divvy_Bicycle_Stations_-_All_-_Map.csv').rename(columns = key)
stat_df = stat_df[col_list]
except FileNotFoundError:
stat_df = pd.DataFrame(columns = col_list)
for file in stat_files:
df = pd.read_csv(f'./data/{file}')[col_list]
stat_df = pd.concat([stat_df, df], sort = False)
if stat_df.size == 0:
raise FileNotFoundError(
'No data files containing station data found. Please read the docstring for more information.') from exc
stat_df.drop_duplicates(subset = 'name', inplace = True)
with open('./python_variables/Chicago_stations.pickle', 'wb') as file:
pickle.dump(stat_df, file)
print('Pickle loaded')
return stat_df
def get_JC_blacklist():
"""
Constructs/updates a blacklist of stations in Jersey City area. The
blacklist is created using historical biketrip datasets for the area.
Use only if you know what you are doing.
The relevant files can be found at:
https://www.citibikenyc.com/system-data
Raises
------
FileNotFoundError
Raised if no Jersey City dataset is found.
Returns
-------
blacklist : list
List of IDs of the Jersey City docking stations.
"""
try:
with open('./python_variables/JC_blacklist', 'rb') as file:
blacklist = pickle.load(file)
except FileNotFoundError:
print('No previous blacklist found. Creating blacklist...')
blacklist = set()
JC_files = [file for file in os.listdir('data') if 'JC' in file]
if len(JC_files) == 0:
raise FileNotFoundError(
'No JC files found. Please have a JC file in the data directory to create/update blacklist.')
for file in JC_files:
df = pd.read_csv('data/' + file)
df = df.rename(columns = dataframe_key.get_key('nyc'))
JC_start_stat_indices = df.loc[df['start_stat_long'] < 74.02]
JC_end_stat_indices = df.loc[df['end_stat_long'] < 74.02]
stat_IDs = set(
df['start_stat_id'][JC_start_stat_indices]) | set(df['end_stat_id'][JC_end_stat_indices])
blacklist = blacklist | stat_IDs
with open('./python_variables/JC_blacklist', 'wb') as file:
pickle.dump(blacklist, file)
print('Blacklist updated')
return blacklist
def days_index(df):
"""
Find indices of daily trips.
Parameters
----------
df : pandas DataFrame
Dataframe containing bikeshare trip data with columns that have been
renamed to the common key.
Returns
-------
d_i : dict
Contains the indices of the first trip per day.
"""
days = df['start_dt'].dt.day
d_i = [(days == i).idxmax() for i in range(1, max(days)+1)]
return dict(zip(range(1, max(days)+1), d_i))
def pickle_data(df, city, year, month):
"""
Generate pickle of days' starting indices.
Parameters
----------
df : pandas DataFrame
bikeshare trip data with columns that have been renamed to the common
key.
city : str
The identification of the city. For a list of supported cities, see
the documentation for the Data class.
year : int
The year of interest in YYYY format.
month : int
The month of interest in MM format.
Returns
-------
d : dict
Contains the indices of the first trip per day.
"""
d = days_index(df)
with open(f'./python_variables/day_index_{city}{year:d}{month:02d}.pickle', 'wb') as file:
pickle.dump(d, file)
return d
def get_data(city, year, month, blacklist=None):
"""
Read data from csv files.
Parameters
----------
city : str
The identification of the city. For a list of supported cities, see
the documentation for the Data class.
year : int
The year of interest in YYYY format.
month : int
The month of interest in MM format.
blacklist : list, optional
List of IDs of stations to remove. Default is None.
Returns
-------
df : pandas DataFrame
Dataframe containing bikeshare trip data.
days : dict
Contains the indices of the first trip per day.
"""
supported_cities = ['nyc', 'sfran', 'sjose',
'washDC', 'chic', 'london',
'oslo', 'edinburgh', 'bergen',
'buenos_aires', 'madrid',
'mexico', 'taipei'] # Remember to update this list
if city not in supported_cities:
raise ValueError("This city is not currently supported. Supported cities are {}".format(supported_cities))
# Make folder for dataframes if not found
if not os.path.exists('python_variables/big_data'):
os.makedirs('python_variables/big_data')
try:
with open(f'./python_variables/big_data/{city}{year:d}{month:02d}_dataframe_blcklst={blacklist}.pickle', 'rb') as file:
df = pickle.load(file)
print('Pickle loaded')
except FileNotFoundError:
print('No dataframe pickle found. Pickling dataframe...')
if city == "nyc":
try:
df = pd.read_csv(f'./data/{year:d}{month:02d}-citibike-tripdata.csv')
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant files can be found at https://www.citibikenyc.com/system-data') from exc
df = df.rename(columns = dataframe_key.get_key(city))
try:
with open('./python_variables/JC_blacklist', 'rb') as file:
JC_blacklist = pickle.load(file)
df = df[~df['start_stat_id'].isin(JC_blacklist)]
df = df[~df['end_stat_id'].isin(JC_blacklist)]
except FileNotFoundError:
print('No JC blacklist found. Continuing...')
df.dropna(inplace=True)
df.reset_index(inplace = True, drop = True)
df['start_dt'] = pd.to_datetime(df['start_t'])
df['end_dt'] = pd.to_datetime(df['end_t'])
elif city == "washDC":
try:
df = pd.read_csv(f'./data/{year:d}{month:02d}-capitalbikeshare-tripdata.csv')
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant files can be found at https://www.capitalbikeshare.com/system-data') from exc
df = df.rename(columns = dataframe_key.get_key(city))
df['start_stat_lat'] = ''
df['start_stat_long'] = ''
df['end_stat_lat'] = ''
df['end_stat_long'] = ''
stat_df = pd.read_csv('data/Capital_Bike_Share_Locations.csv')
for _ , stat in stat_df.iterrows():
start_matches = np.where(df['start_stat_id'] == stat['TERMINAL_NUMBER'])
end_matches = np.where(df['end_stat_id'] == stat['TERMINAL_NUMBER'])
df.at[start_matches[0], 'start_stat_lat'] = stat['LATITUDE']
df.at[start_matches[0], 'start_stat_long'] = stat['LONGITUDE']
df.at[end_matches[0], 'end_stat_lat'] = stat['LATITUDE']
df.at[end_matches[0], 'end_stat_long'] = stat['LONGITUDE']
df.replace('', np.nan, inplace = True)
df.dropna(inplace=True)
max_lat = 38.961029
min_lat = 38.792686
max_long= -76.909415
min_long= -77.139396
df = df.iloc[np.where(
(df['start_stat_lat'] < max_lat) &
(df['start_stat_lat'] > min_lat) &
(df['start_stat_long'] < max_long) &
(df['start_stat_long'] > min_long))]
df = df.iloc[np.where(
(df['end_stat_lat'] < max_lat) &
(df['end_stat_lat'] > min_lat) &
(df['end_stat_long'] < max_long) &
(df['end_stat_long'] > min_long))]
df.reset_index(inplace = True, drop = True)
df['start_dt'] = pd.to_datetime(df['start_t'])
df['end_dt'] = pd.to_datetime(df['end_t'])
elif city == "chic":
q = int(np.ceil(month/3))
try:
df = pd.read_csv(f'./data/Divvy_Trips_{year:d}_Q{q}.csv')
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant files can be found at https://www.divvybikes.com/system-data') from exc
df = df.rename(columns = dataframe_key.get_key(city))
n_days = calendar.monthrange(year, month)[1]
df = df.iloc[np.where(df['start_t'] > f'{year:d}-{month:02d}-01 00:00:00')]
df = df.iloc[np.where(df['start_t'] < f'{year:d}-{month:02d}-{n_days} 23:59:59')]
df.reset_index(inplace = True, drop = True)
df['start_stat_lat'] = ''
df['start_stat_long'] = ''
df['end_stat_lat'] = ''
df['end_stat_long'] = ''
try:
with open('./python_variables/Chicago_stations.pickle', 'rb') as file:
stat_df = pickle.load(file)
except FileNotFoundError as exc:
compile_chicago_stations()
with open('./python_variables/Chicago_stations.pickle', 'rb') as file:
stat_df = pickle.load(file)
for _, stat in stat_df.iterrows():
start_matches = np.where(df['start_stat_name'] == stat['name'])
end_matches = np.where(df['end_stat_name'] == stat['name'])
df.at[start_matches[0], 'start_stat_lat'] = stat['latitude']
df.at[start_matches[0], 'start_stat_long'] = stat['longitude']
df.at[end_matches[0], 'end_stat_lat'] = stat['latitude']
df.at[end_matches[0], 'end_stat_long'] = stat['longitude']
df.replace('', np.nan, inplace = True)
df.dropna(subset = ['start_stat_lat',
'start_stat_long',
'end_stat_lat',
'end_stat_long'], inplace = True)
df.reset_index(inplace = True, drop = True)
df['start_dt'] = pd.to_datetime(df['start_t'])
df['end_dt'] = pd.to_datetime(df['end_t'])
df['duration'] = df['duration'].str.replace(',', '').astype(float)
elif city == "sfran":
try:
df = pd.read_csv(f'./data/{year:d}{month:02d}-baywheels-tripdata.csv')
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant files can be found at https://www.lyft.com/bikes/bay-wheels/system-data') from exc
df = df.rename(columns = dataframe_key.get_key(city))
df.dropna(inplace=True)
df = df.iloc[np.where(df['start_stat_lat'] > 37.593220)]
df = df.iloc[np.where(df['end_stat_lat'] > 37.593220)]
df.sort_values(by = 'start_t', inplace = True)
df.reset_index(inplace = True, drop = True)
df['start_dt'] = pd.to_datetime(df['start_t'])
df['end_dt'] = pd.to_datetime(df['end_t'])
elif city == "sjose":
try:
df = pd.read_csv(f'./data/{year:d}{month:02d}-baywheels-tripdata.csv')
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant files can be found at https://www.lyft.com/bikes/bay-wheels/system-data') from exc
df = df.rename(columns = dataframe_key.get_key(city))
df.dropna(inplace=True)
df = df.iloc[np.where(df['start_stat_lat'] < 37.593220)]
df = df.iloc[np.where(df['end_stat_lat'] < 37.593220)]
df.sort_values(by = 'start_t', inplace = True)
df.reset_index(inplace = True, drop = True)
df['start_dt'] = pd.to_datetime(df['start_t'])
df['end_dt'] = pd.to_datetime(df['end_t'])
elif city == "london":
month_dict = {1:'Jan', 2:'Feb', 3:'Mar', 4:'Apr', 5:'May',
6:'Jun', 7:'Jul', 8:'Aug', 9:'Sep', 10:'Oct',
11:'Nov', 12:'Dec'}
data_files = [file for file in os.listdir('data') if 'JourneyDataExtract' in file]
data_files = [file for file in data_files if '{}'.format(year)
and '{}'.format(month_dict[month]) in file]
if len(data_files) == 0:
raise FileNotFoundError('No London data for {}. {} found. All relevant files can be found at https://cycling.data.tfl.gov.uk/.'.format(month_dict[month], year))
if isinstance(data_files, str):
warnings.warn('Only one data file found. Please check that you have all available data.')
df = pd.read_csv('./data/' + data_files[0])
for file in data_files[1:]:
df_temp = pd.read_csv('./data/' + file)
df = pd.concat([df, df_temp], sort = False)
df.rename(columns = dataframe_key.get_key(city), inplace = True)
n_days = calendar.monthrange(year, month)[1]
df = df.iloc[np.where(df['start_t'] >= f'01/{month:02d}/{year} 00:00')]
df = df.iloc[np.where(df['start_t'] <= f'{n_days}/{month:02d}/{year} 23:59')]
df.sort_values(by = 'start_t', inplace = True)
df.reset_index(inplace = True)
df['start_t'] = pd.to_datetime(df['start_t'], format = '%d/%m/%Y %H:%M').astype(str)
df['end_t'] = pd.to_datetime(df['end_t'], format = '%d/%m/%Y %H:%M').astype(str)
stat_df = pd.read_csv('./data/london_stations.csv')
stat_df.at[np.where(stat_df['station_id'] == 502)[0][0], 'latitude'] = 51.53341
df['start_stat_lat'] = ''
df['start_stat_long'] = ''
df['end_stat_lat'] = ''
df['end_stat_long'] = ''
for _ , stat in stat_df.iterrows():
start_matches = np.where(df['start_stat_name'] == stat['station_name'])
end_matches = np.where(df['end_stat_name'] == stat['station_name'])
df.at[start_matches[0], 'start_stat_lat'] = stat['latitude']
df.at[start_matches[0], 'start_stat_long'] = stat['longitude']
df.at[end_matches[0], 'end_stat_lat'] = stat['latitude']
df.at[end_matches[0], 'end_stat_long'] = stat['longitude']
df.replace('', np.nan, inplace = True)
df.dropna(inplace = True)
df.reset_index(inplace = True, drop = True)
df['start_dt'] = pd.to_datetime(df['start_t'])
df['end_dt'] = pd.to_datetime(df['end_t'])
df = df[df.start_dt.dt.month == month]
df.reset_index(inplace = True, drop = True)
elif city == "oslo":
try:
df = pd.read_csv(f'./data/{year:d}{month:02d}-oslo.csv')
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant files can be found at https://oslobysykkel.no/en/open-data/historical') from exc
df = df.rename(columns = dataframe_key.get_key(city))
df.dropna(inplace=True)
df.reset_index(inplace = True, drop = True)
df['start_dt'] = pd.to_datetime(df['start_t'])
df['end_dt'] = pd.to_datetime(df['end_t'])
elif city == "edinburgh":
try:
df = pd.read_csv(f'./data/{year:d}{month:02d}-edinburgh.csv')
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant files can be found at https://edinburghcyclehire.com/open-data/historical') from exc
df = df.rename(columns = dataframe_key.get_key(city))
df.dropna(inplace=True)
df.reset_index(inplace = True, drop = True)
df['start_dt'] = pd.to_datetime(df['start_t'])
df['end_dt'] = pd.to_datetime(df['end_t'])
elif city == "bergen":
try:
df = pd.read_csv(f'./data/{year:d}{month:02d}-bergen.csv')
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant files can be found at https://bergenbysykkel.no/en/open-data/historical') from exc
df = df.rename(columns = dataframe_key.get_key(city))
df.dropna(inplace=True)
df.reset_index(inplace = True, drop = True)
df['start_dt'] = pd.to_datetime(df['start_t'])
df['end_dt'] = pd.to_datetime(df['end_t'])
elif city == "buenos_aires":
try:
df_year = pd.read_csv(f"./data/recorridos-realizados-{year:d}.csv")
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant files can be found at https://data.buenosaires.gob.ar/dataset/bicicletas-publicas') from exc
df_year = df_year.rename(columns = dataframe_key.get_key(city))
#df_year['month'] = pd.to_datetime(df_year['fecha_origen_recorrido']).dt.month
df_year['month'] = pd.to_datetime(df_year['start_t']).dt.month
df = df_year.loc[df_year.month == month]
df.sort_values(by=['start_t'], inplace=True)
df.reset_index(inplace = True, drop = True)
df['start_dt'] = pd.to_datetime(df['start_t'])
df['end_dt'] = pd.to_datetime(df['end_t'])
elif city == "madrid":
try:
df = pd.read_json(f"./data/{year:d}{month:02d}_movements.json", lines=True)
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant files can be found at https://opendata.emtmadrid.es/Datos-estaticos/Datos-generales-(1)') from exc
try:
df_pre = pd.read_json(f"./data/{year:d}{(month-1):02d}_movements.json", lines=True)
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant files can be found at https://opendata.emtmadrid.es/Datos-estaticos/Datos-generales-(1)') from exc
df = df.rename(columns = dataframe_key.get_key(city))
df_pre = df_pre.rename(columns = dataframe_key.get_key(city))
df['start_dt'] = pd.to_datetime(df['start_t'], format = '%Y-%m-%dT%H:%M:%SZ') + pd.DateOffset(hours=2)
df_pre['start_dt'] = pd.to_datetime(df_pre['start_t'], format = '%Y-%m-%dT%H:%M:%SZ') + pd.DateOffset(hours=2)
df = df[df['start_dt'].dt.month == 9]
df_pre = df_pre[df_pre['start_dt'].dt.month == 9]
df = pd.concat((df_pre, df))
df['start_t'] = df['start_dt'].astype(str)
df['end_dt'] = df['start_dt'] + pd.to_timedelta(df['duration'], unit='s')
#df['end_t'] = pd.to_datetime(df['end_dt']).astype(str)
_ , stations = pd.read_json(
f"./data/{year:d}{month:02d}_stations_madrid.json",
lines=True).iloc[-1]
stations = pd.DataFrame(stations)
name_dict = dict(zip(stations['id'], stations['name']))
long_dict = dict(zip(stations['id'], stations['longitude'].astype(float)))
lat_dict = dict(zip(stations['id'], stations['latitude'].astype(float)))
addr_dict = dict(zip(stations['id'], stations['address']))
df['start_stat_name'] = df['start_stat_id'].map(name_dict)
df['start_stat_lat'] = df['start_stat_id'].map(lat_dict)
df['start_stat_long'] = df['start_stat_id'].map(long_dict)
df['start_stat_desc'] = df['start_stat_id'].map(addr_dict)
df['end_stat_name'] = df['end_stat_id'].map(name_dict)
df['end_stat_lat'] = df['end_stat_id'].map(lat_dict)
df['end_stat_long'] = df['end_stat_id'].map(long_dict)
df['end_stat_desc'] = df['end_stat_id'].map(addr_dict)
df.reset_index(inplace = True, drop = True)
elif city == "mexico":
try:
df = pd.read_csv(f"./data/{year:d}-{month:02d}-mexico.csv")
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant files can be found at https://www.ecobici.cdmx.gob.mx/en/informacion-del-servicio/open-data') from exc
df.rename(columns = dataframe_key.get_key(city), inplace=True)
df['start_dt'] = pd.to_datetime(df['start_date'] + df['start_time'],
format='%d/%m/%Y%H:%M:%S')
df['end_dt'] = pd.to_datetime(df['end_date'] + df['end_time'],
format='%d/%m/%Y%H:%M:%S')
df.drop(['start_date','start_time','end_date','end_time'], axis=1, inplace=True)
df['duration'] = (df['end_dt'] - df['start_dt']).dt.total_seconds()
df['start_t'] = df['start_dt'].astype(str)
stations = pd.DataFrame(pd.read_json("./data/stations_mexico.json",
lines=True)['stations'][0])
name_dict = dict(zip(stations['id'], stations['address']))
locations = stations['location'].apply(pd.Series)
long_dict = dict(zip(stations['id'], locations['lon'].astype(float)))
lat_dict = dict(zip(stations['id'], locations['lat'].astype(float)))
type_dict = dict(zip(stations['id'], stations['stationType']))
df['start_stat_name'] = df['start_stat_id'].map(name_dict)
df['start_stat_lat'] = df['start_stat_id'].map(lat_dict)
df['start_stat_long'] = df['start_stat_id'].map(long_dict)
df['end_stat_name'] = df['end_stat_id'].map(name_dict)
df['end_stat_lat'] = df['end_stat_id'].map(lat_dict)
df['end_stat_long'] = df['end_stat_id'].map(long_dict)
df['station_type'] = df['end_stat_id'].map(type_dict)
df.dropna(inplace=True)
df = df[df.start_dt.dt.month == 9]
df.sort_values(by=['start_dt'], inplace=True)
df.reset_index(inplace = True, drop = True)
elif city == "taipei":
colnames = ['start_t', 'start_stat_name_zh',
'end_t', 'end_stat_name_zh', 'duration']
try:
df = pd.read_csv(f"./data/{year:d}{month:02d}-taipei.csv",
usecols=range(5), names=colnames)
except FileNotFoundError as exc:
raise FileNotFoundError('No trip data found. All relevant data can be found at https://data.taipei/#/ and https://drive.google.com/drive/folders/1QsROgp8AcER6qkTJDxpuV8Mt1Dy6lGQO') from exc
# Update names of stations
df.replace(to_replace='信義杭州路口(中華電信總公司', value='信義杭州路口(中華電信總公司)', inplace=True)
df.replace(to_replace='捷運科技大樓站', value='捷運科技大樓站(台北教育大學)', inplace=True)
df.replace(to_replace='?公公園', value='瑠公公園', inplace=True)
df.replace(to_replace='饒河夜市', value='饒河夜市(八德路側)', inplace=True)
df.replace(to_replace='捷運大坪林站(3號出口)', value='捷運大坪林站(1號出口)', inplace=True)
df.replace(to_replace='新明路321巷口', value='新明路262巷口', inplace=True)
df['start_dt'] = pd.to_datetime(df['start_t'], format='%Y-%m-%d %H:%M:%S')
df['end_dt'] = pd.to_datetime(df['end_t'], format='%Y-%m-%d %H:%M:%S')
df['duration'] = pd.to_timedelta(df.duration).dt.total_seconds()
try:
stations = pd.DataFrame.from_dict(
list(pd.read_json("./data/YouBikeTP.json")['retVal']))
except FileNotFoundError as exc:
raise FileNotFoundError('No station data found. The data can be found at https://tcgbusfs.blob.core.windows.net/blobyoubike/YouBikeTP.json') from exc
stations['sno'] = stations['sno'].astype(int)
stations['lat'] = stations['lat'].astype(float)
stations['lng'] = stations['lng'].astype(float)
id_dict = dict(zip(stations['sna'], stations['sno']))
# stations_ntpc = pd.read_csv("./data/stations_new_taipei.csv")
# stations_ntpc['sno'] = stations_ntpc['sno'].astype(int)
# stations_ntpc['lat'] = stations_ntpc['lat'].astype(float)
# stations_ntpc['lng'] = stations_ntpc['lng'].astype(float)
# id_dict_ntpc = dict(zip(stations_ntpc['sna'], stations_ntpc['sno']))
# id_dict = {**id_dict_tp, **id_dict_ntpc}
df['start_stat_id'] = df['start_stat_name_zh'].map(id_dict)
df['end_stat_id'] = df['end_stat_name_zh'].map(id_dict)
name_dict = dict(zip(stations['sno'], stations['snaen']))
long_dict = dict(zip(stations['sno'], stations['lng']))
lat_dict = dict(zip(stations['sno'], stations['lat']))
addr_dict = dict(zip(stations['sno'], stations['aren']))
# name_dict_ntpc = dict(zip(stations_ntpc['sno'], stations_ntpc['snaen']))
# long_dict_ntpc = dict(zip(stations_ntpc['sno'], stations_ntpc['lng']))
# lat_dict_ntpc = dict(zip(stations_ntpc['sno'], stations_ntpc['lat']))
# addr_dict_ntpc = dict(zip(stations_ntpc['sno'], stations_ntpc['aren']))
# name_dict = {**name_dict_tp, **name_dict_ntpc}
# long_dict = {**long_dict_tp, **long_dict_ntpc}
# lat_dict = {**lat_dict_tp, **lat_dict_ntpc}
# addr_dict = {**addr_dict_tp, **addr_dict_ntpc}
df['start_stat_name'] = df['start_stat_id'].map(name_dict)
df['start_stat_lat'] = df['start_stat_id'].map(lat_dict)
df['start_stat_long'] = df['start_stat_id'].map(long_dict)
df['start_stat_desc'] = df['start_stat_id'].map(addr_dict)
df['end_stat_name'] = df['end_stat_id'].map(name_dict)
df['end_stat_lat'] = df['end_stat_id'].map(lat_dict)
df['end_stat_long'] = df['end_stat_id'].map(long_dict)
df['end_stat_desc'] = df['end_stat_id'].map(addr_dict)
#df_nan = df[df.isna().any(axis=1)]
df.dropna(inplace=True)
df.sort_values(by=['start_dt'], inplace=True)
df.reset_index(inplace=True, drop = True)
if blacklist:
df = df[~df['start_stat_id'].isin(blacklist)]
df = df[~df['end_stat_id'].isin(blacklist)]
with open(f'./python_variables/big_data/{city}{year:d}{month:02d}_dataframe_blcklst={blacklist}.pickle', 'wb') as file:
pickle.dump(df, file)
print('Pickling done.')
try:
with open(f'./python_variables/day_index_{city}{year:d}{month:02d}.pickle', 'rb') as file:
days = pickle.load(file)
except FileNotFoundError:
print("Pickle does not exist. Pickling day indices...")
days = pickle_data(df, city, year, month)
print("Pickling done.")
print(f"Data loaded: {city}{year:d}{month:02d}")
return df, days
def station_locations(df, id_index):
"""
Creates a dictionary with station IDs as keys and locations as values.
Parameters
----------
df : pandas DataFrame
Bikeshare trip data.
id_index : dict
Maps station ID (arbitrary integer) to the range from 0 to number of stations
Returns
-------
locations : dict
key : station index (returned from id_index)
value : tuple (longitude, latitude)
"""
# Create Dictionary Station : Position
locations = dict()
for e in id_index.keys():
if df[df['start_stat_id'] == e]['start_stat_lat'].shape[0]:
locations[id_index[e]] = (df[df['start_stat_id'] == e]['start_stat_long'].iloc[0],
df[df['start_stat_id'] == e]['start_stat_lat'].iloc[0])
else:
locations[id_index[e]] = (df[df['end_stat_id'] == e]['end_stat_long'].iloc[0],
df[df['end_stat_id'] == e]['end_stat_lat'].iloc[0])
return locations
def station_names(df, id_index):
"""
Creates a dictionary with station IDs as keys and station names as values.
Parameters
----------
df : pandas DataFrame
Bikeshare trip data.
id_index : dict
Maps station ID (arbitrary integer) to the range from 0 to number of stations
Returns
-------
names : dict
key : station index (returned from id_index)
value : string containing station name
"""
# Create Dictionary Station : Names
names = dict()
for e in id_index.keys():
if df[df['start_stat_id'] == e]['start_stat_name'].shape[0]:
names[id_index[e]] = df[df['start_stat_id'] == e]['start_stat_name'].iloc[0]
else:
names[id_index[e]] = df[df['end_stat_id'] == e]['end_stat_name'].iloc[0]
return names
def diradjacency(df, city, year, month, day_index, days, stations,
threshold=1, remove_self_loops=True):
"""
Calculate the directed adjacency matrix for the network.
Parameters
----------
df : pandas DataFrame
bikesharing data.
city : str
The identification of the city. For a list of supported cities, see
the documentation for the Data class.
year : int
The year of interest in YYYY format.
month : int
The month of interest in MM format.
day_index : list
Indices of the first trip per day.
days : iterable
Days in consideration.
stations : Stat class
Station class containing station information.
threshold : int, optional
Threshold for weights. If an edge has a weight below the threshold
then the weight is set to zero. The default threshold is 1.
remove_self_loops : bool, optional
Does not count trips which start and end at the same station if
True. The default is True.
Returns
-------
d_adj : ndarray
Array containing the directed adjacency matrix.
"""
try:
# If Pickle exists, load it
with open(f'./python_variables/directedadjacency_{city}{year:d}{month:02d}{tuple(days)}thr_{threshold:d}.pickle', 'rb') as file:
d_adj = pickle.load(file)
print("Pickle loaded")
except FileNotFoundError:
# If not, calculate weighted adjacency matrix and create Pickle
print(f"Pickle does not exist. Pickling directed adjacency matrix: directedadjacency_{city}{year:d}{month:02d}{tuple(days)}thr_{threshold:d}.pickle...")
d_adj = np.zeros((stations.n_tot, stations.n_tot))
for day in days:
if day is max(days):
for _, row in df.iloc[day_index[day]:].iterrows():
d_adj[stations.id_index[row['start_stat_id']],
stations.id_index[row['end_stat_id']]] += 1
print('Day {} loaded...'.format(day))
else:
for _, row in df.iloc[day_index[day]:day_index[day+1]].iterrows():
d_adj[stations.id_index[row['start_stat_id']],
stations.id_index[row['end_stat_id']]] += 1
print('Day {} loaded...'.format(day))
d_adj[d_adj <= threshold] = 0
if remove_self_loops:
for i in range(stations.n_tot):
d_adj[i, i] = 0
with open(f'./python_variables/directedadjacency_{city}{year:d}{month:02d}{tuple(days)}thr_{threshold:d}.pickle', 'wb') as file:
pickle.dump(d_adj, file)
print("Pickling done.")
return d_adj
def get_degree_matrix(adj):
"""
Computes the degree matrix of the network.
Parameters
----------
adj : ndarray
Adjacency matrix.
Returns
-------
deg_matrix: ndarray
The degree matrix.
"""
deg_matrix = np.zeros_like(adj)
for i in range(len(adj)):
deg_matrix[i,i] = np.sum(adj[[i],:])
return deg_matrix
def data_pickle_load(city, year, month):
"""
Load data from a Data class object pickle. See Data.pickle_dump
Parameters
----------
city : str
The identification of the city. For a list of supported cities, see
the documentation for the Data class.
year : int
The year of interest in YYYY format.
month : int
The month of interest in MM format.
Returns
-------
object of Data class
"""
with open(f'./python_variables/big_data/data_{city}{year:d}{month:02d}.pickle', 'rb') as file:
return pickle.load(file)
def adjacency(df, n_tot, id_index, threshold=1, remove_self_loops=True):
"""
Calculate the weighted adjacency matrix for the network assuming an
undirected graph.
Parameters
----------
df : pandas DataFrame
Contains the data over which the adjacency matrix is calculated.
n_tot : int
Number of stations.
id_index : dict
Translates station id to an index starting from 0.
threshold : int, optional
Threshold for weights. If an edge has a weight below the threshold
then the weight is set to zero. The default threshold is 1.
remove_self_loops : bool, optional
Does not count trips which start and end at the same station if
True. The default is True.
Returns
-------
adj : ndarray
Adjacency matrix of the network.
"""
adj = np.zeros((n_tot, n_tot))
si = df['start_stat_id'].map(id_index)
ei = df['end_stat_id'].map(id_index)
#start_stat_index = id_index(df['start_stat_id'])
for i, j in zip(si, ei):
adj[i, j] += 1
adj = adj + adj.T
adj[adj <= threshold] = 0
if remove_self_loops:
for i in range(n_tot):
adj[i, i] = 0
return adj
def PageRank(adj, d=0.85, iterations=100, initialisation="rdm"):
"""
Calculates the PageRank of each vertex in a graph.
Parameters
----------
adj : ndarray
Directed and weighted adjacency matrix.
d : float, optional
Dampening factor. The default is 0.85.
iterations : int, optional
The amount of iterations we run the PageRank algortihm. The default is
100.
initialisation : str, optional
Determines if we have random initialisation or 1/n initialisation. The
default is "rdm".
Returns
-------
v : ndarray
contains the PageRank of each vertex.
"""
N = adj.shape[0]
weightlist = []
for i in range(N):
weight = 0
for n in range(N):
weight += adj[i,n]
weightlist.append(weight)
if initialisation == "rdm":
v = np.random.rand(N, 1)
v = v / np.linalg.norm(v, 1)
else: # Uniform initialisation
v = np.linspace(1/N, 1/N, N)
for i in range(iterations):
for n in range(N):
if weightlist[n] != 0:
v[n] = v[n]/weightlist[n]
v = (1 - d)/(N+1) + d * adj @ v
return v
def get_elevation(lat, long, dataset="mapzen"):
"""
Finds the elevation for a specific coordinate.
Elevation data is taken from https://www.opentopodata.org/
Parameters
----------
lat : float or iterable
Latitude or iterable containing latitudes.
long : float or iterable
Longitude or iterable containing longitudes.
dataset : str, optional
Dataset used for elevation data. The default is "mapzen".
Returns
-------
elevation : ndarray
Array containing elevations.
"""
if lat is None or long is None:
return None
elevation = np.array([])
if isinstance(long, float):
query = (f'https://api.opentopodata.org/v1/{dataset}?locations='
f'{lat},{long}')
print(query)
# Request with a timeout for slow responses
r = get(query, timeout = 60)
# Only get the json response in case of 200 or 201
if r.status_code == 200 or r.status_code == 201:
elevation = pd.json_normalize(r.json(), 'results')['elevation']
else:
# if it is a list or iterable
i = 100
for n in range(0, len(long), i):
lo = long[n:n+i]
la = lat[n:n+i]
loc_string = f'https://api.opentopodata.org/v1/{dataset}?locations='
for at, ong in zip(la, lo):
loc_string = loc_string + f"{at},{ong}|"
loc_string = loc_string[:-1]
query = (loc_string)
r = get(query, timeout = 60)
# Only get the json response in case of 200 or 201
if r.status_code == 200 or r.status_code == 201:
elevation = np.append(elevation,
np.array(pd.json_normalize(r.json(), 'results')['elevation'])
)
return elevation
def get_weather(city, year, month):
"""
Get weather data for the given city, year and month.
Parameters
----------
city : str
The identification of the city. For a list of supported cities, see
the documentation for the Data class.
year : int
The year of interest in YYYY format.
month : int
The month of interest in MM format.
Returns
-------
request : str
DESCRIPTION.
rain :
DESCRIPTION.
"""
cities = ['chic', 'london', 'madrid', 'mexico', 'nyc', 'sfran', 'taipei', 'washDC']
if city in cities:
name_dict = {'chic':'Chicago', 'london':'London', 'madrid':'Madrid',
'mexico':'Mexico City', 'nyc':'New York City',
'sfran':'San Francisco', 'taipei':'Taipei',
'washDC':'Washington DC'}
city = name_dict[city]
n_days = calendar.monthrange(year, month)[1]
tp = 1
query = (f"http://api.worldweatheronline.com/premium/v1/past-weather.ashx?"
f"key=7886f8387f8c4c0484f83623210305&q={city}&format=json&date={year}-{month}-01&enddate={year}-{month}-{n_days}&tp={tp}")# Request with a timeout for slow responses
r = get(query, timeout = 60)
# Only get the json response in case of 200 or 201
if r.status_code == 200 or r.status_code == 201:
result = r.json()['data']
request = result['request']
weather = pd.DataFrame(result['weather'])
hourweather = [pd.DataFrame(i) for i in weather['hourly']]
for day, wea in zip(weather['date'], hourweather):
wea['day'] = day[-2:]
hweather = pd.concat(hourweather)
hweather.reset_index(inplace=True)
hweather['hour'] = (hweather['time'].astype(int)//100).astype(str)
hweather['precipMM'] = hweather['precipMM'].astype(float)
hweather['time_dt'] = pd.to_datetime(
str(year) + str(month) + hweather['day'] + hweather['hour'],
format='%Y%m%d%H')
hweather['day'] = hweather['day'].astype(int)
hweather['hour'] = hweather['hour'].astype(int)
hweather['desc'] = pd.DataFrame(hweather['weatherDesc'].explode().tolist())
rain = hweather[['day', 'hour', 'time_dt', 'precipMM', 'tempC', 'windspeedKmph', 'desc']]
return request, rain
def TotalVariation(adj, cutoff):
"""
Calculates the total variation of given graph with the degree as the signal.
Parameters
----------
adj : ndarray
Adjacency matrix.
threshold : float
Threshold for when the signal is high or low frequency.
Returns
-------
filterarray : ndarray
Binary array. 1 indicates low frequency and 0 indicates high frequency.
"""
n = len(adj)
Lambda, u = np.linalg.eig(adj)
Lambda_max = np.max(abs(Lambda))
W_tilde = adj * 1/Lambda_max
T = np.zeros(n)
filterarray = np.zeros(n)
for m in range(n):
T[m] = np.linalg.norm(u[:,m] - (W_tilde @ u[:,m]), ord = 1)
if T[m] < cutoff:
filterarray[m] = 1
return filterarray
def subframe(filterarray, df, id_index, low):
"""
Creates a lowpass- or highpass-filtered dataframe
Parameters
----------
filterarray : ndarray
Binary array. 1 indicates low frequency and 0 indicates high frequency.
df : pandas dataframe
Original city data dataframe.
low : Logival, optional
Tells us if the filtered dataframe will be low or high frequency.
The default is True.
Returns
-------
df_done : pandas dataframe
Filtered pandas dataframe.
"""
filtered_positions = np.argwhere(filterarray == 1)
l = len(filtered_positions)
filtered_positions = filtered_positions.reshape(l)
if low:
df_filtered = df[df['start_stat_id'].map(id_index).isin(filtered_positions)]
df_done = df_filtered[df_filtered['end_stat_id'].map(id_index).isin(filtered_positions)]
else:
df_filtered = df[~df['start_stat_id'].map(id_index).isin(filtered_positions)]
df_done = df_filtered[~df_filtered['end_stat_id'].map(id_index).isin(filtered_positions)]
return df_done
def adjacency_filtered(df, day_index, days, n_tot, id_index, threshold=1, remove_self_loops=True):
"""
Calculate weighted adjacency matrix (undirected)
Parameters
----------
days : tuple
Tuple of days in consideration.
threshold : int, optional
Threshold for weights. If an edge has a weight below the threshold
then the weight is set to zero. The default threshold is 1.
remove_self_loops : bool, optional
Does not count trips which start and end at the same station if
True. The default is True.
Returns
-------
adj : ndarray
Adjacency matrix of the network.
"""
adj = np.zeros((n_tot, n_tot))
si = df['start_stat_id'].map(id_index)
ei = df['end_stat_id'].map(id_index)
for day in days:
if day is max(days):
for i, j in zip(si[day_index[day]:], ei[day_index[day]:]):
adj[i, j] += 1
adj[j, i] += 1
else:
for i, j in zip(si[day_index[day]:day_index[day+1]], ei[day_index[day]:day_index[day+1]]):
adj[i, j] += 1
adj[j, i] += 1
adj[adj <= threshold] = 0
if remove_self_loops == True:
for i in range(n_tot):
adj[i, i] = 0
return adj
def coverage(g, p):
"""
Calculates the covergae of the partition.
Parameters
----------
g : networkx graph class
graph of the data.
p : dictionary
tells which verticies belongs to which communities.
Returns
-------
float
the coverage of our partition.
"""
d_i = dict(zip(np.arange(g.number_of_nodes()), list(g.nodes())))
n = g.number_of_nodes()
ad = nx.adjacency_matrix(g)
p_sum = np.sum(ad) / 2
num = 0
for i in range(n):
for j in range(i + 1, n):
if p[d_i[i]] == p[d_i[j]]:
num += ad[i, j]
return num / p_sum
def distance(lat1, lon1, lat2, lon2):
"""
Calculates the distance between two coordiantes.
Parameters
----------
lat1 : float
Latitude of first coordinate.
lon1 : float
Longitude of first coordinate.
lat2 : float
Latitude of second coordinate.
lon2 : float
Longitude of second coordinate.
Returns
-------
res : float
Distance between the two coordinates.
"""
r = 6371000
phi1 = np.radians(lat1)
phi2 = np.radians(lat2)
delta_phi = np.radians(lat2 - lat1)
delta_lambda = np.radians(lon2 - lon1)
a = | np.sin(delta_phi / 2) | numpy.sin |
"""Most utility functions here has been adopted from:
https://github.com/guillaumegenthial/sequence_tagging/blob/master/model/data_utils.py
"""
import numpy as np
import os
import math
# shared global variables to be imported from model also
UNK = "$UNK$"
NUM = "$NUM$"
NONE = "O"
# read the word importance scores
class AnnotationDataset(object):
def __init__(self, filename, processing_word=None):
self.filename = filename
self.processing_word = processing_word
self.length = None
def __iter__(self):
with open(self.filename) as f:
words, tags = [], []
for line in f:
line = line.strip()
if (len(line) == 0):
if len(words) != 0:
yield words, tags
words, tags = [], []
else:
ls = line.split(' ')
word, tag = ls[0], ls[-1]
if self.processing_word is not None:
word = self.processing_word(word)
words += [word]
tags += [tag]
def __len__(self):
if self.length is None:
self.length = 0
for _ in self:
self.length += 1
return self.length
def get_vocabs(datasets):
print("Building vocab...")
vocab_words = set()
vocab_tags = set()
for dataset in datasets:
for words, tags in dataset:
vocab_words.update(words)
vocab_tags.update(tags)
print("- done. {} tokens".format(len(vocab_words)))
return vocab_words, vocab_tags
def get_char_vocab(dataset):
vocab_char = set()
for words, _ in dataset:
for word in words:
vocab_char.update(word)
return vocab_char
def get_glove_vocab(filename):
print("Building vocab...")
vocab = set()
with open(filename) as f:
for line in f:
word = line.strip().split(' ')[0]
vocab.add(word)
print("- done. {} tokens".format(len(vocab)))
return vocab
def get_google_vocab(filename):
from gensim.models import Word2Vec
model = Word2Vec.load_word2vec_format(filename, binary=True)
print ("Building vocab...")
vocab = set(model.vocab.keys())
print ("- done. {} tokens".format(len(vocab)))
return model, vocab
def get_senna_vocab(filename):
print ("Building vocab...")
vocab = set()
with open(filename) as f:
for line in f:
word = line.strip()
vocab.add(word)
print ("- done. {} tokens".format(len(vocab)))
return vocab
def write_vocab(vocab, filename):
print("Writing vocab...")
with open(filename, "w") as f:
for i, word in enumerate(vocab):
if i != len(vocab) - 1:
f.write("{}\n".format(word))
else:
f.write(word)
print("- done. {} tokens".format(len(vocab)))
def load_vocab(filename):
try:
d = dict()
with open(filename) as f:
for idx, word in enumerate(f):
word = word.strip()
d[word] = idx
except IOError:
raise MyIOError(filename)
return d
def export_trimmed_glove_vectors(vocab, glove_filename, trimmed_filename, dim):
embeddings = np.zeros([len(vocab), dim])
with open(glove_filename) as f:
for line in f:
line = line.strip().split(' ')
word = line[0]
embedding = [float(x) for x in line[1:]]
if word in vocab:
word_idx = vocab[word]
embeddings[word_idx] = np.asarray(embedding)
np.savez_compressed(trimmed_filename, embeddings=embeddings)
def export_trimmed_google_vectors(vocab, google_model, trimmed_filename, dim, random):
embeddings = np.asarray(random.normal(loc=0.0, scale=0.1, size= [len(vocab), dim]), dtype=np.float32)
for word in google_model.vocab.keys():
if word in vocab:
word_idx = vocab[word]
embedding = google_model[word]
embeddings[word_idx] = np.asarray(embedding)
np.savez_compressed(trimmed_filename, embeddings=embeddings)
def export_trimmed_senna_vectors(vocab, vocab_emb, senna_filename, trimmed_filename, dim):
embeddings = np.zeros([len(vocab), dim])
vocab_emb = list(vocab_emb)
with open(senna_filename) as f:
for i, line in enumerate(f):
line = line.strip().split(' ')
word = vocab_emb[i]
embedding = map(float, line)
if word in vocab:
word_idx = vocab[word]
embeddings[word_idx] = np.asarray(embedding)
| np.savez_compressed(trimmed_filename, embeddings=embeddings) | numpy.savez_compressed |
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